{"id":2572,"date":"2016-03-15T10:02:12","date_gmt":"2016-03-15T10:02:12","guid":{"rendered":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/?p=2572"},"modified":"2016-03-15T10:02:12","modified_gmt":"2016-03-15T10:02:12","slug":"gas-mixtures-and-psychrometricsp-v-t-behavior-of-gas-mixtures-ideal-and-real-gases","status":"publish","type":"post","link":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/gas-mixtures-and-psychrometricsp-v-t-behavior-of-gas-mixtures-ideal-and-real-gases\/","title":{"rendered":"GAS MIXTURES AND PSYCHROMETRICS:P-v-T BEHAVIOR OF GAS MIXTURES: IDEAL AND REAL GASES"},"content":{"rendered":"<div class=\"umhxv6a0dce4f46fe5\" ><script type=\"text\/javascript\">\n\tatOptions = {\n\t\t'key' : '61e5902552e2353963d8d2f1bd1f4a8f',\n\t\t'format' : 'iframe',\n\t\t'height' : 250,\n\t\t'width' : 300,\n\t\t'params' : {}\n\t};\n<\/script>\n<script type=\"text\/javascript\" src=\"\/\/www.highperformanceformat.com\/61e5902552e2353963d8d2f1bd1f4a8f\/invoke.js\"><\/script><\/div><style type=\"text\/css\">\r\n@media screen and (min-width: 1201px) {\r\n.umhxv6a0dce4f46fe5 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.umhxv6a0dce4f46fe5 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.umhxv6a0dce4f46fe5 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.umhxv6a0dce4f46fe5 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.umhxv6a0dce4f46fe5 {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n<p align=\"justify\"><font size=\"5\">\u25a0 <b><i>P-v-<\/i><\/b><b><i>T <\/i><\/b><b>BEH<\/b><b>A<\/b><b>VIO<\/b><b>R OF GAS MIXTURES:<\/b><b> <\/b><b>IDEA<\/b><b>L AND REAL GASES<\/b><\/font>  <\/p>\n<p align=\"justify\">\n<p align=\"justify\"><font size=\"5\"><i><\/i><\/font><\/p>\n<p align=\"justify\"><font size=\"5\">An ideal gas is defined as a gas whose molecules are spaced far apart so that the behavior of a molecule is not influenced by the presence of other molecules\u2014a situation encountered at low densities. We also mentioned that real gases approximate this behavior closely when they are at a low pressure or high temperature relative to their critical-point values. The <i>P<\/i>-\u03c5-<i>T <\/i>behavior of an ideal gas is expressed by the simple relation <i>P<\/i>\u03c5 = <i>RT<\/i>, which is called the <i>ideal-ga<\/i><i>s equation of state. <\/i>The <i>P<\/i>-\u03c5-<i>T <\/i>behavior of real gases is expressed by more complex equations of state or by <i>P<\/i>\u03c5 = <i>ZR<\/i><i>T<\/i>, where <i>Z <\/i>is the compressibility factor.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">When two or more ideal gases are mixed, the behavior of a molecule normally is not influenced by the presence of other similar or dissimilar molecules, and therefore a nonreacting mixture of ideal gases also behaves as an ideal gas. Air, for example, is conveniently treated as an ideal gas in the range where nitrogen and oxygen behave as ideal gases. When a gas mixture consists of real (nonideal) gases, however, the prediction of the <i>P<\/i>-\u03c5-<i>T <\/i>behavior of the mixture becomes rather involved.<\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\">The prediction of the <i>P<\/i>-\u03c5-<i>T <\/i>behavior of gas mixtures is usually based on two models: <i>Dalton\u2019s law of additive pressures <\/i>and <i>Amagat\u2019s law of additive volumes. <\/i>Both models are described and discussed below.<\/font>  <\/p>\n<h6 align=\"justify\"><font size=\"5\"><b>Dalton\u2019s law of additive pressures: <\/b>The pressure of a gas mixture is equal to the sum of the pressures each gas would exert if it existed alone at the mixture temperature and volume (Fig. 9\u20135).<\/font><\/h6>\n<p align=\"justify\"><font size=\"5\"><b><i>Amagat<\/i><\/b><b><i>\u2019<\/i><\/b><b><i>s law of additive volumes: <\/i><\/b><i>Th<\/i><i>e volume of a gas mixture is equal to the sum of the volumes each gas would occupy if it existed alone at the mixture temperature and pressure (Fig. 9\u20136).<\/i><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">Dalton\u2019s and Amagat\u2019s laws hold exactly for ideal-gas mixtures, but only approximately for real-gas mixtures. This is due to intermolecular forces that may be significant for real gases at high densities. For ideal gases, these two laws are identical and give identical results.<\/font><\/p>\n<p align=\"justify\"><font size=\"5\">Dalton\u2019s and Amagat\u2019s laws can be expressed as follows:<\/font>  <\/p>\n<p align=\"justify\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/GAS-MIXTURES-AND-PSYCHROMETRICS-0011.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"GAS MIXTURES AND PSYCHROMETRICS-0011\" border=\"0\" alt=\"GAS MIXTURES AND PSYCHROMETRICS-0011\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/GAS-MIXTURES-AND-PSYCHROMETRICS-0011_thumb.jpg\" width=\"392\" height=\"73\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/GAS-MIXTURES-AND-PSYCHROMETRICS-0012.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"GAS MIXTURES AND PSYCHROMETRICS-0012\" border=\"0\" alt=\"GAS MIXTURES AND PSYCHROMETRICS-0012\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/GAS-MIXTURES-AND-PSYCHROMETRICS-0012_thumb.jpg\" width=\"205\" height=\"420\"><\/a> <\/p>\n<p align=\"justify\"><font size=\"5\">In these relations, <i>P<\/i><i>i <\/i>is called the <b>component pressure <\/b>and <i>V<\/i><i>i <\/i>is called the <b>component volume <\/b>(Fig. 9\u20137). Note that <i>V<\/i><i>i <\/i>is the volume a component <i>would <\/i>occupy if it existed alone at <i>T<\/i><i>m <\/i>and <i>P<\/i><i>m<\/i>, not the actual volume occupied by the<\/font>&nbsp; <font size=\"5\">The volume a component would occupy if it existed alone at the mixture <i>T <\/i>and <i>P <\/i>is called the <i>component volume <\/i>(for ideal gases, it is equal to the partial volume <i>y<\/i><i>i<\/i><i>V<\/i><i>m<\/i>).<\/font>  <\/p><div class=\"kmfno6a0dce4f4722b\" ><script type=\"text\/javascript\">\n\tatOptions = {\n\t\t'key' : '0c1eb4c533eaedb7b996f49a5a4983a9',\n\t\t'format' : 'iframe',\n\t\t'height' : 300,\n\t\t'width' : 160,\n\t\t'params' : {}\n\t};\n<\/script>\n<script type=\"text\/javascript\" src=\"\/\/www.highperformanceformat.com\/0c1eb4c533eaedb7b996f49a5a4983a9\/invoke.js\"><\/script><\/div><style type=\"text\/css\">\r\n@media screen and (min-width: 1201px) {\r\n.kmfno6a0dce4f4722b {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.kmfno6a0dce4f4722b {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.kmfno6a0dce4f4722b {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.kmfno6a0dce4f4722b {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.kmfno6a0dce4f4722b {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n<div class=\"tgial6a0dce4f470f6\" ><script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-0778475562755157\"\n     crossorigin=\"anonymous\"><\/script>\n<!-- 300x600 hydraulics-and-pneumatics -->\n<ins class=\"adsbygoogle\"\n     style=\"display:inline-block;width:300px;height:600px\"\n     data-ad-client=\"ca-pub-0778475562755157\"\n     data-ad-slot=\"3735577695\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script><\/div><style type=\"text\/css\">\r\n@media screen and (min-width: 1201px) {\r\n.tgial6a0dce4f470f6 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.tgial6a0dce4f470f6 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.tgial6a0dce4f470f6 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.tgial6a0dce4f470f6 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.tgial6a0dce4f470f6 {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n\n<p align=\"justify\"><font size=\"5\">component in the mixture. (In a vessel that holds a gas mixture, each compo<\/font><font size=\"5\">nent fills the entire volume of the vessel. Therefore, the volume of each component is equal to the volume of the vessel.) Also, the ratio <i>P<\/i><i>i <\/i>\/<i>P<\/i><i>m <\/i>is called the <b>pressure fraction <\/b>and the ratio <i>V<\/i><i>i <\/i>\/<i>V<\/i><i>m <\/i>is called the <b>volume fraction <\/b>of component <i>i.<\/i><\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\"><strong>Ideal-Gas Mixtures<\/strong><\/font> <\/p>\n<h6 align=\"justify\"><font size=\"5\">For ideal gases, <i>P<\/i><i>i <\/i>and <i>V<\/i><i>i <\/i>can be related to <i>y<\/i><i>i <\/i>by using the ideal-gas relation for <\/font><font size=\"5\">both the components and the gas mixture:<\/font> <\/h6>\n<p align=\"justify\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/GAS-MIXTURES-AND-PSYCHROMETRICS-0013.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"GAS MIXTURES AND PSYCHROMETRICS-0013\" border=\"0\" alt=\"GAS MIXTURES AND PSYCHROMETRICS-0013\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/GAS-MIXTURES-AND-PSYCHROMETRICS-0013_thumb.jpg\" width=\"422\" height=\"121\"><\/a><\/p>\n<p align=\"justify\"><font size=\"5\">Equation 9\u20138 is strictly valid for ideal-gas mixtures since it is derived by assuming ideal-gas behavior for the gas mixture and each of its components. The quantity <i>y<\/i><i>i<\/i><i>P<\/i><i>m <\/i>is called the <b>partial pressure <\/b>(identical to the <i>component pressure <\/i>for ideal gases), and the quantity <i>y<\/i><i>i<\/i><i>V<\/i><i>m <\/i>is called the <b>partial volume <\/b>(identical to the <i>component volume <\/i>for ideal gases). <i>Note that for an ideal-gas mixture, the mole fraction, the pressure fraction, and the volume fraction of a component are identical.<\/i><\/font> <\/p>\n<h6 align=\"justify\"><font size=\"5\">The composition of an ideal-gas mixture (such as the exhaust gases leaving a combustion chamber) is frequently determined by a volumetric analysis (called the Orsat Analysis) and Eq. 9\u20138. A sample gas at a known volume, pressure, and temperature is passed into a vessel containing reagents that absorb one of the gases. The volume of the remaining gas is then measured at the original pressure and temperature. The ratio of the reduction in volume to the original volume (volume fraction) represents the mole fraction of that particular gas.<\/font><\/h6>\n<p align=\"justify\"><font size=\"5\"><b>Real-Ga<\/b><b>s Mixtures<\/b><\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\">Dalton\u2019s law of additive pressures and Amagat\u2019s law of additive volumes can<\/font>&nbsp; <font size=\"5\">also be used for real gases, often with reasonable accuracy. This time, how- ever, the component pressures or component volumes should be evaluated from relations that take into account the deviation of each component from ideal-gas behavior. One way of doing that is to use more exact equations of state (van der Waals, Beattie\u2013Bridgeman, Benedict\u2013Webb\u2013Rubin, etc.) in- stead of the ideal-gas equation of state. Another way is to use the compressibility factor (Fig. 9\u20138) as<\/font>  <\/p>\n<p align=\"justify\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/GAS-MIXTURES-AND-PSYCHROMETRICS-0014.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"GAS MIXTURES AND PSYCHROMETRICS-0014\" border=\"0\" alt=\"GAS MIXTURES AND PSYCHROMETRICS-0014\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/GAS-MIXTURES-AND-PSYCHROMETRICS-0014_thumb.jpg\" width=\"207\" height=\"172\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/GAS-MIXTURES-AND-PSYCHROMETRICS-0015.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"GAS MIXTURES AND PSYCHROMETRICS-0015\" border=\"0\" alt=\"GAS MIXTURES AND PSYCHROMETRICS-0015\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/GAS-MIXTURES-AND-PSYCHROMETRICS-0015_thumb.jpg\" width=\"417\" height=\"104\"><\/a> <\/p>\n<p align=\"justify\"><font size=\"5\">where <i>Z<\/i><i>i <\/i>is determined either at <i>T<\/i><i>m <\/i>and <i>V<\/i><i>m <\/i>(Dalton\u2019s law) or at <i>T<\/i><i>m <\/i>and <i>P<\/i><i>m <\/i>(Amagat\u2019s law) for each individual gas. It may seem that using either law will give the same result, but it does not.<\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\">The compressibility-factor approach, in general, gives more accurate results when the <i>Z<\/i><i>i<\/i>\u2019s in Eq. 9\u201310 are evaluated by using Amagat\u2019s law instead of<\/font>&nbsp; <font size=\"5\">Dalton\u2019s law. This is because Amagat\u2019s law involves the use of mixture pressure <i>P<\/i><i>m<\/i>, which accounts for the influence of intermolecular forces between the molecules of different gases. Dalton\u2019s law disregards the influence of dissimilar molecules in a mixture on each other. As a result, it tends to underpredict the pressure of a gas mixture for a given <i>V<\/i><i>m <\/i>and <i>T<\/i><i>m<\/i>. Therefore, Dalton\u2019s law is more appropriate for gas mixtures at low pressures. Amagat\u2019s law is more appropriate at high pressures.<\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\">Note that there is a significant difference between using the compressibility factor for a single gas and for a mixture of gases. The compressibility factor predicts the <i>P<\/i>-\u03c5-<i>T <\/i>behavior of single gases rather accurately, as discussed in Chap. 3, but not for mixtures of gases. When we use compressibility factors for the components of a gas mixture, we account for the influence of like molecules on each other; the influence of dissimilar molecules remains largely unaccounted for. Consequently, a property value predicted by this approach may be considerably different from the experimentally determined value.<\/font><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u25a0 P-v-T BEHAVIOR OF GAS MIXTURES: IDEAL AND REAL GASES An ideal gas is defined as a gas whose molecules are spaced far apart so that the behavior of a molecule is not influenced by the presence of other molecules\u2014a situation encountered at low densities. We also mentioned that real gases approximate this behavior closely [&hellip;]<br \/><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/gas-mixtures-and-psychrometricsp-v-t-behavior-of-gas-mixtures-ideal-and-real-gases\/\" class=\"more-link\" >Continue reading&#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/posts\/2572"}],"collection":[{"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/comments?post=2572"}],"version-history":[{"count":1,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/posts\/2572\/revisions"}],"predecessor-version":[{"id":2573,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/posts\/2572\/revisions\/2573"}],"wp:attachment":[{"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/media?parent=2572"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/categories?post=2572"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/tags?post=2572"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}