{"id":614,"date":"2017-10-27T16:30:24","date_gmt":"2017-10-27T16:30:24","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/chapter\/cohesion-and-adhesion-in-liquids-surface-tension-and-capillary-action\/"},"modified":"2017-11-08T03:25:00","modified_gmt":"2017-11-08T03:25:00","slug":"cohesion-and-adhesion-in-liquids-surface-tension-and-capillary-action","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/chapter\/cohesion-and-adhesion-in-liquids-surface-tension-and-capillary-action\/","title":{"raw":"Cohesion and Adhesion in Liquids: Surface Tension and Capillary Action","rendered":"Cohesion and Adhesion in Liquids: Surface Tension and Capillary Action"},"content":{"raw":"\n<div class=\"textbox learning-objectives\">\n<h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>\n<ul>\n<li>Understand cohesive and adhesive forces.<\/li>\n<li>Define surface tension.<\/li>\n<li>Understand capillary action.<\/li>\n<\/ul>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id2406446\">\n<h1 data-type=\"title\">Cohesion and Adhesion in Liquids<\/h1>\n<p id=\"import-auto-id1574788\">Children blow soap bubbles and play in the spray of a sprinkler on a hot summer day. (See <a href=\"#import-auto-id2058131\" class=\"autogenerated-content\">(Figure)<\/a>.) An underwater spider keeps his air supply in a shiny bubble he carries wrapped around him. A technician draws blood into a small-diameter tube just by touching it to a drop on a pricked finger. A premature infant struggles to inflate her lungs. What is the common thread? All these activities are dominated by the attractive forces between atoms and molecules in liquids\u2014both within a liquid and between the liquid and its surroundings.<\/p>\n<p id=\"import-auto-id1344655\">Attractive forces between molecules of the same type are called <span data-type=\"term\">cohesive forces<\/span>. Liquids can, for example, be held in open containers because cohesive forces hold the molecules together. Attractive forces between molecules of different types are called <span data-type=\"term\" id=\"import-auto-id2949896\">adhesive forces<\/span>. Such forces cause liquid drops to cling to window panes, for example. In this section we examine effects directly attributable to cohesive and adhesive forces in liquids.<\/p>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" id=\"fs-id2391728\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">Cohesive Forces<\/div>\n<p id=\"import-auto-id1933298\">Attractive forces between molecules of the same type are called cohesive forces.<\/p>\n<\/div>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" id=\"fs-id2639833\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">Adhesive Forces<\/div>\n<p id=\"import-auto-id3177773\">Attractive forces between molecules of different types are called adhesive forces.<\/p>\n<\/div>\n<div class=\"bc-figure figure\" id=\"import-auto-id2058131\">\n<div class=\"bc-figcaption figcaption\">The soap bubbles in this photograph are caused by cohesive forces among molecules in liquids. (credit: Steve Ford Elliott)<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id2969220\" data-alt=\"The soap bubbles that the child blows into the air maintain their shape because of the attractive force between the molecules of the soap bubble.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_08_01a.jpg\" data-media-type=\"image\/png\" alt=\"The soap bubbles that the child blows into the air maintain their shape because of the attractive force between the molecules of the soap bubble.\" width=\"400\"><\/span><\/p><\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id3454572\">\n<h1 data-type=\"title\">Surface Tension<\/h1>\n<p id=\"import-auto-id2662953\">Cohesive forces between molecules cause the surface of a liquid to contract to the smallest possible surface area. This general effect is called <span data-type=\"term\" id=\"import-auto-id1011283\">surface tension<\/span>. Molecules on the surface are pulled inward by cohesive forces, reducing the surface area. Molecules inside the liquid experience zero net force, since they have neighbors on all sides.<\/p>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" id=\"fs-id2062954\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">Surface Tension<\/div>\n<p id=\"import-auto-id1471706\">Cohesive forces between molecules cause the surface of a liquid to contract to the smallest possible surface area. This general effect is called surface tension.<\/p>\n<\/div>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" id=\"fs-id3250489\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">Making Connections: Surface Tension<\/div>\n<p id=\"import-auto-id2661790\">Forces between atoms and molecules underlie the macroscopic effect called surface tension. These attractive forces pull the molecules closer together and tend to minimize the surface area. This is another example of a submicroscopic explanation for a macroscopic phenomenon.<\/p>\n<\/div>\n<p id=\"import-auto-id3094705\">The model of a liquid surface acting like a stretched elastic sheet can effectively explain surface tension effects. For example, some insects can walk on water (as opposed to floating in it) as we would walk on a trampoline\u2014they dent the surface as shown in <a href=\"#import-auto-id2970796\" class=\"autogenerated-content\">(Figure)<\/a>(a). <a href=\"#import-auto-id2970796\" class=\"autogenerated-content\">(Figure)<\/a>(b) shows another example, where a needle rests on a water surface. The iron needle cannot, and does not, float, because its density is greater than that of water. Rather, its weight is supported by forces in the stretched surface that try to make the surface smaller or flatter. If the needle were placed point down on the surface, its weight acting on a smaller area would break the surface, and it would sink.<\/p>\n<p id=\"import-auto-id2000364\">\n<\/p><div class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">Surface tension supporting the weight of an insect and an iron needle, both of which rest on the surface without penetrating it. They are not floating; rather, they are supported by the surface of the liquid. (a) An insect leg dents the water surface. [latex]{F}_{\\text{ST}}[\/latex] is a restoring force (surface tension) parallel to the surface. (b) An iron needle similarly dents a water surface until the restoring force (surface tension) grows to equal its weight.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id2391711\" data-alt=\"A leg of an insect resting on the water surface is shown in the first figure. In the second figure an iron needle rests on the surface of water without sinking. Both are possible due to the tension on the surface of the liquid.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_08_03a.jpg\" data-media-type=\"image\/jpg\" alt=\"A leg of an insect resting on the water surface is shown in the first figure. In the second figure an iron needle rests on the surface of water without sinking. Both are possible due to the tension on the surface of the liquid.\" width=\"475\"><\/span><\/p><\/div>\n<p id=\"import-auto-id1935393\">Surface tension is proportional to the strength of the cohesive force, which varies with the type of liquid. Surface tension [latex]\\gamma [\/latex] is defined to be the force <em data-effect=\"italics\">F<\/em> per unit length [latex]L[\/latex] exerted by a stretched liquid membrane:<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-170\">[latex]\\gamma =\\frac{F}{L}.[\/latex]<\/div>\n<p id=\"import-auto-id1864125\"><a href=\"#import-auto-id1816998\" class=\"autogenerated-content\">(Figure)<\/a> lists values of [latex]\\gamma [\/latex] for some liquids. For the insect of <a href=\"#import-auto-id2970796\" class=\"autogenerated-content\">(Figure)<\/a>(a), its weight [latex]w[\/latex] is supported by the upward components of the surface tension force: [latex]w=\\mathrm{\\gamma L}\\phantom{\\rule{0.25em}{0ex}}\\text{sin}\\phantom{\\rule{0.25em}{0ex}}\\theta [\/latex], where [latex]L[\/latex] is the circumference of the insect\u2019s foot in contact with the water. <a href=\"#import-auto-id3306680\" class=\"autogenerated-content\">(Figure)<\/a> shows one way to measure surface tension. The liquid film exerts a force on the movable wire in an attempt to reduce its surface area. The magnitude of this force depends on the surface tension of the liquid and can be measured accurately.<\/p>\n<p id=\"import-auto-id3399108\">Surface tension is the reason why liquids form bubbles and droplets. The inward surface tension force causes bubbles to be approximately spherical and raises the pressure of the gas trapped inside relative to atmospheric pressure outside. It can be shown that the gauge pressure [latex]P[\/latex]    inside a spherical bubble is given by<\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]P=\\frac{4\\gamma }{r},[\/latex]<\/div>\n<p id=\"import-auto-id3013426\">where [latex]r[\/latex] is the radius of the bubble. Thus the pressure inside a bubble is greatest when the bubble is the smallest. Another bit of evidence for this is illustrated in <a href=\"#import-auto-id2054965\" class=\"autogenerated-content\">(Figure)<\/a>. When air is allowed to flow between two balloons of unequal size, the smaller balloon tends to collapse, filling the larger balloon.<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id3306680\">\n<div class=\"bc-figcaption figcaption\">Sliding wire device used for measuring surface tension; the device exerts a force to reduce the film\u2019s surface area. The force needed to hold the wire in place is [latex]F=\\mathrm{\\gamma L}=\\gamma \\left(2l\\right)[\/latex], since there are <em data-effect=\"italics\">two<\/em> liquid surfaces attached to the wire. This force remains nearly constant as the film is stretched, until the film approaches its breaking point.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id2448669\" data-alt=\"Sliding wire device which is used to measure surface tension shows the force exerted on the two surfaces of the liquid. This force remains a constant until the film\u2019s breaking point.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_08_04a.jpg\" data-media-type=\"image\/jpg\" alt=\"Sliding wire device which is used to measure surface tension shows the force exerted on the two surfaces of the liquid. This force remains a constant until the film\u2019s breaking point.\" width=\"250\"><\/span><\/p><\/div>\n<div class=\"bc-figure figure\" id=\"import-auto-id2054965\">\n<div class=\"bc-figcaption figcaption\">With the valve closed, two balloons of different sizes are attached to each end of a tube. Upon opening the valve, the smaller balloon decreases in size with the air moving to fill the larger balloon. The pressure in a spherical balloon is inversely proportional to its radius, so that the smaller balloon has a greater internal pressure than the larger balloon, resulting in this flow.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id3184818\" data-alt=\"When two balloons are attached to the ends of a glass tube air flows from one to the other if their sizes are different.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_08_05a.jpg\" data-media-type=\"image\/png\" alt=\"When two balloons are attached to the ends of a glass tube air flows from one to the other if their sizes are different.\" width=\"400\"><\/span><\/p><\/div>\n<table id=\"import-auto-id1816998\" summary=\"The table gives the surface tension of water at zero, twenty, and one hundred degrees Celsius. The surface tension of some other liquids at twenty degrees Celsius is also given.\">\n<caption><span data-type=\"title\">Surface Tension of Some Liquids<a data-type=\"footnote-number\" href=\"#footnote1\"><sup>1<\/sup><\/a><\/span><\/caption>\n<thead>\n<tr>\n<th>\n              Liquid\n            <\/th>\n<th>\n              Surface tension \u03b3(N\/m)\n            <\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Water at [latex]0\\text{\u00ba}\\text{C}[\/latex]<\/td>\n<td>0.0756<\/td>\n<\/tr>\n<tr>\n<td>Water at [latex]\\text{20}\\text{\u00ba}\\text{C}[\/latex]<\/td>\n<td>0.0728<\/td>\n<\/tr>\n<tr>\n<td>Water at [latex]\\text{100}\\text{\u00ba}\\text{C}[\/latex]<\/td>\n<td>0.0589<\/td>\n<\/tr>\n<tr>\n<td>Soapy water (typical)<\/td>\n<td>0.0370<\/td>\n<\/tr>\n<tr>\n<td>Ethyl alcohol<\/td>\n<td>0.0223<\/td>\n<\/tr>\n<tr>\n<td>Glycerin<\/td>\n<td>0.0631<\/td>\n<\/tr>\n<tr>\n<td>Mercury<\/td>\n<td>0.465<\/td>\n<\/tr>\n<tr>\n<td>Olive oil<\/td>\n<td>0.032<\/td>\n<\/tr>\n<tr>\n<td>Tissue fluids (typical)<\/td>\n<td>0.050<\/td>\n<\/tr>\n<tr>\n<td>Blood, whole at [latex]\\text{37}\\text{\u00ba}\\text{C}[\/latex]<\/td>\n<td>0.058<\/td>\n<\/tr>\n<tr>\n<td>Blood plasma at [latex]\\text{37}\\text{\u00ba}\\text{C}[\/latex]<\/td>\n<td>0.073<\/td>\n<\/tr>\n<tr>\n<td>Gold at [latex]\\text{1070}\\text{\u00ba}\\text{C}[\/latex]<\/td>\n<td>1.000<\/td>\n<\/tr>\n<tr>\n<td>Oxygen at [latex]-\\text{193}\\text{\u00ba}\\text{C}[\/latex]<\/td>\n<td>0.0157<\/td>\n<\/tr>\n<tr>\n<td>Helium at [latex]-\\text{269}\\text{\u00ba}\\text{C}[\/latex]<\/td>\n<td>0.00012<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div data-type=\"example\" class=\"textbox examples\" id=\"fs-id1848686\">\n<div data-type=\"title\" class=\"title\">Surface Tension: Pressure Inside a Bubble<\/div>\n<p id=\"import-auto-id3130343\">Calculate the gauge pressure inside a soap bubble [latex]2\\text{.}\\text{00}\u00d7{\\text{10}}^{-4}\\phantom{\\rule{0.25em}{0ex}}\\text{m}[\/latex] in radius using the surface tension for soapy water in <a href=\"#import-auto-id1816998\" class=\"autogenerated-content\">(Figure)<\/a>. Convert this pressure to mm Hg.<\/p>\n<p id=\"import-auto-id1383027\"><strong>Strategy<\/strong><\/p>\n<p id=\"import-auto-id2670578\">The radius is given and the surface tension can be found in <a href=\"#import-auto-id1816998\" class=\"autogenerated-content\">(Figure)<\/a>, and so [latex]P[\/latex] can be found directly from the equation [latex]P=\\frac{4\\gamma }{r}[\/latex].<\/p>\n<p id=\"import-auto-id3229369\"><strong>Solution<\/strong><\/p>\n<p>Substituting [latex]r[\/latex] and [latex]\\gamma [\/latex] into the equation [latex]P=\\frac{4\\gamma }{r}[\/latex], we obtain<\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]P=\\frac{4\\gamma }{r}=\\frac{4\\left(0.037 N\/m\\right)}{2\\text{.}\\text{00}\u00d7{\\text{10}}^{-4}\\phantom{\\rule{0.25em}{0ex}}\\text{m}}=\\text{740}\\phantom{\\rule{0.25em}{0ex}}{\\text{N\/m}}^{2}=\\text{740}\\phantom{\\rule{0.25em}{0ex}}\\text{Pa}.[\/latex]<\/div>\n<p id=\"import-auto-id1448906\">We use a conversion factor to get this into units of mm Hg:<\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]P=\\left(\\text{740}\\phantom{\\rule{0.25em}{0ex}}{\\text{N\/m}}^{2}\\right)\\frac{1.00 mm Hg}{\\text{133}\\phantom{\\rule{0.25em}{0ex}}{\\text{N\/m}}^{2}}=5.56 mm Hg.[\/latex]<\/div>\n<p id=\"import-auto-id1870548\"><strong>Discussion<\/strong><\/p>\n<p id=\"import-auto-id1926153\">Note that if a hole were to be made in the bubble, the air would be forced out, the bubble would decrease in radius, and the pressure inside would <em data-effect=\"italics\">increase<\/em> to atmospheric pressure (760 mm Hg).<\/p>\n<\/div>\n<p id=\"import-auto-id1248452\">Our lungs contain hundreds of millions of mucus-lined sacs called <em data-effect=\"italics\">alveoli<\/em>, which are very similar in size, and about 0.1 mm in diameter. (See <a href=\"#import-auto-id774766\" class=\"autogenerated-content\">(Figure)<\/a>.) You can exhale without muscle action by allowing surface tension to contract these sacs. Medical patients whose breathing is aided by a positive pressure respirator have air blown into the lungs, but are generally allowed to exhale on their own. Even if there is paralysis, surface tension in the alveoli will expel air from the lungs. Since pressure increases as the radii of the alveoli decrease, an occasional deep cleansing breath is needed to fully reinflate the alveoli. Respirators are programmed to do this and we find it natural, as do our companion dogs and cats, to take a cleansing breath before settling into a nap.<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id774766\">\n<div class=\"bc-figcaption figcaption\">Bronchial tubes in the lungs branch into ever-smaller structures, finally ending in alveoli. The alveoli act like tiny bubbles. The surface tension of their mucous lining aids in exhalation and can prevent inhalation if too great.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1548374\" data-alt=\"The alveoli at the end of the lung tubes enable exhalation and do not allow inhalation due to the surface tension of the mucous lining.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_08_06a.jpg\" data-media-type=\"image\/jpg\" alt=\"The alveoli at the end of the lung tubes enable exhalation and do not allow inhalation due to the surface tension of the mucous lining.\" width=\"300\"><\/span><\/p><\/div>\n<p id=\"import-auto-id2598952\">The tension in the walls of the alveoli results from the membrane tissue and a liquid on the walls of the alveoli containing a long lipoprotein that acts as a surfactant (a surface-tension reducing substance). The need for the surfactant results from the tendency of small alveoli to collapse and the air to fill into the larger alveoli making them even larger (as demonstrated in <a href=\"#import-auto-id2054965\" class=\"autogenerated-content\">(Figure)<\/a>). During inhalation, the lipoprotein molecules are pulled apart and the wall tension increases as the radius increases (increased surface tension). During exhalation, the molecules slide back together and the surface tension decreases, helping to prevent a collapse of the alveoli. The surfactant therefore serves to change the wall tension so that small alveoli don\u2019t collapse and large alveoli are prevented from expanding too much. This tension change is a unique property of these surfactants, and is not shared by detergents (which simply lower surface tension). (See <a href=\"#import-auto-id2971179\" class=\"autogenerated-content\">(Figure)<\/a>.)<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id2971179\">\n<div class=\"bc-figcaption figcaption\">Surface tension as a function of surface area. The surface tension for lung surfactant decreases with decreasing area. This ensures that small alveoli don\u2019t collapse and large alveoli are not able to over expand. <\/div>\n<p><span data-type=\"media\" id=\"import-auto-id2973139\" data-alt=\"Graph of surface tension as a function of surface area for detergents and interstitial fluids.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_08_07a.jpg\" data-media-type=\"image\/png\" alt=\"Graph of surface tension as a function of surface area for detergents and interstitial fluids.\" width=\"300\"><\/span><\/p><\/div>\n<p id=\"import-auto-id1374919\">If water gets into the lungs, the surface tension is too great and you cannot inhale. This is a severe problem in resuscitating drowning victims. A similar problem occurs in newborn infants who are born without this surfactant\u2014their lungs are very difficult to inflate. This condition is known as <em data-effect=\"italics\">hyaline membrane disease<\/em> and is a leading cause of death for infants, particularly in premature births. Some success has been achieved in treating hyaline membrane disease by spraying a surfactant into the infant\u2019s breathing passages. Emphysema produces the opposite problem with alveoli. Alveolar walls of emphysema victims deteriorate, and the sacs combine to form larger sacs. Because pressure produced by surface tension decreases with increasing radius, these larger sacs produce smaller pressure, reducing the ability of emphysema victims to exhale. A common test for emphysema is to measure the pressure and volume of air that can be exhaled.<\/p>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" id=\"fs-id1414382\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">Making Connections: Take-Home Investigation<\/div>\n<p id=\"import-auto-id2963064\">(1) Try floating a sewing needle on water. In order for this activity to work, the needle needs to be very clean as even the oil from your fingers can be sufficient to affect the surface properties of the needle. (2) Place the bristles of a paint brush into water. Pull the brush out and notice that for a short while, the bristles will stick together. The surface tension of the water surrounding the bristles is sufficient to hold the bristles together. As the bristles dry out, the surface tension effect dissipates. (3) Place a loop of thread on the surface of still water in such a way that all of the thread is in contact with the water. Note the shape of the loop. Now place a drop of detergent into the middle of the loop. What happens to the shape of the loop? Why? (4) Sprinkle pepper onto the surface of water. Add a drop of detergent. What happens? Why? (5) Float two matches parallel to each other and add a drop of detergent between them. What happens? Note: For each new experiment, the water needs to be replaced and the bowl washed to free it of any residual detergent.<\/p>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id2391861\">\n<h1 data-type=\"title\">Adhesion and Capillary Action<\/h1>\n<p id=\"import-auto-id1868222\">Why is it that water beads up on a waxed car but does not on bare paint? The answer is that the adhesive forces between water and wax are much smaller than those between water and paint. Competition between the forces of adhesion and cohesion are important in the macroscopic behavior of liquids. An important factor in studying the roles of these two forces is the angle [latex]\\theta [\/latex] between the tangent to the liquid surface and the surface. (See <a href=\"#import-auto-id1439052\" class=\"autogenerated-content\">(Figure)<\/a>.) The <span data-type=\"term\" id=\"import-auto-id2990625\">contact angle<\/span> [latex]\\theta [\/latex] is directly related to the relative strength of the cohesive and adhesive forces. The larger the strength of the cohesive force relative to the adhesive force, the larger [latex]\\theta [\/latex] is, and the more the liquid tends to form a droplet. The smaller [latex]\\theta [\/latex] is, the smaller the relative strength, so that the adhesive force is able to flatten the drop. <a href=\"#import-auto-id3245851\" class=\"autogenerated-content\">(Figure)<\/a> lists contact angles for several combinations of liquids and solids.<\/p>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" id=\"fs-id2588349\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">Contact Angle<\/div>\n<p id=\"import-auto-id1177794\">The angle [latex]\\theta [\/latex] between the tangent to the liquid surface and the surface is called the contact angle.<\/p>\n<\/div>\n<div class=\"bc-figure figure\" id=\"import-auto-id1439052\">\n<div class=\"bc-figcaption figcaption\">In the photograph, water beads on the waxed car paint and flattens on the unwaxed paint. (a) Water forms beads on the waxed surface because the cohesive forces responsible for surface tension are larger than the adhesive forces, which tend to flatten the drop. (b) Water beads on bare paint are flattened considerably because the adhesive forces between water and paint are strong, overcoming surface tension. The contact angle [latex]\\theta [\/latex] is directly related to the relative strengths of the cohesive and adhesive forces. The larger [latex]\\theta [\/latex] is, the larger the ratio of cohesive to adhesive forces. (credit: P. P. Urone)<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1094155\" data-alt=\"Water is seen to make beads on the waxed surface of car paint and it remains flat on the surface without wax. The beads are due to the greater force of attraction between the water molecules than between the water molecules and the surface. On the surface without wax the force of attraction between the water molecules and paint is greater.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_08_08a.jpg\" data-media-type=\"image\/jpg\" alt=\"Water is seen to make beads on the waxed surface of car paint and it remains flat on the surface without wax. The beads are due to the greater force of attraction between the water molecules than between the water molecules and the surface. On the surface without wax the force of attraction between the water molecules and paint is greater.\" width=\"400\"><\/span><\/p><\/div>\n<p id=\"import-auto-id2400994\">One important phenomenon related to the relative strength of cohesive and adhesive forces is <span data-type=\"term\" id=\"import-auto-id1253557\">capillary action<\/span>\u2014the tendency of a fluid to be raised or suppressed in a narrow tube, or <em data-effect=\"italics\">capillary tube<\/em>. This action causes blood to be drawn into a small-diameter tube when the tube touches a drop.<\/p>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" id=\"fs-id3158905\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">Capillary Action<\/div>\n<p id=\"import-auto-id3137631\">The tendency of a fluid to be raised or suppressed in a narrow tube, or capillary tube, is called capillary action.<\/p>\n<\/div>\n<p id=\"import-auto-id2647701\">If a capillary tube is placed vertically into a liquid, as shown in <a href=\"#fs-id1333088\" class=\"autogenerated-content\">(Figure)<\/a>, capillary action will raise or suppress the liquid inside the tube depending on the combination of substances. The actual effect depends on the relative strength of the cohesive and adhesive forces and, thus, the contact angle [latex]\\theta [\/latex] given in the table. If [latex]\\theta [\/latex] is less than [latex]90\u00ba[\/latex], then the fluid will be raised; if [latex]\\theta [\/latex] is greater than [latex]90\u00ba[\/latex], it will be suppressed. Mercury, for example, has a very large surface tension and a large contact angle with glass. When placed in a tube, the surface of a column of mercury curves downward, somewhat like a drop. The curved surface of a fluid in a tube is called a <strong>meniscus<\/strong>. The tendency of surface tension is always to reduce the surface area. Surface tension thus flattens the curved liquid surface in a capillary tube. This results in a downward force in mercury and an upward force in water, as seen in <a href=\"#fs-id1333088\" class=\"autogenerated-content\">(Figure)<\/a>.<\/p>\n<p id=\"import-auto-id3119502\">\n<\/p><div class=\"bc-figure figure\" id=\"fs-id1333088\">\n<div class=\"bc-figcaption figcaption\">(a) Mercury is suppressed in a glass tube because its contact angle is greater than [latex]90\u00ba[\/latex]. Surface tension exerts a downward force as it flattens the mercury, suppressing it in the tube. The dashed line shows the shape the mercury surface would have without the flattening effect of surface tension. (b) Water is raised in a glass tube because its contact angle is nearly [latex]0\u00ba[\/latex]. Surface tension therefore exerts an upward force when it flattens the surface to reduce its area.<\/div>\n<p><span data-type=\"media\" id=\"fs-id1313828\" data-alt=\"Mercury kept in a container into which a narrow tube is inserted lowers its level inside the tube relative to the level in the rest of the container. In a similar situation, water rises in the tube so that the water level in the tube is above the water level in the rest of the container. This phenomenon is due to the large contact angle of mercury with glass and the smaller contact angle of water with glass.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_08_09a.jpg\" data-media-type=\"image\/jpeg\" alt=\"Mercury kept in a container into which a narrow tube is inserted lowers its level inside the tube relative to the level in the rest of the container. In a similar situation, water rises in the tube so that the water level in the tube is above the water level in the rest of the container. This phenomenon is due to the large contact angle of mercury with glass and the smaller contact angle of water with glass.\" width=\"350\"><\/span><\/p><\/div>\n<table id=\"import-auto-id3245851\" summary=\"The table gives the contact angles of some substances.\">\n<caption><span data-type=\"title\">Contact Angles of Some Substances<\/span><\/caption>\n<thead>\n<tr>\n<th>\n              Interface\n            <\/th>\n<th>\n              Contact angle \u0398\n            <\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Mercury\u2013glass<\/td>\n<td>[latex]\\text{140}\\text{\u00ba}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Water\u2013glass<\/td>\n<td>[latex]0\\text{\u00ba}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Water\u2013paraffin<\/td>\n<td>[latex]\\text{107}\\text{\u00ba}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Water\u2013silver<\/td>\n<td>[latex]\\text{90}\\text{\u00ba}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Organic liquids (most)\u2013glass<\/td>\n<td>[latex]0\\text{\u00ba}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Ethyl alcohol\u2013glass<\/td>\n<td>[latex]0\\text{\u00ba}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Kerosene\u2013glass<\/td>\n<td>[latex]\\text{26}\\text{\u00ba}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"import-auto-id2677223\">Capillary action can move liquids horizontally over very large distances, but the height to which it can raise or suppress a liquid in a tube is limited by its weight. It can be shown that this height [latex]h[\/latex] is given by <\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]h=\\frac{2\\gamma \\phantom{\\rule{0.25em}{0ex}}\\text{cos}\\phantom{\\rule{0.25em}{0ex}}\\theta }{\\rho \\text{gr}}.[\/latex]<\/div>\n<p>If we look at the different factors in this expression, we might see how it makes good sense. The height is directly proportional to the surface tension [latex]\\gamma [\/latex], which is its direct cause. Furthermore, the height is inversely proportional to tube radius\u2014the smaller the radius [latex]r[\/latex], the higher the fluid can be raised, since a smaller tube holds less mass. The height is also inversely proportional to fluid density [latex]\\rho [\/latex], since a larger density means a greater mass in the same volume. (See <a href=\"#import-auto-id2953655\" class=\"autogenerated-content\">(Figure)<\/a>.)<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id2953655\">\n<div class=\"bc-figcaption figcaption\">(a) Capillary action depends on the radius of a tube. The smaller the tube, the greater the height reached. The height is negligible for large-radius tubes. (b) A denser fluid in the same tube rises to a smaller height, all other factors being the same.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id2591168\" data-alt=\"The left image shows liquid in a container with four tubes of progressively smaller diameter inserted into the liquid. The liquid rises higher in the smaller-diameter tubes. The right image shows two containers, one holding a dense liquid and the other holding a less-dense liquid. Identical tubes are inserted into each liquid. The less-dense liquid rises higher in its tube than the more-dense liquid does in its tube.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_08_10a.jpg\" data-media-type=\"image\/jpg\" alt=\"The left image shows liquid in a container with four tubes of progressively smaller diameter inserted into the liquid. The liquid rises higher in the smaller-diameter tubes. The right image shows two containers, one holding a dense liquid and the other holding a less-dense liquid. Identical tubes are inserted into each liquid. The less-dense liquid rises higher in its tube than the more-dense liquid does in its tube.\" width=\"400\"><\/span><\/p><\/div>\n<div data-type=\"example\" class=\"textbox examples\" id=\"fs-id2066941\">\n<div data-type=\"title\" class=\"title\">Calculating Radius of a Capillary Tube: Capillary Action: Tree Sap<\/div>\n<p id=\"import-auto-id3027640\">Can capillary action be solely responsible for sap rising in trees? To answer this question, calculate the radius of a capillary tube that would raise sap 100 m to the top of a giant redwood, assuming that sap\u2019s density is [latex]\\text{1050 kg}{\\text{\/m}}^{3}[\/latex], its contact angle is zero, and its surface tension is the same as that of water at [latex]20.0\u00ba C[\/latex].<\/p>\n<p id=\"import-auto-id3127685\"><strong>Strategy<\/strong><\/p>\n<p id=\"import-auto-id1907791\">The height to which a liquid will rise as a result of capillary action is given by [latex]h=\\frac{2\\gamma \\phantom{\\rule{0.25em}{0ex}}\\text{cos}\\phantom{\\rule{0.25em}{0ex}}\\theta }{\\rho \\text{gr}}[\/latex], and every quantity is known except for [latex]r[\/latex].<\/p>\n<p id=\"import-auto-id2396875\"><strong>Solution<\/strong><\/p>\n<p id=\"import-auto-id3176902\">Solving for [latex]r[\/latex] and substituting known values produces<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-301\">[latex]\\begin{array}{lll}r&amp; =&amp; \\frac{2\\gamma \\phantom{\\rule{0.25em}{0ex}}\\text{cos}\\phantom{\\rule{0.25em}{0ex}}\\theta }{\\rho \\text{gh}}=\\frac{2\\left(\\text{0.0728 N\/m}\\right)\\text{cos}\\left(0\u00ba\\right)}{\\left(\\text{1050}\\phantom{\\rule{0.25em}{0ex}}{\\text{kg\/m}}^{3}\\right)\\left(9\\text{.}\\text{80}\\phantom{\\rule{0.25em}{0ex}}{\\text{m\/s}}^{2}\\right)\\left(\\text{100 m}\\right)}\\\\ &amp; =&amp; 1.41\u00d7{\\text{10}}^{-7}\\phantom{\\rule{0.25em}{0ex}}\\text{m.}\\end{array}[\/latex]<\/div>\n<p id=\"import-auto-id2621794\"><strong>Discussion<\/strong><\/p>\n<p id=\"import-auto-id3089330\">This result is unreasonable. Sap in trees moves through the <em data-effect=\"italics\">xylem<\/em>, which forms tubes with radii as small as [latex]2\\text{.}5\u00d7{\\text{10}}^{-5}\\phantom{\\rule{0.25em}{0ex}}\\text{m}[\/latex]. This value is about 180 times as large as the radius found necessary here to raise sap [latex]\\text{100 m}[\/latex]. This means that capillary action alone cannot be solely responsible for sap getting to the tops of trees.<\/p>\n<\/div>\n<p>How <em data-effect=\"italics\">does<\/em> sap get to the tops of tall trees? (Recall that a column of water can only rise to a height of 10 m  when there is a vacuum at the top\u2014see <a href=\"\/contents\/5f0b0e0e-e825-4aeb-9c8e-1f64a6942233@3#fs-id2937185\" class=\"autogenerated-content\">(Figure)<\/a>.) The question has not been completely resolved, but it appears that it is pulled up like a chain held together by cohesive forces. As each molecule of sap enters a leaf and evaporates (a process called transpiration), the entire chain is pulled up a notch. So a negative pressure created by water evaporation must be present to pull the sap up through the xylem vessels. In most situations, <em data-effect=\"italics\">fluids can push but can exert only negligible pull<\/em>, because the cohesive forces seem to be too small to hold the molecules tightly together. But in this case, the cohesive force of water molecules provides a very strong pull. <a href=\"#import-auto-id2051381\" class=\"autogenerated-content\">(Figure)<\/a> shows one device for studying negative pressure. Some experiments have demonstrated that negative pressures sufficient to pull sap to the tops of the tallest trees <em data-effect=\"italics\">can<\/em> be achieved.<\/p>\n<div class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">(a) When the piston is raised, it stretches the liquid slightly, putting it under tension and creating a negative absolute pressure [latex]P=-F\/A[\/latex]. (b) The liquid eventually separates, giving an experimental limit to negative pressure in this liquid.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1381777\" data-alt=\"When the piston is raised the liquid stretches somewhat, which results in negative pressure.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_08_11a.jpg\" data-media-type=\"image\/jpg\" alt=\"When the piston is raised the liquid stretches somewhat, which results in negative pressure.\" width=\"200\"><\/span><\/p><\/div>\n<\/div>\n<div class=\"section-summary\" data-depth=\"1\" id=\"fs-id3082720\">\n<h1 data-type=\"title\">Section Summary<\/h1>\n<ul id=\"fs-id1827717\">\n<li id=\"import-auto-id3109651\">Attractive forces between molecules of the same type are called cohesive forces.<\/li>\n<li id=\"import-auto-id3028701\">Attractive forces between molecules of different types are called adhesive forces.<\/li>\n<li id=\"import-auto-id3192000\">Cohesive forces between molecules cause the surface of a liquid to contract to the smallest possible surface area. This general effect is called surface tension.<\/li>\n<li>Capillary action is the tendency of a fluid to be raised or suppressed in a narrow tube, or capillary tube which is due to the relative strength of cohesive and adhesive forces.<\/li>\n<\/ul>\n<\/div>\n<div class=\"conceptual-questions\" data-depth=\"1\" id=\"fs-id1383406\" data-element-type=\"conceptual-questions\">\n<h1 data-type=\"title\">Conceptual Questions<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3245014\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3415497\">\n<p>The density of oil is less than that of water, yet a loaded oil tanker sits lower in the water than an empty one. Why?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1921000\">\n<p id=\"import-auto-id2421560\">Is surface tension due to cohesive or adhesive forces, or both?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3028474\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2396594\">\n<p id=\"import-auto-id3009722\">Is capillary action due to cohesive or adhesive forces, or both?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1486629\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1888301\">\n<p id=\"import-auto-id3108344\">Birds such as ducks, geese, and swans have greater densities than water, yet they are able to sit on its surface. Explain this ability, noting that water does not wet their feathers and that they cannot sit on soapy water.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2971778\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2381951\">\n<p>Water beads up on an oily sunbather, but not on her neighbor, whose skin is not oiled. Explain in terms of cohesive and adhesive forces.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2682132\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2403876\">\n<p id=\"import-auto-id2663132\">Could capillary action be used to move fluids in a \u201cweightless\u201d environment, such as in an orbiting space probe?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2437631\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3025302\">\n<p id=\"import-auto-id3119512\">What effect does capillary action have on the reading of a manometer with uniform diameter? Explain your answer.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1993729\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2514692\">\n<p id=\"import-auto-id2666531\">Pressure between the inside chest wall and the outside of the lungs normally remains negative. Explain how pressure inside the lungs can become positive (to cause exhalation) without muscle action.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"problems-exercises\" data-depth=\"1\" id=\"fs-id1425593\" data-element-type=\"problems-exercises\">\n<h1 data-type=\"title\">Problems &amp; Exercises<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3123703\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2402900\">\n<p id=\"import-auto-id2671168\">What is the pressure inside an alveolus having a radius of [latex]2\\text{.}\\text{50}\u00d7{\\text{10}}^{-4}\\phantom{\\rule{0.25em}{0ex}}\\text{m}[\/latex] if the surface tension of the fluid-lined wall is the same as for soapy water? You may assume the pressure is the same as that created by a spherical bubble.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2684015\" data-element-type=\"problems-exercises\">\n[latex]\\text{592}\\phantom{\\rule{0.25em}{0ex}}{\\text{N\/m}}^{2}[\/latex]\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2667857\">\n<p id=\"import-auto-id1848842\">(a) The pressure inside an alveolus with a [latex]2\\text{.}\\text{00}\u00d7{\\text{10}}^{-4}[\/latex]-m radius is [latex]1\\text{.}\\text{40}\u00d7{\\text{10}}^{3}\\phantom{\\rule{0.25em}{0ex}}\\text{Pa}[\/latex], due to its fluid-lined walls. Assuming the alveolus acts like a spherical bubble, what is the surface tension of the fluid? (b) Identify the likely fluid. (You may need to extrapolate between values in <a href=\"#import-auto-id1816998\" class=\"autogenerated-content\">(Figure)<\/a>.)<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2684580\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1588311\">\n<p>What is the gauge pressure in millimeters of mercury inside a soap bubble 0.100 m in diameter?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" data-element-type=\"problems-exercises\">\n<p id=\"import-auto-id2930063\">[latex]2\\text{.}\\text{23}\u00d7{\\text{10}}^{-2}\\phantom{\\rule{0.25em}{0ex}}\\text{mm Hg}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id909629\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1380194\">\n<p id=\"import-auto-id1579340\">Calculate the force on the slide wire in <a href=\"#import-auto-id3306680\" class=\"autogenerated-content\">(Figure)<\/a> if it is 3.50 cm long and the fluid is ethyl alcohol.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3013760\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3416522\">\n<p id=\"import-auto-id1220838\"><a href=\"#import-auto-id2953655\" class=\"autogenerated-content\">(Figure)<\/a>(a) shows the effect of tube radius on the height to which capillary action can raise a fluid. (a) Calculate the height [latex]h[\/latex] for water in a glass tube with a radius of 0.900 cm\u2014a rather large tube like the one on the left. (b) What is the radius of the glass tube on the right if it raises water to 4.00 cm?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2989927\" data-element-type=\"problems-exercises\">\n<p>(a) [latex]1\\text{.}\\text{65}\u00d7{\\text{10}}^{-3}\\phantom{\\rule{0.25em}{0ex}}\\text{m}[\/latex]<\/p>\n<p id=\"import-auto-id1909395\">(b) [latex]3\\text{.}\\text{71}\u00d7{\\text{10}}^{\u20134}\\phantom{\\rule{0.25em}{0ex}}\\text{m}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2405199\">\n<p id=\"import-auto-id2401535\">We stated in <a href=\"#fs-id2066941\" class=\"autogenerated-content\">(Figure)<\/a> that a xylem tube is of radius [latex]2\\text{.}\\text{50}\u00d7{\\text{10}}^{-5}\\phantom{\\rule{0.25em}{0ex}}\\text{m}[\/latex]. Verify that such a tube raises sap less than a meter by finding [latex]h[\/latex] for it, making the same assumptions that sap\u2019s density is [latex]\\text{1050}\\phantom{\\rule{0.25em}{0ex}}{\\text{kg\/m}}^{3}[\/latex], its contact angle is zero, and its surface tension is the same as that of water at [latex]20.0\u00ba C[\/latex].<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1986155\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1954890\">\n<p id=\"import-auto-id1484935\">What fluid is in the device shown in <a href=\"#import-auto-id3306680\" class=\"autogenerated-content\">(Figure)<\/a> if the force is [latex]3\\text{.}\\text{16}\u00d7{\\text{10}}^{-3}\\phantom{\\rule{0.25em}{0ex}}\\text{N}[\/latex] and the length of the wire is 2.50 cm? Calculate the surface tension [latex]\\gamma [\/latex] and find a likely match from <a href=\"#import-auto-id1816998\" class=\"autogenerated-content\">(Figure)<\/a>.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2441420\" data-element-type=\"problems-exercises\">\n<p id=\"import-auto-id2391306\">[latex]6\\text{.}\\text{32}\u00d7{\\text{10}}^{-2}\\phantom{\\rule{0.25em}{0ex}}\\text{N\/m}[\/latex]<\/p>\n<p id=\"import-auto-id3037197\">Based on the values in table, the fluid is probably glycerin.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1427554\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1343201\">\n<p>If the gauge pressure inside a rubber balloon with a 10.0-cm radius is 1.50 cm of water, what is the effective surface tension of the balloon?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2627309\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2653975\">\n<p id=\"import-auto-id1916804\">Calculate the gauge pressures inside 2.00-cm-radius bubbles of water, alcohol, and soapy water. Which liquid forms the most stable bubbles, neglecting any effects of evaporation?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2052753\" data-element-type=\"problems-exercises\">\n<p id=\"import-auto-id1390466\">[latex]\\begin{array}{lll}{P}_{\\text{w}}&amp; =&amp; \\text{14}\\text{.}6\\phantom{\\rule{0.25em}{0ex}}{\\text{N\/m}}^{2},\\\\ {P}_{\\text{a}}&amp; =&amp; \\text{4.46}\\phantom{\\rule{0.25em}{0ex}}{\\text{N\/m}}^{2},\\\\ {P}_{\\text{sw}}&amp; =&amp; \\text{7.40}\\phantom{\\rule{0.25em}{0ex}}{\\text{N\/m}}^{2}\\text{.}\\end{array}[\/latex]<\/p>\n<p id=\"import-auto-id1934620\">Alcohol forms the most stable bubble, since the absolute pressure inside is closest to atmospheric pressure.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3123947\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2398646\">\n<p id=\"import-auto-id3172495\">Suppose water is raised by capillary action to a height of 5.00 cm in a glass tube. (a) To what height will it be raised in a paraffin tube of the same radius? (b) In a silver tube of the same radius?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3062468\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1485735\">\n<p id=\"import-auto-id3191626\">Calculate the contact angle [latex]\\theta [\/latex] for olive oil if capillary action raises it to a height of 7.07 cm in a glass tube with a radius of 0.100 mm. Is this value consistent with that for most organic liquids?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2583363\" data-element-type=\"problems-exercises\">\n<p id=\"import-auto-id2453951\">[latex]5.1\u00ba[\/latex]<\/p>\n<p id=\"import-auto-id1587278\">This is near the value of [latex]\\theta =0\u00ba[\/latex] for most organic liquids.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3091822\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1427415\">\n<p id=\"import-auto-id3027871\">When two soap bubbles touch, the larger is inflated by the smaller until they form a single bubble. (a) What is the gauge pressure inside a soap bubble with a 1.50-cm radius? (b) Inside a 4.00-cm-radius soap bubble? (c) Inside the single bubble they form if no air is lost when they touch?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1910033\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3176215\">\n<p>Calculate the ratio of the heights to which water and mercury are raised by capillary action in the same glass tube.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2056256\" data-element-type=\"problems-exercises\">\n<p id=\"import-auto-id3255891\">[latex]-2\\text{.}\\text{78}[\/latex]<\/p>\n<p id=\"import-auto-id3397701\">The ratio is negative because water is raised whereas mercury is lowered.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3035905\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3035906\">\n<p id=\"import-auto-id3260674\">What is the ratio of heights to which ethyl alcohol and water are raised by capillary action in the same glass tube?<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"footnote-refs\">\n<h2 data-type=\"footnote-title\">Footnotes<\/h2>\n<ol>\n<li><a data-type=\"footnote-ref\" href=\"#footnote-ref1\">1<\/a> At 20\u00baC unless otherwise stated.<\/li>\n<\/ol>\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-id1419756\">\n<dt>adhesive forces<\/dt>\n<dd id=\"fs-id2601877\">the attractive forces between molecules of different types<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id1546590\">\n<dt>capillary action<\/dt>\n<dd id=\"fs-id2658153\">the tendency of a fluid to be raised or lowered in a narrow tube<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2949904\">\n<dt>cohesive forces<\/dt>\n<dd id=\"fs-id1303384\">the attractive forces between molecules of the same type<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id3175910\">\n<dt>contact angle<\/dt>\n<dd id=\"fs-id2410483\">the angle [latex]\\theta [\/latex] between the tangent to the liquid surface and the surface<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id3101618\">\n<dt>surface tension<\/dt>\n<dd id=\"fs-id1561031\">the cohesive forces between molecules which cause the surface of a liquid to contract to the smallest possible surface area<\/dd>\n<\/dl>\n<\/div>\n\n","rendered":"<div class=\"textbox learning-objectives\">\n<h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>\n<ul>\n<li>Understand cohesive and adhesive forces.<\/li>\n<li>Define surface tension.<\/li>\n<li>Understand capillary action.<\/li>\n<\/ul>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id2406446\">\n<h1 data-type=\"title\">Cohesion and Adhesion in Liquids<\/h1>\n<p id=\"import-auto-id1574788\">Children blow soap bubbles and play in the spray of a sprinkler on a hot summer day. (See <a href=\"#import-auto-id2058131\" class=\"autogenerated-content\">(Figure)<\/a>.) An underwater spider keeps his air supply in a shiny bubble he carries wrapped around him. A technician draws blood into a small-diameter tube just by touching it to a drop on a pricked finger. A premature infant struggles to inflate her lungs. What is the common thread? All these activities are dominated by the attractive forces between atoms and molecules in liquids\u2014both within a liquid and between the liquid and its surroundings.<\/p>\n<p id=\"import-auto-id1344655\">Attractive forces between molecules of the same type are called <span data-type=\"term\">cohesive forces<\/span>. Liquids can, for example, be held in open containers because cohesive forces hold the molecules together. Attractive forces between molecules of different types are called <span data-type=\"term\" id=\"import-auto-id2949896\">adhesive forces<\/span>. Such forces cause liquid drops to cling to window panes, for example. In this section we examine effects directly attributable to cohesive and adhesive forces in liquids.<\/p>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" id=\"fs-id2391728\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">Cohesive Forces<\/div>\n<p id=\"import-auto-id1933298\">Attractive forces between molecules of the same type are called cohesive forces.<\/p>\n<\/div>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" id=\"fs-id2639833\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">Adhesive Forces<\/div>\n<p id=\"import-auto-id3177773\">Attractive forces between molecules of different types are called adhesive forces.<\/p>\n<\/div>\n<div class=\"bc-figure figure\" id=\"import-auto-id2058131\">\n<div class=\"bc-figcaption figcaption\">The soap bubbles in this photograph are caused by cohesive forces among molecules in liquids. (credit: Steve Ford Elliott)<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id2969220\" data-alt=\"The soap bubbles that the child blows into the air maintain their shape because of the attractive force between the molecules of the soap bubble.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_08_01a.jpg\" data-media-type=\"image\/png\" alt=\"The soap bubbles that the child blows into the air maintain their shape because of the attractive force between the molecules of the soap bubble.\" width=\"400\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id3454572\">\n<h1 data-type=\"title\">Surface Tension<\/h1>\n<p id=\"import-auto-id2662953\">Cohesive forces between molecules cause the surface of a liquid to contract to the smallest possible surface area. This general effect is called <span data-type=\"term\" id=\"import-auto-id1011283\">surface tension<\/span>. Molecules on the surface are pulled inward by cohesive forces, reducing the surface area. Molecules inside the liquid experience zero net force, since they have neighbors on all sides.<\/p>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" id=\"fs-id2062954\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">Surface Tension<\/div>\n<p id=\"import-auto-id1471706\">Cohesive forces between molecules cause the surface of a liquid to contract to the smallest possible surface area. This general effect is called surface tension.<\/p>\n<\/div>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" id=\"fs-id3250489\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">Making Connections: Surface Tension<\/div>\n<p id=\"import-auto-id2661790\">Forces between atoms and molecules underlie the macroscopic effect called surface tension. These attractive forces pull the molecules closer together and tend to minimize the surface area. This is another example of a submicroscopic explanation for a macroscopic phenomenon.<\/p>\n<\/div>\n<p id=\"import-auto-id3094705\">The model of a liquid surface acting like a stretched elastic sheet can effectively explain surface tension effects. For example, some insects can walk on water (as opposed to floating in it) as we would walk on a trampoline\u2014they dent the surface as shown in <a href=\"#import-auto-id2970796\" class=\"autogenerated-content\">(Figure)<\/a>(a). <a href=\"#import-auto-id2970796\" class=\"autogenerated-content\">(Figure)<\/a>(b) shows another example, where a needle rests on a water surface. The iron needle cannot, and does not, float, because its density is greater than that of water. Rather, its weight is supported by forces in the stretched surface that try to make the surface smaller or flatter. If the needle were placed point down on the surface, its weight acting on a smaller area would break the surface, and it would sink.<\/p>\n<p id=\"import-auto-id2000364\">\n<div class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">Surface tension supporting the weight of an insect and an iron needle, both of which rest on the surface without penetrating it. They are not floating; rather, they are supported by the surface of the liquid. (a) An insect leg dents the water surface. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4d91eb2e61403a182593c40fb7e056d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#70;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#84;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"29\" style=\"vertical-align: -4px;\" \/> is a restoring force (surface tension) parallel to the surface. (b) An iron needle similarly dents a water surface until the restoring force (surface tension) grows to equal its weight.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id2391711\" data-alt=\"A leg of an insect resting on the water surface is shown in the first figure. In the second figure an iron needle rests on the surface of water without sinking. Both are possible due to the tension on the surface of the liquid.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_08_03a.jpg\" data-media-type=\"image\/jpg\" alt=\"A leg of an insect resting on the water surface is shown in the first figure. In the second figure an iron needle rests on the surface of water without sinking. Both are possible due to the tension on the surface of the liquid.\" width=\"475\" \/><\/span><\/p>\n<\/div>\n<p id=\"import-auto-id1935393\">Surface tension is proportional to the strength of the cohesive force, which varies with the type of liquid. Surface tension <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4dfd339d0f13026ff7af56aa6f129380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#103;&#97;&#109;&#109;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> is defined to be the force <em data-effect=\"italics\">F<\/em> per unit length <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-66a9f474fc3c52efdfb0ba6a70199ee8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#76;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\" \/> exerted by a stretched liquid membrane:<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-170\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-1a48e2d779bc7efded26eb975a7e317a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#103;&#97;&#109;&#109;&#97;&#32;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#70;&#125;&#123;&#76;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"52\" style=\"vertical-align: -6px;\" \/><\/div>\n<p id=\"import-auto-id1864125\"><a href=\"#import-auto-id1816998\" class=\"autogenerated-content\">(Figure)<\/a> lists values of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4dfd339d0f13026ff7af56aa6f129380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#103;&#97;&#109;&#109;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> for some liquids. For the insect of <a href=\"#import-auto-id2970796\" class=\"autogenerated-content\">(Figure)<\/a>(a), its weight <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-dfee5c980777976ae8cf6541893fb572_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#119;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"13\" style=\"vertical-align: 0px;\" \/> is supported by the upward components of the surface tension force: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-16d32869ed5c8c7cd94a1e6cbd2a0538_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#119;&#61;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#92;&#103;&#97;&#109;&#109;&#97;&#32;&#76;&#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;&#115;&#105;&#110;&#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;&#104;&#101;&#116;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"98\" style=\"vertical-align: -4px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-66a9f474fc3c52efdfb0ba6a70199ee8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#76;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\" \/> is the circumference of the insect\u2019s foot in contact with the water. <a href=\"#import-auto-id3306680\" class=\"autogenerated-content\">(Figure)<\/a> shows one way to measure surface tension. The liquid film exerts a force on the movable wire in an attempt to reduce its surface area. The magnitude of this force depends on the surface tension of the liquid and can be measured accurately.<\/p>\n<p id=\"import-auto-id3399108\">Surface tension is the reason why liquids form bubbles and droplets. The inward surface tension force causes bubbles to be approximately spherical and raises the pressure of the gas trapped inside relative to atmospheric pressure outside. It can be shown that the gauge 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;\" \/>    inside a spherical bubble is given by<\/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-277f12738f47d2b07ca7677cba73f5ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#92;&#103;&#97;&#109;&#109;&#97;&#32;&#125;&#123;&#114;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"60\" style=\"vertical-align: -6px;\" \/><\/div>\n<p id=\"import-auto-id3013426\">where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> is the radius of the bubble. Thus the pressure inside a bubble is greatest when the bubble is the smallest. Another bit of evidence for this is illustrated in <a href=\"#import-auto-id2054965\" class=\"autogenerated-content\">(Figure)<\/a>. When air is allowed to flow between two balloons of unequal size, the smaller balloon tends to collapse, filling the larger balloon.<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id3306680\">\n<div class=\"bc-figcaption figcaption\">Sliding wire device used for measuring surface tension; the device exerts a force to reduce the film\u2019s surface area. The force needed to hold the wire in place is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-9645e1fdcdb0b02dd35c5c3038aa4f05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#61;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#92;&#103;&#97;&#109;&#109;&#97;&#32;&#76;&#125;&#61;&#92;&#103;&#97;&#109;&#109;&#97;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#108;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"123\" style=\"vertical-align: -4px;\" \/>, since there are <em data-effect=\"italics\">two<\/em> liquid surfaces attached to the wire. This force remains nearly constant as the film is stretched, until the film approaches its breaking point.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id2448669\" data-alt=\"Sliding wire device which is used to measure surface tension shows the force exerted on the two surfaces of the liquid. This force remains a constant until the film\u2019s breaking point.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_08_04a.jpg\" data-media-type=\"image\/jpg\" alt=\"Sliding wire device which is used to measure surface tension shows the force exerted on the two surfaces of the liquid. This force remains a constant until the film\u2019s breaking point.\" width=\"250\" \/><\/span><\/p>\n<\/div>\n<div class=\"bc-figure figure\" id=\"import-auto-id2054965\">\n<div class=\"bc-figcaption figcaption\">With the valve closed, two balloons of different sizes are attached to each end of a tube. Upon opening the valve, the smaller balloon decreases in size with the air moving to fill the larger balloon. The pressure in a spherical balloon is inversely proportional to its radius, so that the smaller balloon has a greater internal pressure than the larger balloon, resulting in this flow.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id3184818\" data-alt=\"When two balloons are attached to the ends of a glass tube air flows from one to the other if their sizes are different.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_08_05a.jpg\" data-media-type=\"image\/png\" alt=\"When two balloons are attached to the ends of a glass tube air flows from one to the other if their sizes are different.\" width=\"400\" \/><\/span><\/p>\n<\/div>\n<table id=\"import-auto-id1816998\" summary=\"The table gives the surface tension of water at zero, twenty, and one hundred degrees Celsius. The surface tension of some other liquids at twenty degrees Celsius is also given.\">\n<caption><span data-type=\"title\">Surface Tension of Some Liquids<a data-type=\"footnote-number\" href=\"#footnote1\"><sup>1<\/sup><\/a><\/span><\/caption>\n<thead>\n<tr>\n<th>\n              Liquid\n            <\/th>\n<th>\n              Surface tension \u03b3(N\/m)\n            <\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Water 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;\" \/><\/td>\n<td>0.0756<\/td>\n<\/tr>\n<tr>\n<td>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;\" \/><\/td>\n<td>0.0728<\/td>\n<\/tr>\n<tr>\n<td>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;\" \/><\/td>\n<td>0.0589<\/td>\n<\/tr>\n<tr>\n<td>Soapy water (typical)<\/td>\n<td>0.0370<\/td>\n<\/tr>\n<tr>\n<td>Ethyl alcohol<\/td>\n<td>0.0223<\/td>\n<\/tr>\n<tr>\n<td>Glycerin<\/td>\n<td>0.0631<\/td>\n<\/tr>\n<tr>\n<td>Mercury<\/td>\n<td>0.465<\/td>\n<\/tr>\n<tr>\n<td>Olive oil<\/td>\n<td>0.032<\/td>\n<\/tr>\n<tr>\n<td>Tissue fluids (typical)<\/td>\n<td>0.050<\/td>\n<\/tr>\n<tr>\n<td>Blood, whole at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-80df375e616af6fa48e4b3705621b053_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;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: 0px;\" \/><\/td>\n<td>0.058<\/td>\n<\/tr>\n<tr>\n<td>Blood plasma at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-80df375e616af6fa48e4b3705621b053_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;&ordm;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: 0px;\" \/><\/td>\n<td>0.073<\/td>\n<\/tr>\n<tr>\n<td>Gold at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a2303fbfa470eb70a16dc5e923717955_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#55;&#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=\"46\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>1.000<\/td>\n<\/tr>\n<tr>\n<td>Oxygen at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-6045644cc4dd37c69fdbd8dd5c7bc621_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#57;&#51;&#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=\"51\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>0.0157<\/td>\n<\/tr>\n<tr>\n<td>Helium at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-94f7f5df5b36e16a4e200921ecf13de8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#54;&#57;&#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=\"51\" style=\"vertical-align: 0px;\" \/><\/td>\n<td>0.00012<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div data-type=\"example\" class=\"textbox examples\" id=\"fs-id1848686\">\n<div data-type=\"title\" class=\"title\">Surface Tension: Pressure Inside a Bubble<\/div>\n<p id=\"import-auto-id3130343\">Calculate the gauge pressure inside a soap bubble <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-aa439059efd02bd288777db797b47eca_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;&#45;&#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;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"87\" style=\"vertical-align: -1px;\" \/> in radius using the surface tension for soapy water in <a href=\"#import-auto-id1816998\" class=\"autogenerated-content\">(Figure)<\/a>. Convert this pressure to mm Hg.<\/p>\n<p id=\"import-auto-id1383027\"><strong>Strategy<\/strong><\/p>\n<p id=\"import-auto-id2670578\">The radius is given and the surface tension can be found in <a href=\"#import-auto-id1816998\" class=\"autogenerated-content\">(Figure)<\/a>, and so <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;\" \/> can be found directly from the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ce81edb8a6c0a7c81d927999f4ec6d8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#92;&#103;&#97;&#109;&#109;&#97;&#32;&#125;&#123;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"54\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<p id=\"import-auto-id3229369\"><strong>Solution<\/strong><\/p>\n<p>Substituting <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4dfd339d0f13026ff7af56aa6f129380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#103;&#97;&#109;&#109;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> into the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ce81edb8a6c0a7c81d927999f4ec6d8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#92;&#103;&#97;&#109;&#109;&#97;&#32;&#125;&#123;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"54\" style=\"vertical-align: -6px;\" \/>, we obtain<\/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-cc1ff3d489b3e15c0055eb25e885d5bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#92;&#103;&#97;&#109;&#109;&#97;&#32;&#125;&#123;&#114;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#48;&#51;&#55;&#32;&#78;&#47;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#123;&#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;&#45;&#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;&#109;&#125;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#55;&#52;&#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;&#78;&#47;&#109;&#125;&#125;&#94;&#123;&#50;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#55;&#52;&#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;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#97;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"341\" style=\"vertical-align: -8px;\" \/><\/div>\n<p id=\"import-auto-id1448906\">We use a conversion factor to get this into units of mm Hg:<\/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-a78972d4d772238294206ac7d7a9763e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#55;&#52;&#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;&#78;&#47;&#109;&#125;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#46;&#48;&#48;&#32;&#109;&#109;&#32;&#72;&#103;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#51;&#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;&#125;&#61;&#53;&#46;&#53;&#54;&#32;&#109;&#109;&#32;&#72;&#103;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"325\" style=\"vertical-align: -12px;\" \/><\/div>\n<p id=\"import-auto-id1870548\"><strong>Discussion<\/strong><\/p>\n<p id=\"import-auto-id1926153\">Note that if a hole were to be made in the bubble, the air would be forced out, the bubble would decrease in radius, and the pressure inside would <em data-effect=\"italics\">increase<\/em> to atmospheric pressure (760 mm Hg).<\/p>\n<\/div>\n<p id=\"import-auto-id1248452\">Our lungs contain hundreds of millions of mucus-lined sacs called <em data-effect=\"italics\">alveoli<\/em>, which are very similar in size, and about 0.1 mm in diameter. (See <a href=\"#import-auto-id774766\" class=\"autogenerated-content\">(Figure)<\/a>.) You can exhale without muscle action by allowing surface tension to contract these sacs. Medical patients whose breathing is aided by a positive pressure respirator have air blown into the lungs, but are generally allowed to exhale on their own. Even if there is paralysis, surface tension in the alveoli will expel air from the lungs. Since pressure increases as the radii of the alveoli decrease, an occasional deep cleansing breath is needed to fully reinflate the alveoli. Respirators are programmed to do this and we find it natural, as do our companion dogs and cats, to take a cleansing breath before settling into a nap.<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id774766\">\n<div class=\"bc-figcaption figcaption\">Bronchial tubes in the lungs branch into ever-smaller structures, finally ending in alveoli. The alveoli act like tiny bubbles. The surface tension of their mucous lining aids in exhalation and can prevent inhalation if too great.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1548374\" data-alt=\"The alveoli at the end of the lung tubes enable exhalation and do not allow inhalation due to the surface tension of the mucous lining.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_08_06a.jpg\" data-media-type=\"image\/jpg\" alt=\"The alveoli at the end of the lung tubes enable exhalation and do not allow inhalation due to the surface tension of the mucous lining.\" width=\"300\" \/><\/span><\/p>\n<\/div>\n<p id=\"import-auto-id2598952\">The tension in the walls of the alveoli results from the membrane tissue and a liquid on the walls of the alveoli containing a long lipoprotein that acts as a surfactant (a surface-tension reducing substance). The need for the surfactant results from the tendency of small alveoli to collapse and the air to fill into the larger alveoli making them even larger (as demonstrated in <a href=\"#import-auto-id2054965\" class=\"autogenerated-content\">(Figure)<\/a>). During inhalation, the lipoprotein molecules are pulled apart and the wall tension increases as the radius increases (increased surface tension). During exhalation, the molecules slide back together and the surface tension decreases, helping to prevent a collapse of the alveoli. The surfactant therefore serves to change the wall tension so that small alveoli don\u2019t collapse and large alveoli are prevented from expanding too much. This tension change is a unique property of these surfactants, and is not shared by detergents (which simply lower surface tension). (See <a href=\"#import-auto-id2971179\" class=\"autogenerated-content\">(Figure)<\/a>.)<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id2971179\">\n<div class=\"bc-figcaption figcaption\">Surface tension as a function of surface area. The surface tension for lung surfactant decreases with decreasing area. This ensures that small alveoli don\u2019t collapse and large alveoli are not able to over expand. <\/div>\n<p><span data-type=\"media\" id=\"import-auto-id2973139\" data-alt=\"Graph of surface tension as a function of surface area for detergents and interstitial fluids.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_08_07a.jpg\" data-media-type=\"image\/png\" alt=\"Graph of surface tension as a function of surface area for detergents and interstitial fluids.\" width=\"300\" \/><\/span><\/p>\n<\/div>\n<p id=\"import-auto-id1374919\">If water gets into the lungs, the surface tension is too great and you cannot inhale. This is a severe problem in resuscitating drowning victims. A similar problem occurs in newborn infants who are born without this surfactant\u2014their lungs are very difficult to inflate. This condition is known as <em data-effect=\"italics\">hyaline membrane disease<\/em> and is a leading cause of death for infants, particularly in premature births. Some success has been achieved in treating hyaline membrane disease by spraying a surfactant into the infant\u2019s breathing passages. Emphysema produces the opposite problem with alveoli. Alveolar walls of emphysema victims deteriorate, and the sacs combine to form larger sacs. Because pressure produced by surface tension decreases with increasing radius, these larger sacs produce smaller pressure, reducing the ability of emphysema victims to exhale. A common test for emphysema is to measure the pressure and volume of air that can be exhaled.<\/p>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" id=\"fs-id1414382\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">Making Connections: Take-Home Investigation<\/div>\n<p id=\"import-auto-id2963064\">(1) Try floating a sewing needle on water. In order for this activity to work, the needle needs to be very clean as even the oil from your fingers can be sufficient to affect the surface properties of the needle. (2) Place the bristles of a paint brush into water. Pull the brush out and notice that for a short while, the bristles will stick together. The surface tension of the water surrounding the bristles is sufficient to hold the bristles together. As the bristles dry out, the surface tension effect dissipates. (3) Place a loop of thread on the surface of still water in such a way that all of the thread is in contact with the water. Note the shape of the loop. Now place a drop of detergent into the middle of the loop. What happens to the shape of the loop? Why? (4) Sprinkle pepper onto the surface of water. Add a drop of detergent. What happens? Why? (5) Float two matches parallel to each other and add a drop of detergent between them. What happens? Note: For each new experiment, the water needs to be replaced and the bowl washed to free it of any residual detergent.<\/p>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id2391861\">\n<h1 data-type=\"title\">Adhesion and Capillary Action<\/h1>\n<p id=\"import-auto-id1868222\">Why is it that water beads up on a waxed car but does not on bare paint? The answer is that the adhesive forces between water and wax are much smaller than those between water and paint. Competition between the forces of adhesion and cohesion are important in the macroscopic behavior of liquids. An important factor in studying the roles of these two forces is the angle <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-761998727948942ceb1b5763e45f01e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#104;&#101;&#116;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> between the tangent to the liquid surface and the surface. (See <a href=\"#import-auto-id1439052\" class=\"autogenerated-content\">(Figure)<\/a>.) The <span data-type=\"term\" id=\"import-auto-id2990625\">contact angle<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-761998727948942ceb1b5763e45f01e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#104;&#101;&#116;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> is directly related to the relative strength of the cohesive and adhesive forces. The larger the strength of the cohesive force relative to the adhesive force, the larger <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-761998727948942ceb1b5763e45f01e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#104;&#101;&#116;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> is, and the more the liquid tends to form a droplet. The smaller <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-761998727948942ceb1b5763e45f01e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#104;&#101;&#116;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> is, the smaller the relative strength, so that the adhesive force is able to flatten the drop. <a href=\"#import-auto-id3245851\" class=\"autogenerated-content\">(Figure)<\/a> lists contact angles for several combinations of liquids and solids.<\/p>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" id=\"fs-id2588349\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">Contact Angle<\/div>\n<p id=\"import-auto-id1177794\">The angle <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-761998727948942ceb1b5763e45f01e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#104;&#101;&#116;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> between the tangent to the liquid surface and the surface is called the contact angle.<\/p>\n<\/div>\n<div class=\"bc-figure figure\" id=\"import-auto-id1439052\">\n<div class=\"bc-figcaption figcaption\">In the photograph, water beads on the waxed car paint and flattens on the unwaxed paint. (a) Water forms beads on the waxed surface because the cohesive forces responsible for surface tension are larger than the adhesive forces, which tend to flatten the drop. (b) Water beads on bare paint are flattened considerably because the adhesive forces between water and paint are strong, overcoming surface tension. The contact angle <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-761998727948942ceb1b5763e45f01e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#104;&#101;&#116;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> is directly related to the relative strengths of the cohesive and adhesive forces. The larger <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-761998727948942ceb1b5763e45f01e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#104;&#101;&#116;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> is, the larger the ratio of cohesive to adhesive forces. (credit: P. P. Urone)<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1094155\" data-alt=\"Water is seen to make beads on the waxed surface of car paint and it remains flat on the surface without wax. The beads are due to the greater force of attraction between the water molecules than between the water molecules and the surface. On the surface without wax the force of attraction between the water molecules and paint is greater.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_08_08a.jpg\" data-media-type=\"image\/jpg\" alt=\"Water is seen to make beads on the waxed surface of car paint and it remains flat on the surface without wax. The beads are due to the greater force of attraction between the water molecules than between the water molecules and the surface. On the surface without wax the force of attraction between the water molecules and paint is greater.\" width=\"400\" \/><\/span><\/p>\n<\/div>\n<p id=\"import-auto-id2400994\">One important phenomenon related to the relative strength of cohesive and adhesive forces is <span data-type=\"term\" id=\"import-auto-id1253557\">capillary action<\/span>\u2014the tendency of a fluid to be raised or suppressed in a narrow tube, or <em data-effect=\"italics\">capillary tube<\/em>. This action causes blood to be drawn into a small-diameter tube when the tube touches a drop.<\/p>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" id=\"fs-id3158905\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">Capillary Action<\/div>\n<p id=\"import-auto-id3137631\">The tendency of a fluid to be raised or suppressed in a narrow tube, or capillary tube, is called capillary action.<\/p>\n<\/div>\n<p id=\"import-auto-id2647701\">If a capillary tube is placed vertically into a liquid, as shown in <a href=\"#fs-id1333088\" class=\"autogenerated-content\">(Figure)<\/a>, capillary action will raise or suppress the liquid inside the tube depending on the combination of substances. The actual effect depends on the relative strength of the cohesive and adhesive forces and, thus, the contact angle <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-761998727948942ceb1b5763e45f01e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#104;&#101;&#116;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> given in the table. If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-761998727948942ceb1b5763e45f01e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#104;&#101;&#116;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> is less than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-82ed7c74803abaf51c710730d5c2ce95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#48;&ordm;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/>, then the fluid will be raised; if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-761998727948942ceb1b5763e45f01e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#104;&#101;&#116;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> is greater than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-82ed7c74803abaf51c710730d5c2ce95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#48;&ordm;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/>, it will be suppressed. Mercury, for example, has a very large surface tension and a large contact angle with glass. When placed in a tube, the surface of a column of mercury curves downward, somewhat like a drop. The curved surface of a fluid in a tube is called a <strong>meniscus<\/strong>. The tendency of surface tension is always to reduce the surface area. Surface tension thus flattens the curved liquid surface in a capillary tube. This results in a downward force in mercury and an upward force in water, as seen in <a href=\"#fs-id1333088\" class=\"autogenerated-content\">(Figure)<\/a>.<\/p>\n<p id=\"import-auto-id3119502\">\n<div class=\"bc-figure figure\" id=\"fs-id1333088\">\n<div class=\"bc-figcaption figcaption\">(a) Mercury is suppressed in a glass tube because its contact angle is greater than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-82ed7c74803abaf51c710730d5c2ce95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#48;&ordm;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/>. Surface tension exerts a downward force as it flattens the mercury, suppressing it in the tube. The dashed line shows the shape the mercury surface would have without the flattening effect of surface tension. (b) Water is raised in a glass tube because its contact angle is nearly <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-b2c86509399d41cd7b0e9ffd8f6fe6ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&ordm;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>. Surface tension therefore exerts an upward force when it flattens the surface to reduce its area.<\/div>\n<p><span data-type=\"media\" id=\"fs-id1313828\" data-alt=\"Mercury kept in a container into which a narrow tube is inserted lowers its level inside the tube relative to the level in the rest of the container. In a similar situation, water rises in the tube so that the water level in the tube is above the water level in the rest of the container. This phenomenon is due to the large contact angle of mercury with glass and the smaller contact angle of water with glass.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_08_09a.jpg\" data-media-type=\"image\/jpeg\" alt=\"Mercury kept in a container into which a narrow tube is inserted lowers its level inside the tube relative to the level in the rest of the container. In a similar situation, water rises in the tube so that the water level in the tube is above the water level in the rest of the container. This phenomenon is due to the large contact angle of mercury with glass and the smaller contact angle of water with glass.\" width=\"350\" \/><\/span><\/p>\n<\/div>\n<table id=\"import-auto-id3245851\" summary=\"The table gives the contact angles of some substances.\">\n<caption><span data-type=\"title\">Contact Angles of Some Substances<\/span><\/caption>\n<thead>\n<tr>\n<th>\n              Interface\n            <\/th>\n<th>\n              Contact angle \u0398\n            <\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Mercury\u2013glass<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e608ae0a7380d558937adb9604c62907_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#52;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Water\u2013glass<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f6879427b2ea99225adb87ceb593ab6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Water\u2013paraffin<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-3b7a54f81d0528aa716033be0cd3a1fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#55;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"26\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Water\u2013silver<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-d237135e055cb753fca9232c2768ec76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#48;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Organic liquids (most)\u2013glass<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f6879427b2ea99225adb87ceb593ab6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Ethyl alcohol\u2013glass<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f6879427b2ea99225adb87ceb593ab6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Kerosene\u2013glass<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e9b7b7dd43aaeba59150a1ff37cd9719_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#54;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&ordm;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"import-auto-id2677223\">Capillary action can move liquids horizontally over very large distances, but the height to which it can raise or suppress a liquid in a tube is limited by its weight. It can be shown that this height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-14b463d0ecd5b350ced6cf1d6a12eef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"10\" style=\"vertical-align: 0px;\" \/> is given by <\/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-64a6b2619c398aa78074f63665101b0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#92;&#103;&#97;&#109;&#109;&#97;&#32;&#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;&#99;&#111;&#115;&#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;&#104;&#101;&#116;&#97;&#32;&#125;&#123;&#92;&#114;&#104;&#111;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#103;&#114;&#125;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"91\" style=\"vertical-align: -9px;\" \/><\/div>\n<p>If we look at the different factors in this expression, we might see how it makes good sense. The height is directly proportional to the surface tension <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4dfd339d0f13026ff7af56aa6f129380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#103;&#97;&#109;&#109;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/>, which is its direct cause. Furthermore, the height is inversely proportional to tube radius\u2014the smaller the radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/>, the higher the fluid can be raised, since a smaller tube holds less mass. The height is also inversely proportional to fluid density <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-43bc8be6acd1d7d6e61afc86bb1767f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#114;&#104;&#111;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>, since a larger density means a greater mass in the same volume. (See <a href=\"#import-auto-id2953655\" class=\"autogenerated-content\">(Figure)<\/a>.)<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id2953655\">\n<div class=\"bc-figcaption figcaption\">(a) Capillary action depends on the radius of a tube. The smaller the tube, the greater the height reached. The height is negligible for large-radius tubes. (b) A denser fluid in the same tube rises to a smaller height, all other factors being the same.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id2591168\" data-alt=\"The left image shows liquid in a container with four tubes of progressively smaller diameter inserted into the liquid. The liquid rises higher in the smaller-diameter tubes. The right image shows two containers, one holding a dense liquid and the other holding a less-dense liquid. Identical tubes are inserted into each liquid. The less-dense liquid rises higher in its tube than the more-dense liquid does in its tube.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_08_10a.jpg\" data-media-type=\"image\/jpg\" alt=\"The left image shows liquid in a container with four tubes of progressively smaller diameter inserted into the liquid. The liquid rises higher in the smaller-diameter tubes. The right image shows two containers, one holding a dense liquid and the other holding a less-dense liquid. Identical tubes are inserted into each liquid. The less-dense liquid rises higher in its tube than the more-dense liquid does in its tube.\" width=\"400\" \/><\/span><\/p>\n<\/div>\n<div data-type=\"example\" class=\"textbox examples\" id=\"fs-id2066941\">\n<div data-type=\"title\" class=\"title\">Calculating Radius of a Capillary Tube: Capillary Action: Tree Sap<\/div>\n<p id=\"import-auto-id3027640\">Can capillary action be solely responsible for sap rising in trees? To answer this question, calculate the radius of a capillary tube that would raise sap 100 m to the top of a giant redwood, assuming that sap\u2019s density is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-7d9419e446d4b6fabda25d7b5de27cb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#53;&#48;&#32;&#107;&#103;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#47;&#109;&#125;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"89\" style=\"vertical-align: -4px;\" \/>, its contact angle is zero, and its surface tension is the same as that of water at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-19874a5aebc273870da551e0f4c2712d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#46;&#48;&ordm;&#32;&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"46\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p id=\"import-auto-id3127685\"><strong>Strategy<\/strong><\/p>\n<p id=\"import-auto-id1907791\">The height to which a liquid will rise as a result of capillary action is given by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-d6e10bd093b8824bfcd40d9f0766cc45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#92;&#103;&#97;&#109;&#109;&#97;&#32;&#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;&#99;&#111;&#115;&#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;&#104;&#101;&#116;&#97;&#32;&#125;&#123;&#92;&#114;&#104;&#111;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#103;&#114;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"85\" style=\"vertical-align: -9px;\" \/>, and every quantity is known except for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p id=\"import-auto-id2396875\"><strong>Solution<\/strong><\/p>\n<p id=\"import-auto-id3176902\">Solving for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> and substituting known values produces<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-301\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-fc384b20756dccf31006f3a4141d0ff7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#108;&#108;&#125;&#114;&#38;&#32;&#61;&#38;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#92;&#103;&#97;&#109;&#109;&#97;&#32;&#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;&#99;&#111;&#115;&#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;&#104;&#101;&#116;&#97;&#32;&#125;&#123;&#92;&#114;&#104;&#111;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#103;&#104;&#125;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#46;&#48;&#55;&#50;&#56;&#32;&#78;&#47;&#109;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#111;&#115;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&ordm;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#53;&#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;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#56;&#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;&#109;&#47;&#115;&#125;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#48;&#32;&#109;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#92;&#92;&#32;&#38;&#32;&#61;&#38;&#32;&#49;&#46;&#52;&#49;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#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;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#46;&#125;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"339\" style=\"vertical-align: -17px;\" \/><\/div>\n<p id=\"import-auto-id2621794\"><strong>Discussion<\/strong><\/p>\n<p id=\"import-auto-id3089330\">This result is unreasonable. Sap in trees moves through the <em data-effect=\"italics\">xylem<\/em>, which forms tubes with radii as small as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-795c13022452976224e9e7c7682e3533_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#53;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#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;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"78\" style=\"vertical-align: -1px;\" \/>. This value is about 180 times as large as the radius found necessary here to raise sap <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-1b07e1c7e5ee123f4e5e10ab3208189f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#48;&#32;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"47\" style=\"vertical-align: -1px;\" \/>. This means that capillary action alone cannot be solely responsible for sap getting to the tops of trees.<\/p>\n<\/div>\n<p>How <em data-effect=\"italics\">does<\/em> sap get to the tops of tall trees? (Recall that a column of water can only rise to a height of 10 m  when there is a vacuum at the top\u2014see <a href=\"\/contents\/5f0b0e0e-e825-4aeb-9c8e-1f64a6942233@3#fs-id2937185\" class=\"autogenerated-content\">(Figure)<\/a>.) The question has not been completely resolved, but it appears that it is pulled up like a chain held together by cohesive forces. As each molecule of sap enters a leaf and evaporates (a process called transpiration), the entire chain is pulled up a notch. So a negative pressure created by water evaporation must be present to pull the sap up through the xylem vessels. In most situations, <em data-effect=\"italics\">fluids can push but can exert only negligible pull<\/em>, because the cohesive forces seem to be too small to hold the molecules tightly together. But in this case, the cohesive force of water molecules provides a very strong pull. <a href=\"#import-auto-id2051381\" class=\"autogenerated-content\">(Figure)<\/a> shows one device for studying negative pressure. Some experiments have demonstrated that negative pressures sufficient to pull sap to the tops of the tallest trees <em data-effect=\"italics\">can<\/em> be achieved.<\/p>\n<div class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">(a) When the piston is raised, it stretches the liquid slightly, putting it under tension and creating a negative absolute pressure <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a8a3f94c589e2c0a6e14f62fdd215387_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#45;&#70;&#47;&#65;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"85\" style=\"vertical-align: -5px;\" \/>. (b) The liquid eventually separates, giving an experimental limit to negative pressure in this liquid.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1381777\" data-alt=\"When the piston is raised the liquid stretches somewhat, which results in negative pressure.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_08_11a.jpg\" data-media-type=\"image\/jpg\" alt=\"When the piston is raised the liquid stretches somewhat, which results in negative pressure.\" width=\"200\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<div class=\"section-summary\" data-depth=\"1\" id=\"fs-id3082720\">\n<h1 data-type=\"title\">Section Summary<\/h1>\n<ul id=\"fs-id1827717\">\n<li id=\"import-auto-id3109651\">Attractive forces between molecules of the same type are called cohesive forces.<\/li>\n<li id=\"import-auto-id3028701\">Attractive forces between molecules of different types are called adhesive forces.<\/li>\n<li id=\"import-auto-id3192000\">Cohesive forces between molecules cause the surface of a liquid to contract to the smallest possible surface area. This general effect is called surface tension.<\/li>\n<li>Capillary action is the tendency of a fluid to be raised or suppressed in a narrow tube, or capillary tube which is due to the relative strength of cohesive and adhesive forces.<\/li>\n<\/ul>\n<\/div>\n<div class=\"conceptual-questions\" data-depth=\"1\" id=\"fs-id1383406\" data-element-type=\"conceptual-questions\">\n<h1 data-type=\"title\">Conceptual Questions<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3245014\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3415497\">\n<p>The density of oil is less than that of water, yet a loaded oil tanker sits lower in the water than an empty one. Why?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1921000\">\n<p id=\"import-auto-id2421560\">Is surface tension due to cohesive or adhesive forces, or both?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3028474\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2396594\">\n<p id=\"import-auto-id3009722\">Is capillary action due to cohesive or adhesive forces, or both?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1486629\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1888301\">\n<p id=\"import-auto-id3108344\">Birds such as ducks, geese, and swans have greater densities than water, yet they are able to sit on its surface. Explain this ability, noting that water does not wet their feathers and that they cannot sit on soapy water.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2971778\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2381951\">\n<p>Water beads up on an oily sunbather, but not on her neighbor, whose skin is not oiled. Explain in terms of cohesive and adhesive forces.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2682132\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2403876\">\n<p id=\"import-auto-id2663132\">Could capillary action be used to move fluids in a \u201cweightless\u201d environment, such as in an orbiting space probe?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2437631\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3025302\">\n<p id=\"import-auto-id3119512\">What effect does capillary action have on the reading of a manometer with uniform diameter? Explain your answer.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1993729\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2514692\">\n<p id=\"import-auto-id2666531\">Pressure between the inside chest wall and the outside of the lungs normally remains negative. Explain how pressure inside the lungs can become positive (to cause exhalation) without muscle action.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"problems-exercises\" data-depth=\"1\" id=\"fs-id1425593\" data-element-type=\"problems-exercises\">\n<h1 data-type=\"title\">Problems &amp; Exercises<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3123703\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2402900\">\n<p id=\"import-auto-id2671168\">What is the pressure inside an alveolus having a radius of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-1d49cb5c742aa2fcf1b633c2be379509_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;&#53;&#48;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#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;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"87\" style=\"vertical-align: -1px;\" \/> if the surface tension of the fluid-lined wall is the same as for soapy water? You may assume the pressure is the same as that created by a spherical bubble.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2684015\" data-element-type=\"problems-exercises\">\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-84920377b973fc38e9f0ec0e42d838d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#57;&#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;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#47;&#109;&#125;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"75\" style=\"vertical-align: -4px;\" \/>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2667857\">\n<p id=\"import-auto-id1848842\">(a) The pressure inside an alveolus with a <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-0ac753258fa592505a2abc286a6944fa_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;&#45;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"67\" style=\"vertical-align: -1px;\" \/>-m radius is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-904f770656a9b50c6fdc876045428d64_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;&#52;&#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=\"81\" style=\"vertical-align: -1px;\" \/>, due to its fluid-lined walls. Assuming the alveolus acts like a spherical bubble, what is the surface tension of the fluid? (b) Identify the likely fluid. (You may need to extrapolate between values in <a href=\"#import-auto-id1816998\" class=\"autogenerated-content\">(Figure)<\/a>.)<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2684580\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1588311\">\n<p>What is the gauge pressure in millimeters of mercury inside a soap bubble 0.100 m in diameter?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" data-element-type=\"problems-exercises\">\n<p id=\"import-auto-id2930063\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-adbea3586808f2e0c8baa249a0f5438e_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;&#50;&#51;&#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;&#109;&#109;&#32;&#72;&#103;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"130\" style=\"vertical-align: -3px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id909629\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1380194\">\n<p id=\"import-auto-id1579340\">Calculate the force on the slide wire in <a href=\"#import-auto-id3306680\" class=\"autogenerated-content\">(Figure)<\/a> if it is 3.50 cm long and the fluid is ethyl alcohol.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3013760\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3416522\">\n<p id=\"import-auto-id1220838\"><a href=\"#import-auto-id2953655\" class=\"autogenerated-content\">(Figure)<\/a>(a) shows the effect of tube radius on the height to which capillary action can raise a fluid. (a) Calculate the height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-14b463d0ecd5b350ced6cf1d6a12eef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"10\" style=\"vertical-align: 0px;\" \/> for water in a glass tube with a radius of 0.900 cm\u2014a rather large tube like the one on the left. (b) What is the radius of the glass tube on the right if it raises water to 4.00 cm?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2989927\" data-element-type=\"problems-exercises\">\n<p>(a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-639735d8387ce7f6c476d6d3a8aaec3c_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;&#53;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#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;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"86\" style=\"vertical-align: -1px;\" \/><\/p>\n<p id=\"import-auto-id1909395\">(b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-b5e029314c1f27865f8d65602bea12fe_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;&#55;&#49;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#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;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"87\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2405199\">\n<p id=\"import-auto-id2401535\">We stated in <a href=\"#fs-id2066941\" class=\"autogenerated-content\">(Figure)<\/a> that a xylem tube is of radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-13b9b966f37095cfce9ee95775585af5_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;&#53;&#48;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#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;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"87\" style=\"vertical-align: -1px;\" \/>. Verify that such a tube raises sap less than a meter by finding <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-14b463d0ecd5b350ced6cf1d6a12eef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"10\" style=\"vertical-align: 0px;\" \/> for it, making the same assumptions that sap\u2019s density is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-8cbf259aa7e24cb7ba8d13aa60ad5a1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#53;&#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=\"88\" style=\"vertical-align: -4px;\" \/>, its contact angle is zero, and its surface tension is the same as that of water at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-19874a5aebc273870da551e0f4c2712d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#46;&#48;&ordm;&#32;&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"46\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1986155\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1954890\">\n<p id=\"import-auto-id1484935\">What fluid is in the device shown in <a href=\"#import-auto-id3306680\" class=\"autogenerated-content\">(Figure)<\/a> if the force is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-603d347bf2f54c5af0059d4b9df83f57_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;&#54;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#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;&#78;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"85\" style=\"vertical-align: -1px;\" \/> and the length of the wire is 2.50 cm? Calculate the surface tension <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4dfd339d0f13026ff7af56aa6f129380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#103;&#97;&#109;&#109;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> and find a likely match from <a href=\"#import-auto-id1816998\" class=\"autogenerated-content\">(Figure)<\/a>.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2441420\" data-element-type=\"problems-exercises\">\n<p id=\"import-auto-id2391306\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-658d26a42e1b222d4035fc91ea71cc96_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;&#50;&#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;&#78;&#47;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/p>\n<p id=\"import-auto-id3037197\">Based on the values in table, the fluid is probably glycerin.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1427554\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1343201\">\n<p>If the gauge pressure inside a rubber balloon with a 10.0-cm radius is 1.50 cm of water, what is the effective surface tension of the balloon?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2627309\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2653975\">\n<p id=\"import-auto-id1916804\">Calculate the gauge pressures inside 2.00-cm-radius bubbles of water, alcohol, and soapy water. Which liquid forms the most stable bubbles, neglecting any effects of evaporation?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2052753\" data-element-type=\"problems-exercises\">\n<p id=\"import-auto-id1390466\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-1d2eecece8cabdefadb2715c715e25c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#108;&#108;&#125;&#123;&#80;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#125;&#125;&#38;&#32;&#61;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#52;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#54;&#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;&#44;&#92;&#92;&#32;&#123;&#80;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#125;&#125;&#38;&#32;&#61;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#46;&#52;&#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;&#44;&#92;&#92;&#32;&#123;&#80;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#119;&#125;&#125;&#38;&#32;&#61;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#55;&#46;&#52;&#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;&#78;&#47;&#109;&#125;&#125;&#94;&#123;&#50;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"68\" width=\"158\" style=\"vertical-align: -28px;\" \/><\/p>\n<p id=\"import-auto-id1934620\">Alcohol forms the most stable bubble, since the absolute pressure inside is closest to atmospheric pressure.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3123947\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2398646\">\n<p id=\"import-auto-id3172495\">Suppose water is raised by capillary action to a height of 5.00 cm in a glass tube. (a) To what height will it be raised in a paraffin tube of the same radius? (b) In a silver tube of the same radius?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3062468\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1485735\">\n<p id=\"import-auto-id3191626\">Calculate the contact angle <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-761998727948942ceb1b5763e45f01e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#104;&#101;&#116;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> for olive oil if capillary action raises it to a height of 7.07 cm in a glass tube with a radius of 0.100 mm. Is this value consistent with that for most organic liquids?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2583363\" data-element-type=\"problems-exercises\">\n<p id=\"import-auto-id2453951\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-d9a2adaac40f08444ab692c1bfaae74c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#46;&#49;&ordm;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"22\" style=\"vertical-align: -1px;\" \/><\/p>\n<p id=\"import-auto-id1587278\">This is near the value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-b575a66b78fa57c473a63a12c9e72f1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#104;&#101;&#116;&#97;&#32;&#61;&#48;&ordm;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: 0px;\" \/> for most organic liquids.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3091822\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1427415\">\n<p id=\"import-auto-id3027871\">When two soap bubbles touch, the larger is inflated by the smaller until they form a single bubble. (a) What is the gauge pressure inside a soap bubble with a 1.50-cm radius? (b) Inside a 4.00-cm-radius soap bubble? (c) Inside the single bubble they form if no air is lost when they touch?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1910033\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3176215\">\n<p>Calculate the ratio of the heights to which water and mercury are raised by capillary action in the same glass tube.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2056256\" data-element-type=\"problems-exercises\">\n<p id=\"import-auto-id3255891\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-0b996903664d1166aa30c023d9447297_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#55;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"45\" style=\"vertical-align: 0px;\" \/><\/p>\n<p id=\"import-auto-id3397701\">The ratio is negative because water is raised whereas mercury is lowered.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3035905\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3035906\">\n<p id=\"import-auto-id3260674\">What is the ratio of heights to which ethyl alcohol and water are raised by capillary action in the same glass tube?<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"footnote-refs\">\n<h2 data-type=\"footnote-title\">Footnotes<\/h2>\n<ol>\n<li><a data-type=\"footnote-ref\" href=\"#footnote-ref1\">1<\/a> At 20\u00baC unless otherwise stated.<\/li>\n<\/ol>\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-id1419756\">\n<dt>adhesive forces<\/dt>\n<dd id=\"fs-id2601877\">the attractive forces between molecules of different types<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id1546590\">\n<dt>capillary action<\/dt>\n<dd id=\"fs-id2658153\">the tendency of a fluid to be raised or lowered in a narrow tube<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2949904\">\n<dt>cohesive forces<\/dt>\n<dd id=\"fs-id1303384\">the attractive forces between molecules of the same type<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id3175910\">\n<dt>contact angle<\/dt>\n<dd id=\"fs-id2410483\">the angle <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-761998727948942ceb1b5763e45f01e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#104;&#101;&#116;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> between the tangent to the liquid surface and the surface<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id3101618\">\n<dt>surface tension<\/dt>\n<dd id=\"fs-id1561031\">the cohesive forces between molecules which cause the surface of a liquid to contract to the smallest possible surface area<\/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-614","chapter","type-chapter","status-publish","hentry","license-all-rights-reserved"],"part":562,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/614","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\/614\/revisions"}],"predecessor-version":[{"id":615,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/614\/revisions\/615"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/parts\/562"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/614\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/media?parent=614"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapter-type?post=614"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/contributor?post=614"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/license?post=614"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}