{"id":714,"date":"2017-10-27T16:30:37","date_gmt":"2017-10-27T16:30:37","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/chapter\/humidity-evaporation-and-boiling\/"},"modified":"2017-11-08T03:25:16","modified_gmt":"2017-11-08T03:25:16","slug":"humidity-evaporation-and-boiling","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/chapter\/humidity-evaporation-and-boiling\/","title":{"raw":"Humidity, Evaporation, and Boiling","rendered":"Humidity, Evaporation, and Boiling"},"content":{"raw":"\n<div class=\"textbox learning-objectives\">\n<h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>\n<ul>\n<li>Explain the relationship between vapor pressure of water and the capacity of air to hold water vapor.<\/li>\n<li>Explain the relationship between relative humidity and partial pressure of water vapor in the air.<\/li>\n<li>Calculate vapor density using vapor pressure.<\/li>\n<li>Calculate humidity and dew point.<\/li>\n<\/ul>\n<\/div>\n<div class=\"bc-figure figure\" id=\"import-auto-id1653277\">\n<div class=\"bc-figcaption figcaption\">Dew drops like these, on a banana leaf photographed just after sunrise, form when the air temperature drops to or below the dew point. At the dew point, the rate at which water molecules join together is greater than the rate at which they separate, and some of the water condenses to form droplets. (credit: Aaron Escobar, Flickr) <\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1661526\" data-alt=\"\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_14_06_00.jpg\" data-media-type=\"image\/jpg\" alt=\"\" width=\"250\"><\/span><\/p><\/div>\n<p id=\"import-auto-id1857764\">The expression \u201cit\u2019s not the heat, it\u2019s the humidity\u201d makes a valid point. We keep cool in hot weather by evaporating sweat from our skin and water from our breathing passages. Because evaporation is inhibited by high humidity, we feel hotter at a given temperature when the humidity is high. Low humidity, on the other hand, can cause discomfort from excessive drying of mucous membranes and can lead to an increased risk of respiratory infections.<\/p>\n<p id=\"import-auto-id1084476\">When we say humidity, we really mean <span data-type=\"term\" id=\"import-auto-id1300275\">relative humidity<\/span>. Relative humidity tells us how much water vapor is in the air compared with the maximum possible. At its maximum, denoted as <span data-type=\"term\" id=\"import-auto-id2045214\">saturation<\/span>, the relative humidity is 100%, and evaporation is inhibited. The amount of water vapor in the air depends on temperature. For example, relative humidity rises in the evening, as air temperature declines, sometimes reaching the <span data-type=\"term\" id=\"import-auto-id2232198\">dew point<\/span>. At the dew point temperature, relative humidity is 100%, and fog may result from the condensation of water droplets if they are small enough to stay in suspension. Conversely, if you wish to dry something (perhaps your hair), it is more effective to blow hot air over it rather than cold air, because, among other things, the increase in temperature increases the energy of the molecules, so the rate of evaporation increases.<\/p>\n<p id=\"import-auto-id2245399\">The amount of water vapor in the air depends on the vapor pressure of water. The liquid and solid phases are continuously giving off vapor because some of the molecules have high enough speeds to enter the gas phase; see <a href=\"#import-auto-id2807071\" class=\"autogenerated-content\">(Figure)<\/a>(a). If a lid is placed over the container, as in <a href=\"#import-auto-id2807071\" class=\"autogenerated-content\">(Figure)<\/a>(b), evaporation continues, increasing the pressure, until sufficient vapor has built up for condensation to balance evaporation. Then equilibrium has been achieved, and the vapor pressure is equal to the partial pressure of water in the container. Vapor pressure increases with temperature because molecular speeds are higher as temperature increases. <a href=\"#import-auto-id1591575\" class=\"autogenerated-content\">(Figure)<\/a> gives representative values of water vapor pressure over a range of temperatures.<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id2807071\">\n<div class=\"bc-figcaption figcaption\">(a) Because of the distribution of speeds and kinetic energies, some water molecules can break away to the vapor phase even at temperatures below the ordinary boiling point. (b) If the container is sealed, evaporation will continue until there is enough vapor density for the condensation rate to equal the evaporation rate. This vapor density and the partial pressure it creates are the saturation values. They increase with temperature and are independent of the presence of other gases, such as air. They depend only on the vapor pressure of water.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1684254\" data-alt=\"Two containers, each filled two-thirds with water. One is open to the atmosphere and the other is sealed at the top. The water molecules are depicted as circles with vector arrows of different lengths and directions to indicate velocity. In the sealed container the density of molecules in the air above the water is greater than in the unsealed container. In the sealed container, water is condensing along the walls and top of the upper part of the container.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_14_06_01.jpg\" data-media-type=\"image\/jpg\" alt=\"Two containers, each filled two-thirds with water. One is open to the atmosphere and the other is sealed at the top. The water molecules are depicted as circles with vector arrows of different lengths and directions to indicate velocity. In the sealed container the density of molecules in the air above the water is greater than in the unsealed container. In the sealed container, water is condensing along the walls and top of the upper part of the container.\" height=\"228\" width=\"331\"><\/span><\/p><\/div>\n<p id=\"import-auto-id2670648\">Relative humidity is related to the partial pressure of water vapor in the air. At 100% humidity, the partial pressure is equal to the vapor pressure, and no more water can enter the vapor phase. If the partial pressure is less than the vapor pressure, then evaporation will take place, as humidity is less than 100%. If the partial pressure is greater than the vapor pressure, condensation takes place. In everyday language, people sometimes refer to the capacity of air to \u201chold\u201d water vapor, but this is not actually what happens. The water vapor is not held by the air. The amount of water in air is determined by the vapor pressure of water and has nothing to do with the properties of air.<\/p>\n<table id=\"import-auto-id1591575\" summary=\"Table of saturation vapor density of water between negative fifty and positive two hundred twenty degrees Celsius.\">\n<caption><span data-type=\"title\">Saturation Vapor Density of Water<\/span><\/caption>\n<thead>\n<tr>\n<th data-align=\"center\">Temperature [latex]\\left(\\text{\u00ba}\\text{C}\\right)[\/latex]<\/th>\n<th data-align=\"center\">Vapor pressure (Pa)<\/th>\n<th data-align=\"center\">Saturation vapor density (g\/m<sup>3<\/sup>)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td data-align=\"center\">\u221250<\/td>\n<td data-align=\"center\">4.0<\/td>\n<td data-align=\"center\">0.039<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">\u221220<\/td>\n<td data-align=\"center\">[latex]1\\text{.}\\text{04}\u00d7{\\text{10}}^{2}[\/latex]<\/td>\n<td data-align=\"center\">0.89<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">\u221210<\/td>\n<td data-align=\"center\">[latex]2\\text{.}\\text{60}\u00d7{\\text{10}}^{2}[\/latex]<\/td>\n<td data-align=\"center\">2.36<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">0<\/td>\n<td data-align=\"center\">[latex]6\\text{.}\\text{10}\u00d7{\\text{10}}^{2}[\/latex]<\/td>\n<td data-align=\"center\">4.84<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">5<\/td>\n<td data-align=\"center\">[latex]8\\text{.}\\text{68}\u00d7{\\text{10}}^{2}[\/latex]<\/td>\n<td data-align=\"center\">6.80<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">10<\/td>\n<td data-align=\"center\">[latex]1\\text{.}\\text{19}\u00d7{\\text{10}}^{3}[\/latex]<\/td>\n<td data-align=\"center\">9.40<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">15<\/td>\n<td data-align=\"center\">[latex]1\\text{.}\\text{69}\u00d7{\\text{10}}^{3}[\/latex]<\/td>\n<td data-align=\"center\">12.8<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">20<\/td>\n<td data-align=\"center\">[latex]2\\text{.}\\text{33}\u00d7{\\text{10}}^{3}[\/latex]<\/td>\n<td data-align=\"center\">17.2<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">25<\/td>\n<td data-align=\"center\">[latex]3\\text{.}\\text{17}\u00d7{\\text{10}}^{3}[\/latex]<\/td>\n<td data-align=\"center\">23.0<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">30<\/td>\n<td data-align=\"center\">[latex]4\\text{.}\\text{24}\u00d7{\\text{10}}^{3}[\/latex]<\/td>\n<td data-align=\"center\">30.4<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">37<\/td>\n<td data-align=\"center\">[latex]6\\text{.}\\text{31}\u00d7{\\text{10}}^{3}[\/latex]<\/td>\n<td data-align=\"center\">44.0<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">40<\/td>\n<td data-align=\"center\">[latex]7\\text{.}\\text{34}\u00d7{\\text{10}}^{3}[\/latex]<\/td>\n<td data-align=\"center\">51.1<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">50<\/td>\n<td data-align=\"center\">[latex]1\\text{.}\\text{23}\u00d7{\\text{10}}^{4}[\/latex]<\/td>\n<td data-align=\"center\">82.4<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">60<\/td>\n<td data-align=\"center\">[latex]1\\text{.}\\text{99}\u00d7{\\text{10}}^{4}[\/latex]<\/td>\n<td data-align=\"center\">130<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">70<\/td>\n<td data-align=\"center\">[latex]3\\text{.}\\text{12}\u00d7{\\text{10}}^{4}[\/latex]<\/td>\n<td data-align=\"center\">197<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">80<\/td>\n<td data-align=\"center\">[latex]4\\text{.}\\text{73}\u00d7{\\text{10}}^{4}[\/latex]<\/td>\n<td data-align=\"center\">294<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">90<\/td>\n<td data-align=\"center\">[latex]7\\text{.}\\text{01}\u00d7{\\text{10}}^{4}[\/latex]<\/td>\n<td data-align=\"center\">418<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">95<\/td>\n<td data-align=\"center\">[latex]8\\text{.}\\text{59}\u00d7{\\text{10}}^{4}[\/latex]<\/td>\n<td data-align=\"center\">505<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\"><strong data-effect=\"bold\">100<\/strong><\/td>\n<td data-align=\"center\">[latex]1\\text{.}\\text{01}\u00d7{\\text{10}}^{5}[\/latex]<\/td>\n<td data-align=\"center\"><strong data-effect=\"bold\">598<\/strong><\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">120<\/td>\n<td data-align=\"center\">[latex]1\\text{.}\\text{99}\u00d7{\\text{10}}^{5}[\/latex]<\/td>\n<td data-align=\"center\">1095<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">150<\/td>\n<td data-align=\"center\">[latex]4\\text{.}\\text{76}\u00d7{\\text{10}}^{5}[\/latex]<\/td>\n<td data-align=\"center\">2430<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">200<\/td>\n<td data-align=\"center\">[latex]1\\text{.}\\text{55}\u00d7{\\text{10}}^{6}[\/latex]<\/td>\n<td data-align=\"center\">7090<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">220<\/td>\n<td data-align=\"center\">[latex]2\\text{.}\\text{32}\u00d7{\\text{10}}^{6}[\/latex]<\/td>\n<td data-align=\"center\">10,200<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div data-type=\"example\" class=\"textbox examples\" id=\"fs-id2013690\">\n<div data-type=\"title\" class=\"title\">Calculating Density Using Vapor Pressure<\/div>\n<p id=\"import-auto-id1684683\"><a href=\"#import-auto-id1591575\" class=\"autogenerated-content\">(Figure)<\/a> gives the vapor pressure of water at [latex]\\text{20}\\text{.}0\\text{\u00ba}\\text{C}[\/latex] as [latex]2\\text{.}\\text{33}\u00d7{\\text{10}}^{3}\\phantom{\\rule{0.25em}{0ex}}\\text{Pa}\\text{.}[\/latex] Use the ideal gas law to calculate the density of water vapor in [latex]\\text{g}\/{\\text{m}}^{3}[\/latex] that would create a partial pressure equal to this vapor pressure. Compare the result with the saturation vapor density given in the table.<\/p>\n<p id=\"import-auto-id2270512\"><strong>Strategy<\/strong><\/p>\n<p id=\"import-auto-id1898263\">To solve this problem, we need to break it down into a two steps. The partial pressure follows the ideal gas law, <\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]\\text{PV}=\\text{nRT,}[\/latex]<\/div>\n<p id=\"import-auto-id2816575\">where [latex]n[\/latex] is the number of moles. If we solve this equation for [latex]n\/V[\/latex] to calculate the number of moles per cubic meter, we can then convert this quantity to grams per cubic meter as requested. To do this, we need to use the molecular mass of water, which is given in the periodic table.<\/p>\n<p id=\"import-auto-id1783632\"><strong>Solution<\/strong><\/p>\n<p id=\"import-auto-id2254806\">1. Identify the knowns and convert them to the proper units:<\/p>\n<ol id=\"eip-id2084977\" data-number-style=\"lower-alpha\">\n<li id=\"import-auto-id1674733\">temperature [latex]T=\\text{20}\\text{\u00ba}\\text{C=293 K}[\/latex]<\/li>\n<li id=\"import-auto-id1544358\">vapor pressure [latex]P[\/latex] of water at [latex]\\text{20}\\text{\u00ba}\\text{C}[\/latex] is [latex]2\\text{.}\\text{33}\u00d7{\\text{10}}^{3}\\phantom{\\rule{0.25em}{0ex}}\\text{Pa}[\/latex]<\/li>\n<li id=\"import-auto-id1612423\">molecular mass of water is [latex]\\text{18}\\text{.}0\\phantom{\\rule{0.25em}{0ex}}\\text{g\/mol}[\/latex]<\/li>\n<\/ol>\n<p id=\"import-auto-id2052284\">2. Solve the ideal gas law for [latex]n\/V[\/latex].<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id1390729\">[latex]\\frac{n}{V}=\\frac{P}{\\text{RT}}[\/latex]<\/div>\n<p id=\"import-auto-id1396332\">3. Substitute known values into the equation and solve for [latex]n\/V[\/latex].<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id954088\">[latex]\\frac{n}{V}=\\frac{P}{\\text{RT}}=\\frac{2\\text{.}\\text{33}\u00d7{\\text{10}}^{3}\\phantom{\\rule{0.25em}{0ex}}\\text{Pa}}{\\left(8\\text{.}\\text{31}\\phantom{\\rule{0.25em}{0ex}}\\text{J\/mol}\\cdot \\text{K}\\right)\\left(\\text{293}\\phantom{\\rule{0.25em}{0ex}}\\text{K}\\right)}=0\\text{.}\\text{957}\\phantom{\\rule{0.25em}{0ex}}{\\text{mol\/m}}^{3}[\/latex]<\/div>\n<p id=\"import-auto-id2271354\">4. Convert the density in moles per cubic meter to grams per cubic meter.<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id2069640\">[latex]\\rho =\\left(0\\text{.}\\text{957}\\frac{\\text{mol}}{{\\text{m}}^{3}}\\right)\\left(\\frac{\\text{18}\\text{.}\\text{0 g}}{\\text{mol}}\\right)=\\text{17}\\text{.}2\\phantom{\\rule{0.25em}{0ex}}{\\text{g\/m}}^{3}[\/latex]<\/div>\n<p id=\"import-auto-id2259303\"><strong>Discussion<\/strong><\/p>\n<p id=\"import-auto-id1893698\">The density is obtained by assuming a pressure equal to the vapor pressure of water at [latex]\\text{20}\\text{.}0\\text{\u00ba}\\text{C}[\/latex]. The density found is identical to the value in <a href=\"#import-auto-id1591575\" class=\"autogenerated-content\">(Figure)<\/a>,  which means that a vapor density of [latex]\\text{17}\\text{.}2\\phantom{\\rule{0.25em}{0ex}}{\\text{g\/m}}^{3}[\/latex] at [latex]\\text{20}\\text{.}0\\text{\u00ba}\\text{C}[\/latex] creates a partial pressure of [latex]2\\text{.}\\text{33}\u00d7{\\text{10}}^{3}\\phantom{\\rule{0.25em}{0ex}}\\text{Pa,}[\/latex] equal to the vapor pressure of water at that temperature. If the partial pressure is equal to the vapor pressure, then the liquid and vapor phases are in equilibrium, and the relative humidity is 100%. Thus, there can be no more than 17.2 g of water vapor per [latex]{\\text{m}}^{3}[\/latex] at [latex]\\text{20}\\text{.}0\\text{\u00ba}\\text{C}[\/latex], so that this value is the saturation vapor density at that temperature. This example illustrates how water vapor behaves like an ideal gas: the pressure and density are consistent with the ideal gas law (assuming the density in the table is correct). The saturation vapor densities listed in <a href=\"#import-auto-id1591575\" class=\"autogenerated-content\">(Figure)<\/a> are the maximum amounts of water vapor that air can hold at various temperatures.<\/p>\n<\/div>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" id=\"fs-id954391\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">Percent Relative Humidity<\/div>\n<p id=\"import-auto-id2898098\">We define <span data-type=\"term\" id=\"import-auto-id2898100\">percent relative humidity<\/span> as the ratio of vapor density to saturation vapor density, or<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id2898104\">[latex]\\text{percent relative humidity}=\\frac{\\text{vapor density}}{\\text{saturation vapor density}}\u00d7\\text{100}[\/latex]<\/div>\n<\/div>\n<p id=\"import-auto-id2898416\">We can use this and the data in <a href=\"#import-auto-id1591575\" class=\"autogenerated-content\">(Figure)<\/a> to do a variety of interesting calculations, keeping in mind that relative humidity is based on the comparison of the partial pressure of water vapor in air and ice.<\/p>\n<div data-type=\"example\" class=\"textbox examples\" id=\"fs-id1610352\">\n<div data-type=\"title\" class=\"title\">Calculating Humidity and Dew Point<\/div>\n<p id=\"import-auto-id2302384\">(a) Calculate the percent relative humidity on a day when the temperature is [latex]\\text{25}\\text{.}0\\text{\u00ba}\\text{C}[\/latex] and the air contains 9.40 g of water vapor per [latex]{\\text{m}}^{3}[\/latex]. (b) At what temperature will this air reach 100% relative humidity (the saturation density)? This temperature is the dew point. (c) What is the humidity when the air temperature is [latex]\\text{25}\\text{.}0\\text{\u00ba}\\text{C}[\/latex] and the dew point is [latex]\u2013\\text{10}\\text{.}0\\text{\u00ba}\\text{C}[\/latex]?<\/p>\n<p id=\"import-auto-id1168465458500\"><strong>Strategy and Solution<\/strong><\/p>\n<p id=\"import-auto-id1168465548024\">(a) Percent relative humidity is defined as the ratio of vapor density to saturation vapor density. <\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id1168465550625\">[latex]\\text{percent relative humidity}=\\frac{\\text{vapor density}}{\\text{saturation vapor density}}\u00d7\\text{100}[\/latex]<\/div>\n<p id=\"import-auto-id1168465549468\">The first is given to be [latex]9\\text{.}{\\text{40 g\/m}}^{3}[\/latex], and the second is found in <a href=\"#import-auto-id1591575\" class=\"autogenerated-content\">(Figure)<\/a> to be [latex]\\text{23}\\text{.}{\\text{0 g\/m}}^{3}[\/latex]. Thus,<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id1168465433320\">[latex]\\text{percent relative humidity}=\\frac{9\\text{.}{\\text{40 g\/m}}^{3}}{\\text{23}\\text{.}{\\text{0 g\/m}}^{3}}\u00d7\\text{100}=\\text{40}\\text{.}9\\text{}\\text{.%}[\/latex]<\/div>\n<p id=\"import-auto-id1168465463861\">(b) The air contains [latex]9\\text{.}{\\text{40 g\/m}}^{3}[\/latex] of water vapor. The relative humidity will be 100% at a temperature where [latex]9\\text{.}{\\text{40 g\/m}}^{3}[\/latex] is the saturation density. Inspection of <a href=\"#import-auto-id1591575\" class=\"autogenerated-content\">(Figure)<\/a> reveals this to be the case at [latex]\\text{10}\\text{.}0\\text{\u00ba}\\text{C}[\/latex], where the relative humidity will be 100%. That temperature is called the dew point for air with this concentration of water vapor.<\/p>\n<p id=\"import-auto-id1168465552646\">(c) Here, the dew point temperature is given to be [latex]\u2013\\text{10}\\text{.}0\\text{\u00ba}\\text{C}[\/latex]. Using <a href=\"#import-auto-id1591575\" class=\"autogenerated-content\">(Figure)<\/a>, we see that the vapor density is [latex]2\\text{.}{\\text{36 g\/m}}^{3}[\/latex], because this value is the saturation vapor density at [latex]\u2013\\text{10}\\text{.}0\\text{\u00ba}\\text{C}[\/latex]. The saturation vapor density at [latex]\\text{25}\\text{.}0\\text{\u00ba}\\text{C}[\/latex] is seen to be [latex]\\text{23}\\text{.}{\\text{0 g\/m}}^{3}[\/latex]. Thus, the relative humidity at [latex]\\text{25}\\text{.}0\\text{\u00ba}\\text{C}[\/latex] is<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id1168465550600\">[latex]\\text{percent relative humidity}=\\frac{2\\text{.}{\\text{36 g\/m}}^{3}}{\\text{23}\\text{.}{\\text{0 g\/m}}^{3}}\u00d7\\text{100}=\\text{10}\\text{.}3\\text{%}\\text{}\\text{.}[\/latex]<\/div>\n<p id=\"import-auto-id1586286\"><strong>Discussion<\/strong><\/p>\n<p id=\"import-auto-id2187925\">The importance of dew point is that air temperature cannot drop below [latex]\\text{10}\\text{.}0\\text{\u00ba}\\text{C}[\/latex] in part (b), or [latex]\u2013\\text{10}\\text{.}0\\text{\u00ba}\\text{C}[\/latex] in part (c), without water vapor condensing out of the air. If condensation occurs, considerable transfer of heat occurs (discussed in <a href=\"\/contents\/7892cddd-833e-42b8-bcaa-a1e94fb9eb9c\">Heat and Heat Transfer Methods<\/a>), which prevents the temperature from further dropping. When dew points are below [latex]0\\text{\u00baC}[\/latex], freezing temperatures are a greater possibility, which explains why farmers keep track of the dew point. Low humidity in deserts means low dew-point temperatures. Thus condensation is unlikely. If the temperature drops, vapor does not condense in liquid drops. Because no heat is released into the air, the air temperature drops more rapidly compared to air with higher humidity. Likewise, at high temperatures, liquid droplets do not evaporate, so that no heat is removed from the gas to the liquid phase. This explains the large range of temperature in arid regions. <\/p>\n<\/div>\n<p id=\"import-auto-id1168465550071\">Why does water boil at [latex]\\text{100}\\text{\u00ba}\\text{C}[\/latex]? You will note from <a href=\"#import-auto-id1591575\" class=\"autogenerated-content\">(Figure)<\/a> that the vapor pressure of water at [latex]\\text{100}\\text{\u00ba}\\text{C}[\/latex] is [latex]1\\text{.}\\text{01}\u00d7{\\text{10}}^{5}\\phantom{\\rule{0.25em}{0ex}}\\text{Pa}[\/latex], or 1.00 atm. Thus, it can evaporate without limit at this temperature and pressure. But why does it form bubbles when it boils? This is because water ordinarily contains significant amounts of dissolved air and other impurities, which are observed as small bubbles of air in a glass of water. If a bubble starts out at the bottom of the container at [latex]\\text{20}\\text{\u00ba}\\text{C}[\/latex], it contains water vapor (about 2.30%). The pressure inside the bubble is fixed at 1.00 atm (we ignore the slight pressure exerted by the water around it). As the temperature rises, the amount of air in the bubble stays the same, but the water vapor increases; the bubble expands to keep the pressure at 1.00 atm. At [latex]\\text{100}\\text{\u00ba}\\text{C}[\/latex], water vapor enters the bubble continuously since the partial pressure of water is equal to 1.00 atm in equilibrium. It cannot reach this pressure, however, since the bubble also contains air and total pressure is 1.00 atm. The bubble grows in size and thereby increases the buoyant force. The bubble breaks away and rises rapidly to the surface\u2014we call this boiling! (See <a href=\"#import-auto-id1168465549482\" class=\"autogenerated-content\">(Figure)<\/a>.)<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id1168465549482\">\n<div class=\"bc-figcaption figcaption\">(a) An air bubble in water starts out saturated with water vapor at [latex]\\text{20}\\text{\u00ba}\\text{C}[\/latex]. (b) As the temperature rises, water vapor enters the bubble because its vapor pressure increases. The bubble expands to keep its pressure at 1.00 atm. (c) At [latex]\\text{100}\\text{\u00ba}\\text{C}[\/latex], water vapor enters the bubble continuously because water\u2019s vapor pressure exceeds its partial pressure in the bubble, which must be less than 1.00 atm. The bubble grows and rises to the surface.\n      <\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1168465458434\" data-alt=\"A beaker of water being heated over a flame. The beaker is shown at three different times. In the first, at twenty degrees C, a small bubble sits on the bottom of the beaker. In the second step, the water temperature is fifty degrees C and the bubble is larger, though still sitting on the bottom of the beaker. In the third step, the water temperature is one hundred degrees C. The bubble is larger and is rising toward the surface.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/graphics4-3.jpg\" data-media-type=\"image\/jpg\" alt=\"A beaker of water being heated over a flame. The beaker is shown at three different times. In the first, at twenty degrees C, a small bubble sits on the bottom of the beaker. In the second step, the water temperature is fifty degrees C and the bubble is larger, though still sitting on the bottom of the beaker. In the third step, the water temperature is one hundred degrees C. The bubble is larger and is rising toward the surface.\" height=\"212\" width=\"250\"><\/span><\/p><\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2722050\" data-element-type=\"check-understanding\" data-label=\"\">\n<div data-type=\"title\">Check Your Understanding<\/div>\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1830235\">\n<p id=\"import-auto-id1168465464207\">Freeze drying is a process in which substances, such as foods, are dried by placing them in a vacuum chamber and lowering the atmospheric pressure around them. How does the lowered atmospheric pressure speed the drying process, and why does it cause the temperature of the food to drop?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2258999\">\n<p id=\"import-auto-id1168465464214\">Decreased the atmospheric pressure results in decreased partial pressure of water, hence a lower humidity. So evaporation of water from food, for example, will be enhanced. The molecules of water most likely to break away from the food will be those with the greatest velocities. Those remaining thus have a lower average velocity and a lower temperature. This can (and does) result in the freezing and drying of the food; hence the process is aptly named freeze drying.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" id=\"fs-id2104921\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">PhET Explorations: States of Matter<\/div>\n<p id=\"import-auto-id1168465538008\">Watch different types of molecules form a solid, liquid, or gas. Add or remove heat and watch the phase change. Change the temperature or volume of a container and see a pressure-temperature diagram respond in real time. Relate the interaction potential to the forces between molecules. <\/p>\n<div class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\"><a href=\"http:\/\/phet.colorado.edu\/en\/simulation\/states-of-matter\">States of Matter: Basics<\/a><\/div>\n<p><span data-type=\"media\" data-alt=\"\"><a href=\"\/resources\/52e49aa5d0d2bc0e4dc7726deafbd4e9ff1c66f4\/states-of-matter-basics_en.jar\" data-type=\"image\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/PhET_Icon.png\" data-media-type=\"image\/png\" alt=\"\" data-print=\"false\" width=\"450\"><\/a><span data-media-type=\"image\/png\" data-print=\"true\" data-src=\"\/resources\/075500ad9f71890a85fe3f7a4137ac08e2b7907c\/PhET_Icon.png\" data-type=\"image\"><\/span><\/span><\/p><\/div>\n<\/div>\n<div class=\"section-summary\" data-depth=\"1\" id=\"fs-id1530186\">\n<h1 data-type=\"title\">Section Summary<\/h1>\n<ul id=\"fs-id1698455\">\n<li id=\"import-auto-id1168465538186\">Relative humidity is the fraction of water vapor in a gas compared to the saturation value.<\/li>\n<li id=\"import-auto-id1168465538190\">The saturation vapor density can be determined from the vapor pressure for a given temperature.<\/li>\n<li id=\"import-auto-id1168465538193\">Percent relative humidity is defined to be\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id1168465538195\">[latex]\\text{percent relative humidity}=\\frac{\\text{vapor density}}{\\text{saturation vapor density}}\u00d7\\text{100}\\text{.}[\/latex]<\/div>\n<\/li>\n<li id=\"import-auto-id1168465551772\">The dew point is the temperature at which air reaches 100% relative humidity.<\/li>\n<\/ul>\n<\/div>\n<div class=\"conceptual-questions\" data-depth=\"1\" id=\"fs-id1907369\" data-element-type=\"conceptual-questions\">\n<h1 data-type=\"title\">Conceptual Questions<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1439139\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1614758\">\n<p id=\"import-auto-id1168465550503\">Because humidity depends only on water\u2019s vapor pressure and temperature, are the saturation vapor densities listed in <a href=\"#import-auto-id1591575\" class=\"autogenerated-content\">(Figure)<\/a> valid in an atmosphere of helium at a pressure of [latex]1\\text{.}\\text{01}\u00d7{\\text{10}}^{5}\\phantom{\\rule{0.25em}{0ex}}{\\text{N\/m}}^{2}[\/latex], rather than air? Are those values affected by altitude on Earth?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1438869\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2322601\">\n<p id=\"import-auto-id1168465460029\">Why does a beaker of [latex]\\text{40}\\text{.}0\\text{\u00ba}\\text{C}[\/latex] water placed in a vacuum chamber start to boil as the chamber is evacuated (air is pumped out of the chamber)? At what pressure does the boiling begin? Would food cook any faster in such a beaker? <\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1854910\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1746204\">\n<p id=\"import-auto-id2184131\">Why does rubbing alcohol evaporate much more rapidly than water at STP (standard temperature and pressure)? <\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"problems-exercises\" data-depth=\"1\" id=\"fs-id1604734\" data-element-type=\"problems-exercises\">\n<h1 data-type=\"title\">Problems &amp; Exercises<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1893897\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1695017\">\n<p id=\"import-auto-id2938875\">Dry air is 78.1% nitrogen. What is the partial pressure of nitrogen when the atmospheric pressure is [latex]1\\text{.}\\text{01}\u00d7{\\text{10}}^{5}\\phantom{\\rule{0.25em}{0ex}}{\\text{N\/m}}^{2}[\/latex]?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2249777\">\n<p id=\"eip-id3199847\">[latex]7\\text{.}\\text{89}\u00d7{\\text{10}}^{4}\\phantom{\\rule{0.25em}{0ex}}\\text{Pa}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1423931\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1697977\">\n<p id=\"import-auto-id1168465440225\">(a) What is the vapor pressure of water at [latex]\\text{20}\\text{.}0\\text{\u00ba}\\text{C}[\/latex]? (b) What percentage of atmospheric pressure does this correspond to? (c) What percent of [latex]\\text{20}\\text{.}0\\text{\u00ba}\\text{C}[\/latex] air is water vapor if it has 100% relative humidity? (The density of dry air at [latex]\\text{20}\\text{.}0\\text{\u00ba}\\text{C}[\/latex] is [latex]1\\text{.}\\text{20}\\phantom{\\rule{0.25em}{0ex}}{\\text{kg\/m}}^{3}[\/latex].) <\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2720918\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1611394\">\n<p id=\"import-auto-id1168465455761\">Pressure cookers increase cooking speed by raising the boiling temperature of water above its value at atmospheric pressure. (a) What pressure is necessary to raise the boiling point to [latex]\\text{120}\\text{.}0\\text{\u00ba}\\text{C}[\/latex]? (b) What gauge pressure does this correspond to?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1498210\">\n<p id=\"import-auto-id1168465426468\">(a) [latex]1\\text{.}\\text{99}\u00d7{\\text{10}}^{5}\\phantom{\\rule{0.25em}{0ex}}\\text{Pa}[\/latex]<\/p>\n<p id=\"import-auto-id1168465435245\">(b) 0.97 atm<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1423468\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1907426\">\n<p id=\"import-auto-id1168465426913\">(a) At what temperature does water boil at an altitude of 1500 m (about 5000 ft) on a day when atmospheric pressure is [latex]8\\text{.}\\text{59}\u00d7{\\text{10}}^{4}\\phantom{\\rule{0.25em}{0ex}}{\\text{N\/m}}^{2}\\text{?}[\/latex] (b) What about at an altitude of 3000 m (about 10,000 ft) when atmospheric pressure is [latex]7\\text{.}\\text{00}\u00d7{\\text{10}}^{4}\\phantom{\\rule{0.25em}{0ex}}{\\text{N\/m}}^{2}\\text{?}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2385042\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3293921\">\n<p id=\"import-auto-id1168465459979\">What is the atmospheric pressure on top of Mt. Everest on a day when water boils there at a temperature of [latex]\\text{70}\\text{.}0\\text{\u00ba}\\text{C?}[\/latex]<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2563526\">\n<p id=\"eip-id1647917\">[latex]3\\text{.}\\text{12}\u00d7{\\text{10}}^{4}\\phantom{\\rule{0.25em}{0ex}}\\text{Pa}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1861214\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2716378\">\n<p id=\"import-auto-id1168465464181\">At a spot in the high Andes, water boils at [latex]\\text{80}\\text{.}0\\text{\u00ba}\\text{C}[\/latex], greatly reducing the cooking speed of potatoes, for example. What is atmospheric pressure at this location? <\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2378107\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1391142\">\n<p id=\"import-auto-id1168465460156\">What is the relative humidity on a [latex]\\text{25}\\text{.}0\\text{\u00ba}\\text{C}[\/latex] day when the air contains [latex]\\text{18}\\text{.}0\\phantom{\\rule{0.25em}{0ex}}{\\text{g\/m}}^{3}[\/latex] of water vapor?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2688458\">\n<p id=\"import-auto-id1868578\">78.3%<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1477204\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1490105\">\n<p id=\"import-auto-id1804618\">What is the density of water vapor in [latex]{\\text{g\/m}}^{3}[\/latex] on a hot dry day in the desert when the temperature is [latex]\\text{40}\\text{.}0\\text{\u00ba}\\text{C}[\/latex] and the relative humidity is 6.00%?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2377418\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1462926\">\n<p id=\"import-auto-id1168465438267\">A deep-sea diver should breathe a gas mixture that has the same oxygen partial pressure as at sea level, where dry air contains 20.9% oxygen and has a total pressure of [latex]1\\text{.}\\text{01}\u00d7{\\text{10}}^{5}\\phantom{\\rule{0.25em}{0ex}}{\\text{N\/m}}^{2}[\/latex]. (a) What is the partial pressure of oxygen at sea level? (b) If the diver breathes a gas mixture at a pressure of [latex]2\\text{.}\\text{00}\u00d7{\\text{10}}^{6}\\phantom{\\rule{0.25em}{0ex}}{\\text{N\/m}}^{2}[\/latex], what percent oxygen should it be to have the same oxygen partial pressure as at sea level?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1861296\">\n<p id=\"import-auto-id1168465458014\">(a) [latex]2\\text{.}\\text{12}\u00d7{\\text{10}}^{4}\\phantom{\\rule{0.25em}{0ex}}\\text{Pa}[\/latex]<\/p>\n<p id=\"import-auto-id1168465438322\">(b) [latex]1\\text{.}\\text{06}\\phantom{\\rule{0.25em}{0ex}}\\text{%}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2206267\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1527017\">\n<p id=\"import-auto-id1168465548459\">The vapor pressure of water at [latex]\\text{40}\\text{.}0\\text{\u00ba}\\text{C}[\/latex] is [latex]7\\text{.}\\text{34}\u00d7{\\text{10}}^{3}\\phantom{\\rule{0.25em}{0ex}}{\\text{N\/m}}^{2}[\/latex]. Using the ideal gas law, calculate the density of water vapor in [latex]{\\text{g\/m}}^{3}[\/latex] that creates a partial pressure equal to this vapor pressure. The result should be the same as the saturation vapor density at that temperature [latex]\\left(\\text{51}\\text{.}{\\text{1 g\/m}}^{3}\\right)\\text{.}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2094936\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2699756\">\n<p id=\"import-auto-id1168465550332\">Air in human lungs has a temperature of [latex]\\text{37}\\text{.}0\\text{\u00ba}\\text{C}[\/latex] and a saturation vapor density of [latex]\\text{44}\\text{.}{\\text{0 g\/m}}^{3}[\/latex]. (a) If 2.00 L of air is exhaled and very dry air inhaled, what is the maximum loss of water vapor by the person? (b) Calculate the partial pressure of water vapor having this density, and compare it with the vapor pressure of [latex]6\\text{.}\\text{31}\u00d7{\\text{10}}^{3}\\phantom{\\rule{0.25em}{0ex}}{\\text{N\/m}}^{2}[\/latex].<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1443552\">\n<p id=\"import-auto-id1168465554249\">(a) [latex]8\\text{.}\\text{80}\u00d7{\\text{10}}^{-2}\\phantom{\\rule{0.25em}{0ex}}\\text{g}[\/latex]<\/p>\n<p id=\"import-auto-id2383432\">(b) [latex]6\\text{.}\\text{30}\u00d7{\\text{10}}^{3}\\phantom{\\rule{0.25em}{0ex}}\\text{Pa}[\/latex]; the two values are nearly identical. <\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2635848\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2635851\">\n<p id=\"import-auto-id1168465551440\">If the relative humidity is 90.0% on a muggy summer morning when the temperature is [latex]\\text{20}\\text{.}0\\text{\u00ba}\\text{C}[\/latex], what will it be later in the day when the temperature is [latex]\\text{30}\\text{.}0\\text{\u00ba}\\text{C}[\/latex], assuming the water vapor density remains constant? <\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2599998\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1470438\">\n<p id=\"import-auto-id1168465435123\">Late on an autumn day, the relative humidity is 45.0% and the temperature is [latex]\\text{20}\\text{.}0\\text{\u00ba}\\text{C}[\/latex]. What will the relative humidity be that evening when the temperature has dropped to [latex]\\text{10}\\text{.}0\\text{\u00ba}\\text{C}[\/latex], assuming constant water vapor density?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1600891\">\n<p id=\"import-auto-id1168465551043\">82.3%<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2085047\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2721954\">\n<p id=\"import-auto-id1168465551065\">Atmospheric pressure atop Mt. Everest is [latex]3\\text{.}\\text{30}\u00d7{\\text{10}}^{4}\\phantom{\\rule{0.25em}{0ex}}{\\text{N\/m}}^{2}[\/latex]. (a) What is the partial pressure of oxygen there if it is 20.9% of the air? (b) What percent oxygen should a mountain climber breathe so that its partial pressure is the same as at sea level, where atmospheric pressure is [latex]1\\text{.}\\text{01}\u00d7{\\text{10}}^{5}\\phantom{\\rule{0.25em}{0ex}}{\\text{N\/m}}^{2}\\text{?}[\/latex] (c) One of the most severe problems for those climbing very high mountains is the extreme drying of breathing passages. Why does this drying occur? <\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1509093\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1509095\">\n<p id=\"import-auto-id1168465538126\">What is the dew point (the temperature at which 100% relative humidity would occur) on a day when relative humidity is 39.0% at a temperature of [latex]\\text{20}\\text{.}0\\text{\u00ba}\\text{C}[\/latex]?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1412837\">\n<p id=\"eip-id3222544\">[latex]4\\text{.}\\text{77}\\text{\u00ba}\\text{C}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1806668\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1806670\">\n<p id=\"import-auto-id1168465478336\">On a certain day, the temperature is [latex]\\text{25}\\text{.}0\\text{\u00ba}\\text{C}[\/latex] and the relative humidity is 90.0%. How many grams of water must condense out of each cubic meter of air if the temperature falls to [latex]\\text{15}\\text{.}0\\text{\u00ba}\\text{C}[\/latex]? Such a drop in temperature can, thus, produce heavy dew or fog. <\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2386969\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1615107\">\n<p id=\"import-auto-id1168465553959\"><strong>Integrated Concepts<\/strong><\/p>\n<p id=\"eip-id2396285\">The boiling point of water increases with depth because pressure increases with depth. At what depth will fresh water have a boiling point of [latex]\\text{150}\\text{\u00ba}\\text{C}[\/latex], if the surface of the water is at sea level?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1856385\">\n<p id=\"eip-id3422225\">[latex]\\text{38}\\text{.}3\\phantom{\\rule{0.25em}{0ex}}\\text{m}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2298434\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2298436\">\n<p id=\"import-auto-id1168465552564\"><strong>Integrated Concepts<\/strong><\/p>\n<p id=\"import-auto-id1168465552566\">(a) At what depth in fresh water is the critical pressure of water reached, given that the surface is at sea level? (b) At what temperature will this water boil? (c) Is a significantly higher temperature needed to boil water at a greater depth? <\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1543836\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2193148\">\n<p id=\"import-auto-id1168465552576\"><strong>Integrated Concepts<\/strong><\/p>\n<p id=\"import-auto-id1168465552578\">To get an idea of the small effect that temperature has on Archimedes\u2019 principle, calculate the fraction of a copper block\u2019s weight that is supported by the buoyant force in [latex]0\\text{\u00ba}\\text{C}[\/latex] water and compare this fraction with the fraction supported in [latex]\\text{95}\\text{.}0\\text{\u00ba}\\text{C}[\/latex] water.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1830450\">\n<p id=\"import-auto-id1168465552620\">[latex]\\frac{\\left({F}_{\\text{B}}\/{w}_{\\text{Cu}}\\right)}{{\\left({F}_{\\text{B}}\/{w}_{\\text{Cu}}\\right)}^{\\prime }}=1\\text{.}\\text{02}[\/latex]. The buoyant force supports nearly the exact same amount of force on the copper block in both circumstances.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2688861\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1487389\">\n<p id=\"import-auto-id1168465451621\"><strong>Integrated Concepts<\/strong><\/p>\n<p id=\"import-auto-id1168465451604\">If you want to cook in water at [latex]\\text{150}\\text{\u00ba}\\text{C}[\/latex], you need a pressure cooker that can withstand the necessary pressure. (a) What pressure is required for the boiling point of water to be this high? (b) If the lid of the pressure cooker is a disk 25.0 cm in diameter, what force must it be able to withstand at this pressure? <\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1582923\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2694568\">\n<p id=\"import-auto-id1168465551397\"><strong>Unreasonable Results<\/strong><\/p>\n<p id=\"eip-id2215990\">(a) How many moles per cubic meter of an ideal gas are there at a pressure of [latex]1\\text{.}\\text{00}\u00d7{\\text{10}}^{\\text{14}}\\phantom{\\rule{0.25em}{0ex}}{\\text{N\/m}}^{2}[\/latex] and at [latex]0\\text{\u00ba}\\text{C}[\/latex]? (b) What is unreasonable about this result? (c) Which premise or assumption is responsible?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2304325\">\n<p id=\"import-auto-id1168465550196\">(a) [latex]4\\text{.}\\text{41}\u00d7{\\text{10}}^{\\text{10}}\\phantom{\\rule{0.25em}{0ex}}{\\text{mol\/m}}^{3}[\/latex]<\/p>\n<p id=\"import-auto-id1168465550230\">(b) It\u2019s unreasonably large.<\/p>\n<p id=\"import-auto-id1168465550239\">(c) At high pressures such as these, the ideal gas law can no longer be applied. As a result, unreasonable answers come up when it is used.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1669904\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1669906\">\n<p id=\"eip-id2076330\"><strong>Unreasonable Results<\/strong><\/p>\n<p id=\"import-auto-id1168465550238\"> (a) An automobile mechanic claims that an aluminum rod fits loosely into its hole on an aluminum engine block because the engine is hot and the rod is cold. If the hole is 10.0% bigger in diameter than the [latex]\\text{22}\\text{.}0\\text{\u00ba}\\text{C}[\/latex] rod, at what temperature will the rod be the same size as the hole? (b) What is unreasonable about this temperature? (c) Which premise is responsible? <\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2705483\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1513742\">\n<p id=\"import-auto-id1168465552259\"><strong>Unreasonable Results<\/strong><\/p>\n<p id=\"import-auto-id1168465552262\">The temperature inside a supernova explosion is said to be [latex]2\\text{.}\\text{00}\u00d7{\\text{10}}^{\\text{13}}\\phantom{\\rule{0.25em}{0ex}}\\text{K}[\/latex]. (a) What would the average velocity [latex]{v}_{\\text{rms}}[\/latex] of hydrogen atoms be? (b) What is unreasonable about this velocity? (c) Which premise or assumption is responsible?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2258269\">\n<p id=\"import-auto-id1168465426342\">(a) [latex]7\\text{.}\\text{03}\u00d7{\\text{10}}^{8}\\phantom{\\rule{0.25em}{0ex}}\\text{m\/s}[\/latex]<\/p>\n<p id=\"import-auto-id1168465426389\">(b) The velocity is too high\u2014it\u2019s greater than the speed of light.<\/p>\n<p id=\"import-auto-id1168465426391\">(c) The assumption that hydrogen inside a supernova behaves as an idea gas is responsible, because of the great temperature and density in the core of a star. Furthermore, when a velocity greater than the speed of light is obtained, classical physics must be replaced by relativity, a subject not yet covered.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1689262\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1689263\">\n<p id=\"import-auto-id1168465426400\"><strong>Unreasonable Results<\/strong><\/p>\n<p id=\"import-auto-id1168465426403\">Suppose the relative humidity is 80% on a day when the temperature is [latex]\\text{30}\\text{.}0\\text{\u00ba}\\text{C}[\/latex]. (a) What will the relative humidity be if the air cools to [latex]\\text{25}\\text{.}0\\text{\u00ba}\\text{C}[\/latex] and the vapor density remains constant? (b) What is unreasonable about this result? (c) Which premise is responsible? <\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"glossary\" class=\"textbox shaded\">\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl class=\"definition\" id=\"import-auto-id1168465548876\">\n<dt>dew point<\/dt>\n<dd id=\"fs-id1746250\">the temperature at which relative humidity is 100%; the temperature at which water starts to condense out of the air<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id1168465548880\">\n<dt>saturation<\/dt>\n<dd id=\"fs-id1847032\">the condition of 100% relative humidity<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id1168465548882\">\n<dt>percent relative humidity<\/dt>\n<dd id=\"fs-id1688807\">the ratio of vapor density to saturation vapor density <\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id1168465548885\">\n<dt>relative humidity<\/dt>\n<dd id=\"fs-id1803443\">the amount of water in the air relative to the maximum amount the air can hold<\/dd>\n<\/dl>\n<\/div>\n\n","rendered":"<div class=\"textbox learning-objectives\">\n<h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>\n<ul>\n<li>Explain the relationship between vapor pressure of water and the capacity of air to hold water vapor.<\/li>\n<li>Explain the relationship between relative humidity and partial pressure of water vapor in the air.<\/li>\n<li>Calculate vapor density using vapor pressure.<\/li>\n<li>Calculate humidity and dew point.<\/li>\n<\/ul>\n<\/div>\n<div class=\"bc-figure figure\" id=\"import-auto-id1653277\">\n<div class=\"bc-figcaption figcaption\">Dew drops like these, on a banana leaf photographed just after sunrise, form when the air temperature drops to or below the dew point. At the dew point, the rate at which water molecules join together is greater than the rate at which they separate, and some of the water condenses to form droplets. (credit: Aaron Escobar, Flickr) <\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1661526\" data-alt=\"\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_14_06_00.jpg\" data-media-type=\"image\/jpg\" alt=\"\" width=\"250\" \/><\/span><\/p>\n<\/div>\n<p id=\"import-auto-id1857764\">The expression \u201cit\u2019s not the heat, it\u2019s the humidity\u201d makes a valid point. We keep cool in hot weather by evaporating sweat from our skin and water from our breathing passages. Because evaporation is inhibited by high humidity, we feel hotter at a given temperature when the humidity is high. Low humidity, on the other hand, can cause discomfort from excessive drying of mucous membranes and can lead to an increased risk of respiratory infections.<\/p>\n<p id=\"import-auto-id1084476\">When we say humidity, we really mean <span data-type=\"term\" id=\"import-auto-id1300275\">relative humidity<\/span>. Relative humidity tells us how much water vapor is in the air compared with the maximum possible. At its maximum, denoted as <span data-type=\"term\" id=\"import-auto-id2045214\">saturation<\/span>, the relative humidity is 100%, and evaporation is inhibited. The amount of water vapor in the air depends on temperature. For example, relative humidity rises in the evening, as air temperature declines, sometimes reaching the <span data-type=\"term\" id=\"import-auto-id2232198\">dew point<\/span>. At the dew point temperature, relative humidity is 100%, and fog may result from the condensation of water droplets if they are small enough to stay in suspension. Conversely, if you wish to dry something (perhaps your hair), it is more effective to blow hot air over it rather than cold air, because, among other things, the increase in temperature increases the energy of the molecules, so the rate of evaporation increases.<\/p>\n<p id=\"import-auto-id2245399\">The amount of water vapor in the air depends on the vapor pressure of water. The liquid and solid phases are continuously giving off vapor because some of the molecules have high enough speeds to enter the gas phase; see <a href=\"#import-auto-id2807071\" class=\"autogenerated-content\">(Figure)<\/a>(a). If a lid is placed over the container, as in <a href=\"#import-auto-id2807071\" class=\"autogenerated-content\">(Figure)<\/a>(b), evaporation continues, increasing the pressure, until sufficient vapor has built up for condensation to balance evaporation. Then equilibrium has been achieved, and the vapor pressure is equal to the partial pressure of water in the container. Vapor pressure increases with temperature because molecular speeds are higher as temperature increases. <a href=\"#import-auto-id1591575\" class=\"autogenerated-content\">(Figure)<\/a> gives representative values of water vapor pressure over a range of temperatures.<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id2807071\">\n<div class=\"bc-figcaption figcaption\">(a) Because of the distribution of speeds and kinetic energies, some water molecules can break away to the vapor phase even at temperatures below the ordinary boiling point. (b) If the container is sealed, evaporation will continue until there is enough vapor density for the condensation rate to equal the evaporation rate. This vapor density and the partial pressure it creates are the saturation values. They increase with temperature and are independent of the presence of other gases, such as air. They depend only on the vapor pressure of water.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1684254\" data-alt=\"Two containers, each filled two-thirds with water. One is open to the atmosphere and the other is sealed at the top. The water molecules are depicted as circles with vector arrows of different lengths and directions to indicate velocity. In the sealed container the density of molecules in the air above the water is greater than in the unsealed container. In the sealed container, water is condensing along the walls and top of the upper part of the container.\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_14_06_01.jpg\" data-media-type=\"image\/jpg\" alt=\"Two containers, each filled two-thirds with water. One is open to the atmosphere and the other is sealed at the top. The water molecules are depicted as circles with vector arrows of different lengths and directions to indicate velocity. In the sealed container the density of molecules in the air above the water is greater than in the unsealed container. In the sealed container, water is condensing along the walls and top of the upper part of the container.\" height=\"228\" width=\"331\" \/><\/span><\/p>\n<\/div>\n<p id=\"import-auto-id2670648\">Relative humidity is related to the partial pressure of water vapor in the air. At 100% humidity, the partial pressure is equal to the vapor pressure, and no more water can enter the vapor phase. If the partial pressure is less than the vapor pressure, then evaporation will take place, as humidity is less than 100%. If the partial pressure is greater than the vapor pressure, condensation takes place. In everyday language, people sometimes refer to the capacity of air to \u201chold\u201d water vapor, but this is not actually what happens. The water vapor is not held by the air. The amount of water in air is determined by the vapor pressure of water and has nothing to do with the properties of air.<\/p>\n<table id=\"import-auto-id1591575\" summary=\"Table of saturation vapor density of water between negative fifty and positive two hundred twenty degrees Celsius.\">\n<caption><span data-type=\"title\">Saturation Vapor Density of Water<\/span><\/caption>\n<thead>\n<tr>\n<th data-align=\"center\">Temperature <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-5741c40fa5e0573c35215b11567f2872_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"25\" style=\"vertical-align: -4px;\" \/><\/th>\n<th data-align=\"center\">Vapor pressure (Pa)<\/th>\n<th data-align=\"center\">Saturation vapor density (g\/m<sup>3<\/sup>)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td data-align=\"center\">\u221250<\/td>\n<td data-align=\"center\">4.0<\/td>\n<td data-align=\"center\">0.039<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">\u221220<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-65cec94248cfe7c1b95b9b5ab893ac48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#52;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -1px;\" \/><\/td>\n<td data-align=\"center\">0.89<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">\u221210<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c3f4b07d7b35985eb4a3e27e977efe0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/td>\n<td data-align=\"center\">2.36<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">0<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-5b66583a589f74923ae639cddc604de4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/td>\n<td data-align=\"center\">4.84<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">5<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-973fd274382b2321c7cbded23a6a82af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#56;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/td>\n<td data-align=\"center\">6.80<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">10<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c941ed642058b6622001364e261bbaf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#57;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -1px;\" \/><\/td>\n<td data-align=\"center\">9.40<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">15<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-729b25d494083fe2c60d52ae859d45a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#57;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -1px;\" \/><\/td>\n<td data-align=\"center\">12.8<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">20<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f3ed7440d83e2d36ec3c8841daeff0eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#51;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/td>\n<td data-align=\"center\">17.2<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">25<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-fe1ac33f80be5c0798ddd3c8f142ee79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#55;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/td>\n<td data-align=\"center\">23.0<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">30<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e65a5ed71d7e623504201207baac8676_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#52;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/td>\n<td data-align=\"center\">30.4<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">37<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a48257556b9531ee94d1ac21467d73be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#49;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/td>\n<td data-align=\"center\">44.0<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">40<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4db51ef708a1bf451cf1007e4156f82c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#52;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/td>\n<td data-align=\"center\">51.1<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">50<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-15553b66d32847dc1776aa2dd1005c20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -1px;\" \/><\/td>\n<td data-align=\"center\">82.4<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">60<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-0b6ea1e71a0e2a47e4e4eebf6b1ebc35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#57;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -1px;\" \/><\/td>\n<td data-align=\"center\">130<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">70<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-3002f79470efbfb2f8ff902fa268d919_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#50;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/td>\n<td data-align=\"center\">197<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">80<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c74cfb15a765a3c30ae675e9ca42c2c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#55;&#51;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/td>\n<td data-align=\"center\">294<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">90<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e39d0f8546a2647ada2c3df3921efe5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#49;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/td>\n<td data-align=\"center\">418<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">95<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a8e0a04a7594cd701985074eabc22f0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#57;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/td>\n<td data-align=\"center\">505<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\"><strong data-effect=\"bold\">100<\/strong><\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4ccc7ce4f43d40a3481add12887faa1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#49;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -1px;\" \/><\/td>\n<td data-align=\"center\"><strong data-effect=\"bold\">598<\/strong><\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">120<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-5e575ffcdd17e7cb5281998190bf3148_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#57;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -1px;\" \/><\/td>\n<td data-align=\"center\">1095<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">150<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-feb113f55ce8c6543573a148a5a3ca86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#55;&#54;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/td>\n<td data-align=\"center\">2430<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">200<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-d9a8e730561b612fc73b1105ca705c59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#53;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -1px;\" \/><\/td>\n<td data-align=\"center\">7090<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">220<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4cd9a3f96810996088f830cc0d292612_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#50;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/td>\n<td data-align=\"center\">10,200<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div data-type=\"example\" class=\"textbox examples\" id=\"fs-id2013690\">\n<div data-type=\"title\" class=\"title\">Calculating Density Using Vapor Pressure<\/div>\n<p id=\"import-auto-id1684683\"><a href=\"#import-auto-id1591575\" class=\"autogenerated-content\">(Figure)<\/a> gives the vapor pressure of water at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f205d73e3e16a867ce37b630c0c5cbaa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"44\" style=\"vertical-align: 0px;\" \/> as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-53ac694e8ab5de1d83e2c428f1ac4bad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#51;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#97;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"86\" style=\"vertical-align: -1px;\" \/> Use the ideal gas law to calculate the density of water vapor in <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e26ef34a316eb8b0fd08085807cc2f05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#103;&#125;&#47;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"40\" style=\"vertical-align: -5px;\" \/> that would create a partial pressure equal to this vapor pressure. Compare the result with the saturation vapor density given in the table.<\/p>\n<p id=\"import-auto-id2270512\"><strong>Strategy<\/strong><\/p>\n<p id=\"import-auto-id1898263\">To solve this problem, we need to break it down into a two steps. The partial pressure follows the ideal gas law, <\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-93011b6e096ef883a57adecf4821b06b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#86;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#82;&#84;&#44;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"87\" style=\"vertical-align: -3px;\" \/><\/div>\n<p id=\"import-auto-id2816575\">where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> is the number of moles. If we solve this equation for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-9adf48733cde0f5cd35e831e11f561d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#47;&#86;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"34\" style=\"vertical-align: -5px;\" \/> to calculate the number of moles per cubic meter, we can then convert this quantity to grams per cubic meter as requested. To do this, we need to use the molecular mass of water, which is given in the periodic table.<\/p>\n<p id=\"import-auto-id1783632\"><strong>Solution<\/strong><\/p>\n<p id=\"import-auto-id2254806\">1. Identify the knowns and convert them to the proper units:<\/p>\n<ol id=\"eip-id2084977\" data-number-style=\"lower-alpha\">\n<li id=\"import-auto-id1674733\">temperature <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-5929d91fc845e596546696fdc4943264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#61;&#50;&#57;&#51;&#32;&#75;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"127\" style=\"vertical-align: -1px;\" \/><\/li>\n<li id=\"import-auto-id1544358\">vapor pressure <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/> of water at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a94a5528991784dff99f941113de9fe2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4978b4bd2567ac1fcaf567548d56e5eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#51;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -1px;\" \/><\/li>\n<li id=\"import-auto-id1612423\">molecular mass of water is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-413443c52b69343397cc52a0b089f1b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#56;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#103;&#47;&#109;&#111;&#108;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<p id=\"import-auto-id2052284\">2. Solve the ideal gas law for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-9adf48733cde0f5cd35e831e11f561d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#47;&#86;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"34\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id1390729\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-5aa06f7146013cd23780ee176cde736e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#110;&#125;&#123;&#86;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#80;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#82;&#84;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"58\" style=\"vertical-align: -7px;\" \/><\/div>\n<p id=\"import-auto-id1396332\">3. Substitute known values into the equation and solve for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-9adf48733cde0f5cd35e831e11f561d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#47;&#86;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"34\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id954088\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-3492e4c4d99d785ad057c78d79dae401_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#110;&#125;&#123;&#86;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#80;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#82;&#84;&#125;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#51;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#97;&#125;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#49;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#74;&#47;&#109;&#111;&#108;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#75;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#57;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#75;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#61;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#53;&#55;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#111;&#108;&#47;&#109;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"351\" style=\"vertical-align: -9px;\" \/><\/div>\n<p id=\"import-auto-id2271354\">4. Convert the density in moles per cubic meter to grams per cubic meter.<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id2069640\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-fa7e5c49d280d19add444614b2ee1c52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#114;&#104;&#111;&#32;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#53;&#55;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#111;&#108;&#125;&#125;&#123;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#125;&#125;&#94;&#123;&#51;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#56;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#32;&#103;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#111;&#108;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#55;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#103;&#47;&#109;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"279\" style=\"vertical-align: -12px;\" \/><\/div>\n<p id=\"import-auto-id2259303\"><strong>Discussion<\/strong><\/p>\n<p id=\"import-auto-id1893698\">The density is obtained by assuming a pressure equal to the vapor pressure of water at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f205d73e3e16a867ce37b630c0c5cbaa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"44\" style=\"vertical-align: 0px;\" \/>. The density found is identical to the value in <a href=\"#import-auto-id1591575\" class=\"autogenerated-content\">(Figure)<\/a>,  which means that a vapor density of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e3145b275a26af5d012461e51f2eec95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#55;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#103;&#47;&#109;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"74\" style=\"vertical-align: -4px;\" \/> at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f205d73e3e16a867ce37b630c0c5cbaa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"44\" style=\"vertical-align: 0px;\" \/> creates a partial pressure of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-bf7a02c1624837e54219bf37424eac36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#51;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#97;&#44;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"86\" style=\"vertical-align: -3px;\" \/> equal to the vapor pressure of water at that temperature. If the partial pressure is equal to the vapor pressure, then the liquid and vapor phases are in equilibrium, and the relative humidity is 100%. Thus, there can be no more than 17.2 g of water vapor per <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e3b87847f2822cabdde235117b9f5dc8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"22\" style=\"vertical-align: 0px;\" \/> at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f205d73e3e16a867ce37b630c0c5cbaa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"44\" style=\"vertical-align: 0px;\" \/>, so that this value is the saturation vapor density at that temperature. This example illustrates how water vapor behaves like an ideal gas: the pressure and density are consistent with the ideal gas law (assuming the density in the table is correct). The saturation vapor densities listed in <a href=\"#import-auto-id1591575\" class=\"autogenerated-content\">(Figure)<\/a> are the maximum amounts of water vapor that air can hold at various temperatures.<\/p>\n<\/div>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" id=\"fs-id954391\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">Percent Relative Humidity<\/div>\n<p id=\"import-auto-id2898098\">We define <span data-type=\"term\" id=\"import-auto-id2898100\">percent relative humidity<\/span> as the ratio of vapor density to saturation vapor density, or<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id2898104\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a97a78eca92c1012520814792717f5c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#101;&#114;&#99;&#101;&#110;&#116;&#32;&#114;&#101;&#108;&#97;&#116;&#105;&#118;&#101;&#32;&#104;&#117;&#109;&#105;&#100;&#105;&#116;&#121;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#118;&#97;&#112;&#111;&#114;&#32;&#100;&#101;&#110;&#115;&#105;&#116;&#121;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#97;&#116;&#117;&#114;&#97;&#116;&#105;&#111;&#110;&#32;&#118;&#97;&#112;&#111;&#114;&#32;&#100;&#101;&#110;&#115;&#105;&#116;&#121;&#125;&#125;&times;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"397\" style=\"vertical-align: -9px;\" \/><\/div>\n<\/div>\n<p id=\"import-auto-id2898416\">We can use this and the data in <a href=\"#import-auto-id1591575\" class=\"autogenerated-content\">(Figure)<\/a> to do a variety of interesting calculations, keeping in mind that relative humidity is based on the comparison of the partial pressure of water vapor in air and ice.<\/p>\n<div data-type=\"example\" class=\"textbox examples\" id=\"fs-id1610352\">\n<div data-type=\"title\" class=\"title\">Calculating Humidity and Dew Point<\/div>\n<p id=\"import-auto-id2302384\">(a) Calculate the percent relative humidity on a day when the temperature is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-cc820ae9a4e31f54215900ec9043cec0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#53;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"44\" style=\"vertical-align: 0px;\" \/> and the air contains 9.40 g of water vapor per <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e3b87847f2822cabdde235117b9f5dc8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"22\" style=\"vertical-align: 0px;\" \/>. (b) At what temperature will this air reach 100% relative humidity (the saturation density)? This temperature is the dew point. (c) What is the humidity when the air temperature is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-cc820ae9a4e31f54215900ec9043cec0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#53;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"44\" style=\"vertical-align: 0px;\" \/> and the dew point is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-20a3411ce8e543f857ff566b4f2b51cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: -1px;\" \/>?<\/p>\n<p id=\"import-auto-id1168465458500\"><strong>Strategy and Solution<\/strong><\/p>\n<p id=\"import-auto-id1168465548024\">(a) Percent relative humidity is defined as the ratio of vapor density to saturation vapor density. <\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id1168465550625\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a97a78eca92c1012520814792717f5c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#101;&#114;&#99;&#101;&#110;&#116;&#32;&#114;&#101;&#108;&#97;&#116;&#105;&#118;&#101;&#32;&#104;&#117;&#109;&#105;&#100;&#105;&#116;&#121;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#118;&#97;&#112;&#111;&#114;&#32;&#100;&#101;&#110;&#115;&#105;&#116;&#121;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#97;&#116;&#117;&#114;&#97;&#116;&#105;&#111;&#110;&#32;&#118;&#97;&#112;&#111;&#114;&#32;&#100;&#101;&#110;&#115;&#105;&#116;&#121;&#125;&#125;&times;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"397\" style=\"vertical-align: -9px;\" \/><\/div>\n<p id=\"import-auto-id1168465549468\">The first is given to be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-fd0a614f317225946ebd47bdd63552eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#48;&#32;&#103;&#47;&#109;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"77\" style=\"vertical-align: -4px;\" \/>, and the second is found in <a href=\"#import-auto-id1591575\" class=\"autogenerated-content\">(Figure)<\/a> to be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-fe109fb4dee108b2cf38ac2c9580af94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#32;&#103;&#47;&#109;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"77\" style=\"vertical-align: -4px;\" \/>. Thus,<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id1168465433320\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-326cf21a6fc1a83f7403ed189b369d55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#101;&#114;&#99;&#101;&#110;&#116;&#32;&#114;&#101;&#108;&#97;&#116;&#105;&#118;&#101;&#32;&#104;&#117;&#109;&#105;&#100;&#105;&#116;&#121;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#48;&#32;&#103;&#47;&#109;&#125;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#32;&#103;&#47;&#109;&#125;&#125;&#94;&#123;&#51;&#125;&#125;&times;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#48;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#57;&#92;&#116;&#101;&#120;&#116;&#123;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#37;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"7261\" width=\"6616\" style=\"vertical-align: -3px;\" \/><\/div>\n<p id=\"import-auto-id1168465463861\">(b) The air contains <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-fd0a614f317225946ebd47bdd63552eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#48;&#32;&#103;&#47;&#109;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"77\" style=\"vertical-align: -4px;\" \/> of water vapor. The relative humidity will be 100% at a temperature where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-fd0a614f317225946ebd47bdd63552eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#48;&#32;&#103;&#47;&#109;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"77\" style=\"vertical-align: -4px;\" \/> is the saturation density. Inspection of <a href=\"#import-auto-id1591575\" class=\"autogenerated-content\">(Figure)<\/a> reveals this to be the case at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b3e9b994189112ed7be4890b58b10b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"43\" style=\"vertical-align: -1px;\" \/>, where the relative humidity will be 100%. That temperature is called the dew point for air with this concentration of water vapor.<\/p>\n<p id=\"import-auto-id1168465552646\">(c) Here, the dew point temperature is given to be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-20a3411ce8e543f857ff566b4f2b51cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: -1px;\" \/>. Using <a href=\"#import-auto-id1591575\" class=\"autogenerated-content\">(Figure)<\/a>, we see that the vapor density is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-bf0bb6814276269735dce373b829bb9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#54;&#32;&#103;&#47;&#109;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"77\" style=\"vertical-align: -4px;\" \/>, because this value is the saturation vapor density at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-20a3411ce8e543f857ff566b4f2b51cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: -1px;\" \/>. The saturation vapor density at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-cc820ae9a4e31f54215900ec9043cec0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#53;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"44\" style=\"vertical-align: 0px;\" \/> is seen to be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-fe109fb4dee108b2cf38ac2c9580af94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#32;&#103;&#47;&#109;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"77\" style=\"vertical-align: -4px;\" \/>. Thus, the relative humidity at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-cc820ae9a4e31f54215900ec9043cec0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#53;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"44\" style=\"vertical-align: 0px;\" \/> is<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id1168465550600\">\n<pre class=\"ql-errors\">*** QuickLaTeX cannot compile formula:\n&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#101;&#114;&#99;&#101;&#110;&#116;&#32;&#114;&#101;&#108;&#97;&#116;&#105;&#118;&#101;&#32;&#104;&#117;&#109;&#105;&#100;&#105;&#116;&#121;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#54;&#32;&#103;&#47;&#109;&#125;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#32;&#103;&#47;&#109;&#125;&#125;&#94;&#123;&#51;&#125;&#125;&times;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#48;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#51;&#92;&#116;&#101;&#120;&#116;&#123;&#37;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;\n\n*** Error message:\n&#70;&#105;&#108;&#101;&#32;&#101;&#110;&#100;&#101;&#100;&#32;&#119;&#104;&#105;&#108;&#101;&#32;&#115;&#99;&#97;&#110;&#110;&#105;&#110;&#103;&#32;&#117;&#115;&#101;&#32;&#111;&#102;&#32;&#92;&#116;&#101;&#120;&#116;&#64;&#46;\r\n&#69;&#109;&#101;&#114;&#103;&#101;&#110;&#99;&#121;&#32;&#115;&#116;&#111;&#112;&#46;\r\n\n<\/pre>\n<\/div>\n<p id=\"import-auto-id1586286\"><strong>Discussion<\/strong><\/p>\n<p id=\"import-auto-id2187925\">The importance of dew point is that air temperature cannot drop below <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b3e9b994189112ed7be4890b58b10b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"43\" style=\"vertical-align: -1px;\" \/> in part (b), or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-20a3411ce8e543f857ff566b4f2b51cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: -1px;\" \/> in part (c), without water vapor condensing out of the air. If condensation occurs, considerable transfer of heat occurs (discussed in <a href=\"\/contents\/7892cddd-833e-42b8-bcaa-a1e94fb9eb9c\">Heat and Heat Transfer Methods<\/a>), which prevents the temperature from further dropping. When dew points are below <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-209757c6d3ae348079d24990098e7e6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/>, freezing temperatures are a greater possibility, which explains why farmers keep track of the dew point. Low humidity in deserts means low dew-point temperatures. Thus condensation is unlikely. If the temperature drops, vapor does not condense in liquid drops. Because no heat is released into the air, the air temperature drops more rapidly compared to air with higher humidity. Likewise, at high temperatures, liquid droplets do not evaporate, so that no heat is removed from the gas to the liquid phase. This explains the large range of temperature in arid regions. <\/p>\n<\/div>\n<p id=\"import-auto-id1168465550071\">Why does water boil at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a6eb54fe6e37f18e8cbc8357c49dad21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"38\" style=\"vertical-align: -1px;\" \/>? You will note from <a href=\"#import-auto-id1591575\" class=\"autogenerated-content\">(Figure)<\/a> that the vapor pressure of water at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a6eb54fe6e37f18e8cbc8357c49dad21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"38\" style=\"vertical-align: -1px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-6493dda222079c65283320ba71cbf5a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#49;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#53;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"81\" style=\"vertical-align: -1px;\" \/>, or 1.00 atm. Thus, it can evaporate without limit at this temperature and pressure. But why does it form bubbles when it boils? This is because water ordinarily contains significant amounts of dissolved air and other impurities, which are observed as small bubbles of air in a glass of water. If a bubble starts out at the bottom of the container at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a94a5528991784dff99f941113de9fe2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/>, it contains water vapor (about 2.30%). The pressure inside the bubble is fixed at 1.00 atm (we ignore the slight pressure exerted by the water around it). As the temperature rises, the amount of air in the bubble stays the same, but the water vapor increases; the bubble expands to keep the pressure at 1.00 atm. At <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a6eb54fe6e37f18e8cbc8357c49dad21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"38\" style=\"vertical-align: -1px;\" \/>, water vapor enters the bubble continuously since the partial pressure of water is equal to 1.00 atm in equilibrium. It cannot reach this pressure, however, since the bubble also contains air and total pressure is 1.00 atm. The bubble grows in size and thereby increases the buoyant force. The bubble breaks away and rises rapidly to the surface\u2014we call this boiling! (See <a href=\"#import-auto-id1168465549482\" class=\"autogenerated-content\">(Figure)<\/a>.)<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id1168465549482\">\n<div class=\"bc-figcaption figcaption\">(a) An air bubble in water starts out saturated with water vapor at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a94a5528991784dff99f941113de9fe2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/>. (b) As the temperature rises, water vapor enters the bubble because its vapor pressure increases. The bubble expands to keep its pressure at 1.00 atm. (c) At <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a6eb54fe6e37f18e8cbc8357c49dad21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"38\" style=\"vertical-align: -1px;\" \/>, water vapor enters the bubble continuously because water\u2019s vapor pressure exceeds its partial pressure in the bubble, which must be less than 1.00 atm. The bubble grows and rises to the surface.\n      <\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1168465458434\" data-alt=\"A beaker of water being heated over a flame. The beaker is shown at three different times. In the first, at twenty degrees C, a small bubble sits on the bottom of the beaker. In the second step, the water temperature is fifty degrees C and the bubble is larger, though still sitting on the bottom of the beaker. In the third step, the water temperature is one hundred degrees C. The bubble is larger and is rising toward the surface.\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/graphics4-3.jpg\" data-media-type=\"image\/jpg\" alt=\"A beaker of water being heated over a flame. The beaker is shown at three different times. In the first, at twenty degrees C, a small bubble sits on the bottom of the beaker. In the second step, the water temperature is fifty degrees C and the bubble is larger, though still sitting on the bottom of the beaker. In the third step, the water temperature is one hundred degrees C. The bubble is larger and is rising toward the surface.\" height=\"212\" width=\"250\" \/><\/span><\/p>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2722050\" data-element-type=\"check-understanding\" data-label=\"\">\n<div data-type=\"title\">Check Your Understanding<\/div>\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1830235\">\n<p id=\"import-auto-id1168465464207\">Freeze drying is a process in which substances, such as foods, are dried by placing them in a vacuum chamber and lowering the atmospheric pressure around them. How does the lowered atmospheric pressure speed the drying process, and why does it cause the temperature of the food to drop?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2258999\">\n<p id=\"import-auto-id1168465464214\">Decreased the atmospheric pressure results in decreased partial pressure of water, hence a lower humidity. So evaporation of water from food, for example, will be enhanced. The molecules of water most likely to break away from the food will be those with the greatest velocities. Those remaining thus have a lower average velocity and a lower temperature. This can (and does) result in the freezing and drying of the food; hence the process is aptly named freeze drying.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" id=\"fs-id2104921\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">PhET Explorations: States of Matter<\/div>\n<p id=\"import-auto-id1168465538008\">Watch different types of molecules form a solid, liquid, or gas. Add or remove heat and watch the phase change. Change the temperature or volume of a container and see a pressure-temperature diagram respond in real time. Relate the interaction potential to the forces between molecules. <\/p>\n<div class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\"><a href=\"http:\/\/phet.colorado.edu\/en\/simulation\/states-of-matter\">States of Matter: Basics<\/a><\/div>\n<p><span data-type=\"media\" data-alt=\"\"><a href=\"\/resources\/52e49aa5d0d2bc0e4dc7726deafbd4e9ff1c66f4\/states-of-matter-basics_en.jar\" data-type=\"image\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/PhET_Icon.png\" data-media-type=\"image\/png\" alt=\"\" data-print=\"false\" width=\"450\" \/><\/a><span data-media-type=\"image\/png\" data-print=\"true\" data-src=\"\/resources\/075500ad9f71890a85fe3f7a4137ac08e2b7907c\/PhET_Icon.png\" data-type=\"image\"><\/span><\/span><\/p>\n<\/div>\n<\/div>\n<div class=\"section-summary\" data-depth=\"1\" id=\"fs-id1530186\">\n<h1 data-type=\"title\">Section Summary<\/h1>\n<ul id=\"fs-id1698455\">\n<li id=\"import-auto-id1168465538186\">Relative humidity is the fraction of water vapor in a gas compared to the saturation value.<\/li>\n<li id=\"import-auto-id1168465538190\">The saturation vapor density can be determined from the vapor pressure for a given temperature.<\/li>\n<li id=\"import-auto-id1168465538193\">Percent relative humidity is defined to be\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id1168465538195\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-00e301ac58aaddcf612597cba59c959d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#101;&#114;&#99;&#101;&#110;&#116;&#32;&#114;&#101;&#108;&#97;&#116;&#105;&#118;&#101;&#32;&#104;&#117;&#109;&#105;&#100;&#105;&#116;&#121;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#118;&#97;&#112;&#111;&#114;&#32;&#100;&#101;&#110;&#115;&#105;&#116;&#121;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#97;&#116;&#117;&#114;&#97;&#116;&#105;&#111;&#110;&#32;&#118;&#97;&#112;&#111;&#114;&#32;&#100;&#101;&#110;&#115;&#105;&#116;&#121;&#125;&#125;&times;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"401\" style=\"vertical-align: -9px;\" \/><\/div>\n<\/li>\n<li id=\"import-auto-id1168465551772\">The dew point is the temperature at which air reaches 100% relative humidity.<\/li>\n<\/ul>\n<\/div>\n<div class=\"conceptual-questions\" data-depth=\"1\" id=\"fs-id1907369\" data-element-type=\"conceptual-questions\">\n<h1 data-type=\"title\">Conceptual Questions<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1439139\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1614758\">\n<p id=\"import-auto-id1168465550503\">Because humidity depends only on water\u2019s vapor pressure and temperature, are the saturation vapor densities listed in <a href=\"#import-auto-id1591575\" class=\"autogenerated-content\">(Figure)<\/a> valid in an atmosphere of helium at a pressure of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-65bd6beaa08295a9cea0d8a7fad6ad59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#49;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#53;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#47;&#109;&#125;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"104\" style=\"vertical-align: -4px;\" \/>, rather than air? Are those values affected by altitude on Earth?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1438869\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2322601\">\n<p id=\"import-auto-id1168465460029\">Why does a beaker of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-d1bd430b787b9aebec8d1e1ca6fcc6ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"44\" style=\"vertical-align: -1px;\" \/> water placed in a vacuum chamber start to boil as the chamber is evacuated (air is pumped out of the chamber)? At what pressure does the boiling begin? Would food cook any faster in such a beaker? <\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1854910\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1746204\">\n<p id=\"import-auto-id2184131\">Why does rubbing alcohol evaporate much more rapidly than water at STP (standard temperature and pressure)? <\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"problems-exercises\" data-depth=\"1\" id=\"fs-id1604734\" data-element-type=\"problems-exercises\">\n<h1 data-type=\"title\">Problems &amp; Exercises<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1893897\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1695017\">\n<p id=\"import-auto-id2938875\">Dry air is 78.1% nitrogen. What is the partial pressure of nitrogen when the atmospheric pressure is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-65bd6beaa08295a9cea0d8a7fad6ad59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#49;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#53;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#47;&#109;&#125;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"104\" style=\"vertical-align: -4px;\" \/>?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2249777\">\n<p id=\"eip-id3199847\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-d83c2b9f6150e7289559d817f32d11ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#56;&#57;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1423931\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1697977\">\n<p id=\"import-auto-id1168465440225\">(a) What is the vapor pressure of water at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f205d73e3e16a867ce37b630c0c5cbaa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"44\" style=\"vertical-align: 0px;\" \/>? (b) What percentage of atmospheric pressure does this correspond to? (c) What percent of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f205d73e3e16a867ce37b630c0c5cbaa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"44\" style=\"vertical-align: 0px;\" \/> air is water vapor if it has 100% relative humidity? (The density of dry air at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f205d73e3e16a867ce37b630c0c5cbaa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"44\" style=\"vertical-align: 0px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-161d02594a91a34373f158c165b6a900_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#48;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#107;&#103;&#47;&#109;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"84\" style=\"vertical-align: -4px;\" \/>.) <\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2720918\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1611394\">\n<p id=\"import-auto-id1168465455761\">Pressure cookers increase cooking speed by raising the boiling temperature of water above its value at atmospheric pressure. (a) What pressure is necessary to raise the boiling point to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c20ee16b524322d1de8a65f02f05e7ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#50;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: -1px;\" \/>? (b) What gauge pressure does this correspond to?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1498210\">\n<p id=\"import-auto-id1168465426468\">(a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f8a04b864312545da5eb3d75c6ea79d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#57;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#53;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"81\" style=\"vertical-align: -1px;\" \/><\/p>\n<p id=\"import-auto-id1168465435245\">(b) 0.97 atm<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1423468\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1907426\">\n<p id=\"import-auto-id1168465426913\">(a) At what temperature does water boil at an altitude of 1500 m (about 5000 ft) on a day when atmospheric pressure is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-07815f8818a6d96f247c2e1629a565f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#57;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#47;&#109;&#125;&#125;&#94;&#123;&#50;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#63;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"114\" style=\"vertical-align: -4px;\" \/> (b) What about at an altitude of 3000 m (about 10,000 ft) when atmospheric pressure is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-2cd5def89110eccb4d757f51c735b63b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#48;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#47;&#109;&#125;&#125;&#94;&#123;&#50;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#63;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"114\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2385042\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3293921\">\n<p id=\"import-auto-id1168465459979\">What is the atmospheric pressure on top of Mt. Everest on a day when water boils there at a temperature of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-2eb34d27f8b2d23ff150e264c8dd04a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#55;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#63;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"53\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2563526\">\n<p id=\"eip-id1647917\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-b6582b4e43c3fa583ded4b19f29521c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#50;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1861214\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2716378\">\n<p id=\"import-auto-id1168465464181\">At a spot in the high Andes, water boils at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-612d26dcfc4b23256af0164dc40cf610_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#56;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"44\" style=\"vertical-align: 0px;\" \/>, greatly reducing the cooking speed of potatoes, for example. What is atmospheric pressure at this location? <\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2378107\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1391142\">\n<p id=\"import-auto-id1168465460156\">What is the relative humidity on a <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-cc820ae9a4e31f54215900ec9043cec0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#53;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"44\" style=\"vertical-align: 0px;\" \/> day when the air contains <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-16f869bf4c2d8fc0a86f0f5a3970f912_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#56;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#103;&#47;&#109;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"74\" style=\"vertical-align: -4px;\" \/> of water vapor?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2688458\">\n<p id=\"import-auto-id1868578\">78.3%<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1477204\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1490105\">\n<p id=\"import-auto-id1804618\">What is the density of water vapor in <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-44bfa3872a8db13fe83954e63fc27e2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#103;&#47;&#109;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"40\" style=\"vertical-align: -4px;\" \/> on a hot dry day in the desert when the temperature is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-d1bd430b787b9aebec8d1e1ca6fcc6ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"44\" style=\"vertical-align: -1px;\" \/> and the relative humidity is 6.00%?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2377418\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1462926\">\n<p id=\"import-auto-id1168465438267\">A deep-sea diver should breathe a gas mixture that has the same oxygen partial pressure as at sea level, where dry air contains 20.9% oxygen and has a total pressure of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-65bd6beaa08295a9cea0d8a7fad6ad59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#49;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#53;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#47;&#109;&#125;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"104\" style=\"vertical-align: -4px;\" \/>. (a) What is the partial pressure of oxygen at sea level? (b) If the diver breathes a gas mixture at a pressure of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a36f1675c30fd9b61afebeddeeaa0ec5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#48;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#54;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#47;&#109;&#125;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"105\" style=\"vertical-align: -4px;\" \/>, what percent oxygen should it be to have the same oxygen partial pressure as at sea level?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1861296\">\n<p id=\"import-auto-id1168465458014\">(a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-6665c556debde7753bcd3a6c3bb8eb4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#50;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -1px;\" \/><\/p>\n<p id=\"import-auto-id1168465438322\">(b) <\/p>\n<pre class=\"ql-errors\">*** QuickLaTeX cannot compile formula:\n&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#54;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#37;&#125;\n\n*** Error message:\n&#70;&#105;&#108;&#101;&#32;&#101;&#110;&#100;&#101;&#100;&#32;&#119;&#104;&#105;&#108;&#101;&#32;&#115;&#99;&#97;&#110;&#110;&#105;&#110;&#103;&#32;&#117;&#115;&#101;&#32;&#111;&#102;&#32;&#92;&#116;&#101;&#120;&#116;&#64;&#46;\r\n&#69;&#109;&#101;&#114;&#103;&#101;&#110;&#99;&#121;&#32;&#115;&#116;&#111;&#112;&#46;\r\n\n<\/pre>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2206267\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1527017\">\n<p id=\"import-auto-id1168465548459\">The vapor pressure of water at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-d1bd430b787b9aebec8d1e1ca6fcc6ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"44\" style=\"vertical-align: -1px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a14d81fa7b2b36732044e627e9bc0c5d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#52;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#47;&#109;&#125;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"105\" style=\"vertical-align: -4px;\" \/>. Using the ideal gas law, calculate the density of water vapor in <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-44bfa3872a8db13fe83954e63fc27e2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#103;&#47;&#109;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"40\" style=\"vertical-align: -4px;\" \/> that creates a partial pressure equal to this vapor pressure. The result should be the same as the saturation vapor density at that temperature <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-b0bdd53dfd16300f707542373f56b81d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#49;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#32;&#103;&#47;&#109;&#125;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"103\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2094936\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2699756\">\n<p id=\"import-auto-id1168465550332\">Air in human lungs has a temperature of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-2f0ca0115a551bff9b106b13d0f34072_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#55;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"44\" style=\"vertical-align: 0px;\" \/> and a saturation vapor density of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-6b7499fe4d1625f7262714b5508bf3ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#52;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#32;&#103;&#47;&#109;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"77\" style=\"vertical-align: -4px;\" \/>. (a) If 2.00 L of air is exhaled and very dry air inhaled, what is the maximum loss of water vapor by the person? (b) Calculate the partial pressure of water vapor having this density, and compare it with the vapor pressure of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a4980b0b81a1ec2302d925194d42ea81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#49;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#47;&#109;&#125;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"105\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1443552\">\n<p id=\"import-auto-id1168465554249\">(a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-0fe39d870c226bb602e3865854673740_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#56;&#48;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#103;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"81\" style=\"vertical-align: -3px;\" \/><\/p>\n<p id=\"import-auto-id2383432\">(b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a4c1f20a387d9072744674172fdfb9c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#48;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -1px;\" \/>; the two values are nearly identical. <\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2635848\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2635851\">\n<p id=\"import-auto-id1168465551440\">If the relative humidity is 90.0% on a muggy summer morning when the temperature is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f205d73e3e16a867ce37b630c0c5cbaa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"44\" style=\"vertical-align: 0px;\" \/>, what will it be later in the day when the temperature is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-28f5822f61c78db32fce1c289e6478f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"44\" style=\"vertical-align: 0px;\" \/>, assuming the water vapor density remains constant? <\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2599998\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1470438\">\n<p id=\"import-auto-id1168465435123\">Late on an autumn day, the relative humidity is 45.0% and the temperature is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f205d73e3e16a867ce37b630c0c5cbaa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"44\" style=\"vertical-align: 0px;\" \/>. What will the relative humidity be that evening when the temperature has dropped to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b3e9b994189112ed7be4890b58b10b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"43\" style=\"vertical-align: -1px;\" \/>, assuming constant water vapor density?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1600891\">\n<p id=\"import-auto-id1168465551043\">82.3%<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2085047\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2721954\">\n<p id=\"import-auto-id1168465551065\">Atmospheric pressure atop Mt. Everest is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-b9037320f8bd5b5ce57c685d7353e4d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#48;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#47;&#109;&#125;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"105\" style=\"vertical-align: -4px;\" \/>. (a) What is the partial pressure of oxygen there if it is 20.9% of the air? (b) What percent oxygen should a mountain climber breathe so that its partial pressure is the same as at sea level, where atmospheric pressure is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-62c50e6df0c512b4281cd239d8bfc92e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#49;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#53;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#47;&#109;&#125;&#125;&#94;&#123;&#50;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#63;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"113\" style=\"vertical-align: -4px;\" \/> (c) One of the most severe problems for those climbing very high mountains is the extreme drying of breathing passages. Why does this drying occur? <\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1509093\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1509095\">\n<p id=\"import-auto-id1168465538126\">What is the dew point (the temperature at which 100% relative humidity would occur) on a day when relative humidity is 39.0% at a temperature of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f205d73e3e16a867ce37b630c0c5cbaa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"44\" style=\"vertical-align: 0px;\" \/>?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1412837\">\n<p id=\"eip-id3222544\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-0b7692f2a4742855b813d288256f8c2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#55;&#55;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"44\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1806668\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1806670\">\n<p id=\"import-auto-id1168465478336\">On a certain day, the temperature is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-cc820ae9a4e31f54215900ec9043cec0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#53;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"44\" style=\"vertical-align: 0px;\" \/> and the relative humidity is 90.0%. How many grams of water must condense out of each cubic meter of air if the temperature falls to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ab6be6afee2a2d296697701ebdda3795_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#53;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"43\" style=\"vertical-align: -1px;\" \/>? Such a drop in temperature can, thus, produce heavy dew or fog. <\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2386969\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1615107\">\n<p id=\"import-auto-id1168465553959\"><strong>Integrated Concepts<\/strong><\/p>\n<p id=\"eip-id2396285\">The boiling point of water increases with depth because pressure increases with depth. At what depth will fresh water have a boiling point of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-86204cb340780040438d7e1578e7811b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#53;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"38\" style=\"vertical-align: -1px;\" \/>, if the surface of the water is at sea level?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1856385\">\n<p id=\"eip-id3422225\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-44aa9430ec58d30045d3fd3cdabbd450_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#56;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2298434\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2298436\">\n<p id=\"import-auto-id1168465552564\"><strong>Integrated Concepts<\/strong><\/p>\n<p id=\"import-auto-id1168465552566\">(a) At what depth in fresh water is the critical pressure of water reached, given that the surface is at sea level? (b) At what temperature will this water boil? (c) Is a significantly higher temperature needed to boil water at a greater depth? <\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1543836\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2193148\">\n<p id=\"import-auto-id1168465552576\"><strong>Integrated Concepts<\/strong><\/p>\n<p id=\"import-auto-id1168465552578\">To get an idea of the small effect that temperature has on Archimedes\u2019 principle, calculate the fraction of a copper block\u2019s weight that is supported by the buoyant force in <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-7eb23a0f0414aab9de988c35ceebe163_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/> water and compare this fraction with the fraction supported in <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-69b00323eeadbcb40ce948655178f47d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#53;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"44\" style=\"vertical-align: 0px;\" \/> water.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1830450\">\n<p id=\"import-auto-id1168465552620\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-765aaeb369f3e7a2d254afa098af03a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#70;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#66;&#125;&#125;&#47;&#123;&#119;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#117;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#70;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#66;&#125;&#125;&#47;&#123;&#119;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#117;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#92;&#112;&#114;&#105;&#109;&#101;&#32;&#125;&#125;&#61;&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"31\" width=\"122\" style=\"vertical-align: -11px;\" \/>. The buoyant force supports nearly the exact same amount of force on the copper block in both circumstances.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2688861\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1487389\">\n<p id=\"import-auto-id1168465451621\"><strong>Integrated Concepts<\/strong><\/p>\n<p id=\"import-auto-id1168465451604\">If you want to cook in water at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-86204cb340780040438d7e1578e7811b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#53;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"38\" style=\"vertical-align: -1px;\" \/>, you need a pressure cooker that can withstand the necessary pressure. (a) What pressure is required for the boiling point of water to be this high? (b) If the lid of the pressure cooker is a disk 25.0 cm in diameter, what force must it be able to withstand at this pressure? <\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1582923\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2694568\">\n<p id=\"import-auto-id1168465551397\"><strong>Unreasonable Results<\/strong><\/p>\n<p id=\"eip-id2215990\">(a) How many moles per cubic meter of an ideal gas are there at a pressure of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-fef51a10a8dba725b036f0658f2daca6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#48;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#52;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#47;&#109;&#125;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"111\" style=\"vertical-align: -4px;\" \/> and at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-7eb23a0f0414aab9de988c35ceebe163_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/>? (b) What is unreasonable about this result? (c) Which premise or assumption is responsible?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2304325\">\n<p id=\"import-auto-id1168465550196\">(a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-fb6727d17e40074c6cf0d8d598617698_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#49;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#111;&#108;&#47;&#109;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"127\" style=\"vertical-align: -4px;\" \/><\/p>\n<p id=\"import-auto-id1168465550230\">(b) It\u2019s unreasonably large.<\/p>\n<p id=\"import-auto-id1168465550239\">(c) At high pressures such as these, the ideal gas law can no longer be applied. As a result, unreasonable answers come up when it is used.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1669904\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1669906\">\n<p id=\"eip-id2076330\"><strong>Unreasonable Results<\/strong><\/p>\n<p id=\"import-auto-id1168465550238\"> (a) An automobile mechanic claims that an aluminum rod fits loosely into its hole on an aluminum engine block because the engine is hot and the rod is cold. If the hole is 10.0% bigger in diameter than the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-5011c524f8c892662f233459dcc9322c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#50;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"44\" style=\"vertical-align: 0px;\" \/> rod, at what temperature will the rod be the same size as the hole? (b) What is unreasonable about this temperature? (c) Which premise is responsible? <\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2705483\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1513742\">\n<p id=\"import-auto-id1168465552259\"><strong>Unreasonable Results<\/strong><\/p>\n<p id=\"import-auto-id1168465552262\">The temperature inside a supernova explosion is said to be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a90b84fd5bd143968577777173b01f24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#48;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#51;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#75;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -1px;\" \/>. (a) What would the average velocity <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-457599ab17c21c27d86746a542c7f8c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#118;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#109;&#115;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: -4px;\" \/> of hydrogen atoms be? (b) What is unreasonable about this velocity? (c) Which premise or assumption is responsible?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2258269\">\n<p id=\"import-auto-id1168465426342\">(a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-445dd2504d216ab310cac63ef33297f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#51;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#56;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#47;&#115;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"92\" style=\"vertical-align: -4px;\" \/><\/p>\n<p id=\"import-auto-id1168465426389\">(b) The velocity is too high\u2014it\u2019s greater than the speed of light.<\/p>\n<p id=\"import-auto-id1168465426391\">(c) The assumption that hydrogen inside a supernova behaves as an idea gas is responsible, because of the great temperature and density in the core of a star. Furthermore, when a velocity greater than the speed of light is obtained, classical physics must be replaced by relativity, a subject not yet covered.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1689262\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1689263\">\n<p id=\"import-auto-id1168465426400\"><strong>Unreasonable Results<\/strong><\/p>\n<p id=\"import-auto-id1168465426403\">Suppose the relative humidity is 80% on a day when the temperature is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-28f5822f61c78db32fce1c289e6478f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"44\" style=\"vertical-align: 0px;\" \/>. (a) What will the relative humidity be if the air cools to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-cc820ae9a4e31f54215900ec9043cec0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#53;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"44\" style=\"vertical-align: 0px;\" \/> and the vapor density remains constant? (b) What is unreasonable about this result? (c) Which premise is responsible? <\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"glossary\" class=\"textbox shaded\">\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl class=\"definition\" id=\"import-auto-id1168465548876\">\n<dt>dew point<\/dt>\n<dd id=\"fs-id1746250\">the temperature at which relative humidity is 100%; the temperature at which water starts to condense out of the air<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id1168465548880\">\n<dt>saturation<\/dt>\n<dd id=\"fs-id1847032\">the condition of 100% relative humidity<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id1168465548882\">\n<dt>percent relative humidity<\/dt>\n<dd id=\"fs-id1688807\">the ratio of vapor density to saturation vapor density <\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id1168465548885\">\n<dt>relative humidity<\/dt>\n<dd id=\"fs-id1803443\">the amount of water in the air relative to the maximum amount the air can hold<\/dd>\n<\/dl>\n<\/div>\n","protected":false},"author":211,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"all-rights-reserved"},"chapter-type":[],"contributor":[],"license":[56],"class_list":["post-714","chapter","type-chapter","status-publish","hentry","license-all-rights-reserved"],"part":669,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/714","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/users\/211"}],"version-history":[{"count":1,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/714\/revisions"}],"predecessor-version":[{"id":715,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/714\/revisions\/715"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/parts\/669"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/714\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/media?parent=714"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapter-type?post=714"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/contributor?post=714"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/license?post=714"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}