{"id":1007,"date":"2020-11-08T20:31:03","date_gmt":"2020-11-09T01:31:03","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/douglasphys1108\/?post_type=chapter&p=1007"},"modified":"2020-11-11T00:34:33","modified_gmt":"2020-11-11T05:34:33","slug":"1-temperature","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/douglasphys1108\/chapter\/1-temperature\/","title":{"raw":"1 Temperature","rendered":"1 Temperature"},"content":{"raw":"The concept of temperature has evolved from the common concepts of hot and cold. Human perception of what feels hot or cold is a relative one. For example, if you place one hand in hot water and the other in cold water, and then place both hands in tepid water, the tepid water will feel cool to the hand that was in hot water, and warm to the one that was in cold water. The scientific definition of temperature is less ambiguous than your senses of hot and cold.\u00a0Temperature<\/span>\u00a0is operationally defined to be what we measure with a thermometer.\u00a0(Many physical quantities are defined solely in terms of how they are measured. We shall see later how temperature is related to the kinetic energies of atoms and molecules, a more physical explanation.) Two accurate thermometers, one placed in hot water and the other in cold water, will show the hot water to have a higher temperature. If they are then placed in the tepid water, both will give identical readings (within measurement uncertainties). In this section, we discuss temperature, its measurement by thermometers, and its relationship to thermal equilibrium. Again, temperature is the quantity measured by a thermometer.\r\n\r\n \r\n
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MISCONCEPTION ALERT: HUMAN PERCEPTION VS. REALITY<\/span><\/h3>\r\n<\/header>
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On a cold winter morning, the wood on a porch feels warmer than the metal of your bike. The wood and bicycle are in thermal equilibrium with the outside air, and are thus the same temperature. They\u00a0feel<\/em>\u00a0different because of the difference in the way that they conduct heat away from your skin. The metal conducts heat away from your body faster than the wood does (see more about conductivity in\u00a0Conduction<\/a>). This is just one example demonstrating that the human sense of hot and cold is not determined by temperature alone.<\/p>\r\n

Another factor that affects our perception of temperature is humidity. Most people feel much hotter on hot, humid days than on hot, dry days. This is because on humid days, sweat does not evaporate from the skin as efficiently as it does on dry days. It is the evaporation of sweat (or water from a sprinkler or pool) that cools us off.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

Any physical property that depends on temperature, and whose response to temperature is reproducible, can be used as the basis of a thermometer. Because many physical properties depend on temperature, the variety of thermometers is remarkable. For example, volume increases with temperature for most substances. This property is the basis for the common alcohol thermometer, the old mercury thermometer, and the bimetallic strip (Figure 13.3<\/a>). Other properties used to measure temperature include electrical resistance and color, as shown in\u00a0Figure 13.4<\/a>, and the emission of infrared radiation, as shown in\u00a0Figure 13.5<\/a>.<\/p>\r\n\r\n

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\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"150\"]\"This The curvature of a bimetallic strip depends on temperature. (a) The strip is straight at the starting temperature, where its two components have the same length. (b) At a higher temperature, this strip bends to the right, because the metal on the left has expanded more than the metal on the right.[\/caption]<\/figure>\r\n
\u00a0<\/span><\/div>\r\n<\/div>\r\n
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\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"250\"]\"A Each of the six squares on this plastic (liquid crystal) thermometer contains a film of a different heat-sensitive liquid crystal material. Below\u00a095\u00baF all six squares are black. When the plastic thermometer is exposed to temperature that increases to 95\u00ba, the first liquid crystal square changes colour. When the temperature increases above 96.8\u00b0F, the second liquid crystal square also changes colour, and so forth. (credit: Arkrishna, Wikimedia Commons)[\/caption]<\/figure>\r\n
\r\n\r\n \r\n\r\n<\/div>\r\n<\/div>\r\n
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\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"175\"]\"A Fireman Jason Ormand uses a pyrometer to check the temperature of an aircraft carrier\u2019s ventilation system[\/caption]<\/figure>\r\n
Infrared radiation (whose emission varies with temperature) from the vent is measured and a temperature readout is quickly produced. Infrared measurements are also frequently used as a measure of body temperature. These modern thermometers, placed in the ear canal, are more accurate than alcohol thermometers placed under the tongue or in the armpit. (credit: Lamel J. Hinton\/U.S. Navy)<\/span><\/div>\r\n<\/div>\r\n
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Temperature Scales<\/h3>\r\n

Thermometers are used to measure temperature according to well-defined scales of measurement, which use pre-defined reference points to help compare quantities. The three most common temperature scales are the Fahrenheit, Celsius, and Kelvin scales. A temperature scale can be created by identifying two easily reproducible temperatures. The freezing and boiling temperatures of water at standard atmospheric pressure are commonly used.<\/p>\r\n

The\u00a0Celsius<\/span>\u00a0scale (which replaced the slightly different\u00a0centigrade<\/em> scale) has the freezing point of water at 0 \u00b0C and the boiling point at 100 \u00b0C.\u00a0Its unit is the degree Celsius (\u00b0C)<\/span>\u00a0On the\u00a0Fahrenheit<\/span> scale (still the most frequently used in the United States), the freezing point of water is at 32 \u00b0F and the boiling point is at 212 \u00b0F. \u00a0The unit of temperature on this scale is the degree Fahrenheit (\u00b0F). <\/span>Note that a temperature difference of one degree Celsius is greater than a temperature difference of one degree Fahrenheit. Only 100 Celsius degrees span the same range as 180 Fahrenheit degrees, thus one degree on the Celsius scale is 1.8 times larger than one degree on the Fahrenheit scale 180\/100 = 9\/5.<\/p>\r\n

The Kelvin<\/span>\u00a0scale is the temperature scale that is commonly used in science. It is an\u00a0absolute temperature<\/em>\u00a0scale defined to have 0 K at the lowest possible temperature, called\u00a0absolute zero<\/span>. The official temperature unit on this scale is the\u00a0kelvin<\/em>, which is abbreviated K, and is not accompanied by a degree sign. The freezing and boiling points of water are 273.15 K and 373.15 K, respectively. Thus, the magnitude of temperature differences is the same in units of kelvins and degrees Celsius. Unlike other temperature scales, the Kelvin scale is an absolute scale. It is used extensively in scientific work because a number of physical quantities, such as the volume of an ideal gas, are directly related to absolute temperature. The kelvin is the SI unit used in scientific work.<\/p>\r\n\r\n

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\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"425\"]\"Three Relationships between the Fahrenheit, Celsius, and Kelvin temperature scales, rounded to the nearest degree. The relative sizes of the scales are also shown.[\/caption]<\/figure>\r\n
The relationships between the three common temperature scales is shown in the figure above.\u00a0 Temperatures on these scales can be converted using the equations in <\/span>Table 13.1<\/a>.<\/span><\/div>\r\n<\/div>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
To convert from . . .<\/th>\r\nUse this equation . . .<\/th>\r\n<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
Celsius to Fahrenheit<\/td>\r\n\r\n
\r\n\r\n\ud835\udc47<\/span>(<\/span>\u00ba<\/span>F<\/span><\/span>) <\/span><\/span>= <\/span>9\/<\/span>5 <\/span><\/span><\/span>\ud835\udc47<\/span>(<\/span>\u00ba<\/span>C<\/span><\/span>)<\/span><\/span>\u00a0 + <\/span>32<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\r\n\r\n \r\n\r\n<\/div><\/td>\r\n
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\r\n\r\n \r\n\r\n \r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n
Fahrenheit to Celsius<\/td>\r\n\r\n
\r\n\r\n\ud835\udc47<\/span>(<\/span>\u00ba<\/span>C<\/span><\/span>)<\/span><\/span>= <\/span>5\/<\/span>9 <\/span><\/span><\/span>(<\/span>\ud835\udc47<\/span>(<\/span>\u00ba<\/span>F <\/span><\/span>) <\/span><\/span>\u2212 <\/span>32<\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\r\n\r\n \r\n\r\n<\/div><\/td>\r\n
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<\/div><\/td>\r\n<\/tr>\r\n
Celsius to Kelvin<\/td>\r\n\r\n
\r\n\r\n\ud835\udc47<\/span>(<\/span>K<\/span>)<\/span><\/span>=<\/span>\ud835\udc47<\/span><\/span>(<\/span>\u00ba<\/span>C<\/span><\/span>) +<\/span><\/span>\u00a0<\/span>273<\/span><\/span>.<\/span>15<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\r\n\r\n \r\n\r\n<\/div><\/td>\r\n
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<\/div><\/td>\r\n<\/tr>\r\n
Kelvin to Celsius<\/td>\r\n\r\n
\r\n\r\n\ud835\udc47<\/span>(<\/span>\u00ba<\/span>C<\/span><\/span>)<\/span><\/span>=<\/span>\ud835\udc47<\/span><\/span>(<\/span>K<\/span>) <\/span><\/span>\u2212 <\/span>273<\/span><\/span>.<\/span>15<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\r\n\r\n \r\n\r\n<\/div><\/td>\r\n
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<\/div><\/td>\r\n<\/tr>\r\n
Fahrenheit to Kelvin<\/td>\r\n\r\n
\r\n\r\n T (K) = 5\/9 (T (\u00b0F) - 32 ) + 273.15<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\r\n\r\n \r\n\r\n<\/div><\/td>\r\n
<\/td>\r\n<\/tr>\r\n
Kelvin to Fahrenheit<\/td>\r\n\r\n
\r\n\r\nT (\u00b0F) = 9\/5 (T (K) - 273.15 ) + 32\r\n\r\n<\/div><\/td>\r\n
<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Table<\/span>13.1<\/span>\u00a0<\/span>Temperature Conversions<\/span><\/h2>\r\n<\/div>\r\nNotice that the conversions between Fahrenheit and Kelvin look quite complicated. In fact, they are simple combinations of the conversions between Fahrenheit and Celsius, and the conversions between Celsius and Kelvin.\r\n
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Example 13.1\u00a0 Converting between Temperature Scales: Room Temperature<\/p>\r\n\r\n<\/header>\r\n

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\u201cRoom temperature\u201d is generally defined to be\u00a025<\/span>\u00ba<\/span>C <\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\r\n(a) What is room temperature in \u00ba<\/span>F<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\r\n\r\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span>(b) What is it in K?\r\n

Strategy<\/p>\r\n

To answer these questions, all we need to do is choose the correct conversion equations and plug in the known values.<\/p>\r\n

Solution for (a)<\/p>\r\n

1. Choose the right equation. To convert from\u00a0\u00ba<\/span>C <\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>to \u00ba<\/span>F <\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, use the equation<\/span><\/p>\r\n

T \u00b0F = (9\/5) ( T \u00b0C) + 32<\/span><\/p>\r\n

2. Plug the known value into the equation and solve:<\/p>\r\n\r\n

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T \u00b0F = (9\/5) (25\u00b0C ) + 32 = 77 \u00b0F<\/span><\/p>\r\n\r\n<\/div>\r\n

<\/div>\r\n
\r\n\r\nSolution for (b)<\/span>\r\n\r\n<\/div>\r\n

1. Choose the right equation. To convert from\u00a0\u00ba<\/span>C <\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>to K, use the equation<\/p>\r\n

T K = T \u00b0C + 273.15<\/span><\/p>\r\n

2. Plug the known value into the equation and solve:<\/p>\r\n

T K = (25\u00b0C) + 273.15 = 298 K<\/span><\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<\/div>\r\n<\/div>\r\n \r\n\r\n<\/header><\/div>\r\n

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Temperature Ranges in the Universe<\/span><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n<\/section>
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Figure 13.8<\/a> shows the wide range of temperatures found in the universe. Human beings have been known to survive with body temperatures within a small range, from 24 \u00b0C to 44 \u00b0C ( 75-111 \u00b0F). The average normal body temperature is usually given as 37.0 \u00b0C or 98.6 \u00b0F, and variations in this temperature can indicate a medical condition: a fever, an infection, a tumour, or circulatory problems (see Figure 13.7<\/a>).<\/p>\r\n\r\n

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\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"268\"]\"This This image of radiation from a person\u2019s body (an infrared thermograph) shows the location of temperature abnormalities in the upper body. Dark blue corresponds to cold areas and red to white corresponds to hot areas. An elevated temperature might be an indication of malignant tissue (a cancerous tumour in the breast, for example), while a depressed temperature might be due to a decline in blood flow from a clot. In this case, the abnormalities are caused by a condition called hyperhidrosis. (credit: Porcelina81, Wikimedia Commons)[\/caption]<\/figure>\r\n
<\/div>\r\n<\/div>\r\n

The lowest temperatures ever recorded have been measured during laboratory experiments: 4.5 x 10-10<\/sup> K at the Massachusetts Institute of Technology (USA), and 1.0\u00a0x 10-10<\/sup> K\u00a0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>at Helsinki University of Technology (Finland). In comparison, the coldest recorded place on Earth\u2019s surface is Vostok, Antarctica at 183 K ( -89 \u00b0C)\u00a0and the coldest place (outside the lab) known in the universe is the Boomerang Nebula, with a temperature of 1 K.<\/p>\r\n\r\n

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\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"200\"]\"The Each increment on this logarithmic scale indicates an increase by a factor of ten, and thus illustrates the tremendous range of temperatures in nature. Note that zero on a logarithmic scale would occur off the bottom of the page at infinity.[\/caption]<\/figure>\r\n
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MAKING CONNECTIONS: ABSOLUTE ZERO<\/span><\/h3>\r\n<\/header>
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What is absolute zero? Absolute zero is the temperature at which all molecular motion has ceased. The concept of absolute zero arises from the behaviour of gases. Figure 13.9<\/a>\u00a0shows how the pressure of gases at a constant volume decreases as temperature decreases. Various scientists have noted that the pressures of gases extrapolate to zero at the same temperature,\u00a0\u2013<\/span>273<\/span>.<\/span>15<\/span>\u00ba<\/span>C <\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>This extrapolation implies that there is a lowest temperature. This temperature is called\u00a0absolute zero<\/em>. Today we know that most gases first liquefy and then freeze, and it is not actually possible to reach absolute zero. The numerical value of absolute zero temperature is\u00a0\u2013<\/span>273<\/span>.<\/span>15<\/span>\u00ba<\/span>C <\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>or 0 K.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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\"Line<\/span><\/figure>\r\n
Figure\u00a0<\/span>13.9<\/span>\u00a0<\/span>Graph of pressure versus temperature for various gases kept at a constant volume. Note that all of the graphs extrapolate to zero pressure at the same temperature.<\/span><\/div>\r\n<\/div>\r\n
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Thermal Equilibrium and the Zeroth Law of Thermodynamics<\/h4>\r\n

Thermometers actually take their\u00a0own<\/em>\u00a0temperature, not the temperature of the object they are measuring. This raises the question of how we can be certain that a thermometer measures the temperature of the object with which it is in contact. It is based on the fact that any two systems placed in\u00a0thermal contact<\/em>\u00a0(meaning heat transfer can occur between them) will reach the same temperature. That is, heat will flow from the hotter object to the cooler one until they have exactly the same temperature. The objects are then in\u00a0thermal equilibrium<\/span>, and no further changes will occur. The systems interact and change because their temperatures differ, and the changes stop once their temperatures are the same. Thus, if enough time is allowed for this transfer of heat to run its course, the temperature a thermometer registers\u00a0does<\/em>\u00a0represent the system with which it is in thermal equilibrium. Thermal equilibrium is established when two bodies are in contact with each other and can freely exchange energy.<\/p>\r\n

Furthermore, experimentation has shown that if two systems, A and B, are in thermal equilibrium with each another, and B is in thermal equilibrium with a third system C, then A is also in thermal equilibrium with C. This conclusion may seem obvious, because all three have the same temperature, but it is basic to thermodynamics. It is called the\u00a0zeroth law of thermodynamics<\/span>.<\/p>\r\n\r\n

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THE ZEROTH LAW OF THERMODYNAMICS<\/span><\/h3>\r\n<\/header>
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If two systems, A and B, are in thermal equilibrium with each other, and B is in thermal equilibrium with a third system, C, then A is also in thermal equilibrium with C.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

This law was postulated in the 1930s, after the first and second laws of thermodynamics had been developed and named. It is called the\u00a0zeroth law<\/em>\u00a0because it comes logically before the first and second laws (discussed in\u00a0Thermodynamics<\/a>). Suppose, for example, a cold metal block and a hot metal block are both placed on a metal plate at room temperature. Eventually the cold block and the plate will be in thermal equilibrium. In addition, the hot block and the plate will be in thermal equilibrium. By the zeroth law, we can conclude that the cold block and the hot block are also in thermal equilibrium.<\/p>\r\n\r\n

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Check Your Understanding<\/span><\/p>\r\n\r\n<\/header>\r\n

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Does the temperature of a body depend on its size?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/section><\/section>\r\n

Solution<\/span><\/p>\r\n\r\n

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No, the system can be divided into smaller parts each of which is at the same temperature. We say that the temperature is an\u00a0intensive<\/em> quantity. Intensive quantities are independent of size<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/section>

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Section Summary<\/h2>\r\n