{"id":1463,"date":"2016-03-09T17:38:05","date_gmt":"2016-03-09T17:38:05","guid":{"rendered":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/?p=1463"},"modified":"2016-03-09T17:38:05","modified_gmt":"2016-03-09T17:38:05","slug":"properties-of-pure-substancescompressibility-factora-measure-of-deviation-from-ideal-gas-behavior","status":"publish","type":"post","link":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/properties-of-pure-substancescompressibility-factora-measure-of-deviation-from-ideal-gas-behavior\/","title":{"rendered":"PROPERTIES OF PURE SUBSTANCES:COMPRESSIBILITY FACTOR&mdash;A MEASURE OF DEVIATION FROM IDEAL-GAS BEHAVIOR"},"content":{"rendered":"<div class=\"uykmd6a0dce4f14d22\" ><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.uykmd6a0dce4f14d22 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.uykmd6a0dce4f14d22 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.uykmd6a0dce4f14d22 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.uykmd6a0dce4f14d22 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.uykmd6a0dce4f14d22 {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n<p align=\"justify\"><font size=\"5\"><b>COMPRESSIBILIT<\/b><b>Y FACTOR\u2014A MEASURE OF<\/b><b> <\/b><b>DEVI<\/b><b>A<\/b><b>TIO<\/b><b>N FROM IDEAL-GAS BEHAVIOR<\/b><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">The ideal-gas equation is very simple and thus very convenient to use. But, as illustrated in Fig. 3\u201349, gases deviate from ideal-gas behavior significantly at states near the saturation region and the critical point. This deviation from<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/PROPERTIES-OF-PURE-SUBSTANCES-0149.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=\"PROPERTIES OF PURE SUBSTANCES-0149\" border=\"0\" alt=\"PROPERTIES OF PURE SUBSTANCES-0149\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/PROPERTIES-OF-PURE-SUBSTANCES-0149_thumb.jpg\" width=\"398\" height=\"484\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">for most substances, but not for air. Air (or nitrogen) can be treated as an ideal gas at this temperature and atmospheric pressure with an error under 1 per- cent. This is because nitrogen is well over its critical temperature (-147\u00b0C) and away from the saturation region. At this temperature and pressure, how- ever, most substances would exist in the solid phase. Therefore, the pressure or temperature of a substance is high or low relative to its critical temperature or pressure.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">Gases behave differently at a given temperature and pressure, but they behave very much the same at temperatures and pressures normalized with re- spect to their critical temperatures and pressures. The normalization is done as<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/PROPERTIES-OF-PURE-SUBSTANCES-0150.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=\"PROPERTIES OF PURE SUBSTANCES-0150\" border=\"0\" alt=\"PROPERTIES OF PURE SUBSTANCES-0150\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/PROPERTIES-OF-PURE-SUBSTANCES-0150_thumb.jpg\" width=\"226\" height=\"37\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">Here <i>P<\/i><i>R <\/i>is called the <b>reduced pressure <\/b>and <i>T<\/i><i>R <\/i>the <b>reduced temperature. <\/b>The <i>Z <\/i>factor for all gases is approximately the same at the same reduced pressure and temperature. This is called the <b>principle of corresponding states. <\/b>In Fig. 3\u201351, the experimentally determined <i>Z <\/i>values are plotted against <i>P<\/i><i>R <\/i>and <i>T<\/i><i>R <\/i>for several gases. The gases seem to obey the principle of corresponding states<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/PROPERTIES-OF-PURE-SUBSTANCES-0151.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=\"PROPERTIES OF PURE SUBSTANCES-0151\" border=\"0\" alt=\"PROPERTIES OF PURE SUBSTANCES-0151\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/PROPERTIES-OF-PURE-SUBSTANCES-0151_thumb.jpg\" width=\"523\" height=\"408\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">reasonably well. By curve-fitting all the data, we obtain the <b>generalized com<\/b><\/font><font size=\"5\"><b>p<\/b><b>r<\/b><b>essibilit<\/b><b>y chart <\/b>that can be used for all gases (Fig. A\u201334).<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">The following observations can be made from the generalized compressibility chart:<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/PROPERTIES-OF-PURE-SUBSTANCES-0152.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=\"PROPERTIES OF PURE SUBSTANCES-0152\" border=\"0\" alt=\"PROPERTIES OF PURE SUBSTANCES-0152\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/PROPERTIES-OF-PURE-SUBSTANCES-0152_thumb.jpg\" width=\"181\" height=\"332\"><\/a><\/font> <\/p><div class=\"yebwh6a0dce4f14fe2\" ><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.yebwh6a0dce4f14fe2 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.yebwh6a0dce4f14fe2 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.yebwh6a0dce4f14fe2 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.yebwh6a0dce4f14fe2 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.yebwh6a0dce4f14fe2 {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n<div class=\"ciaxe6a0dce4f14ea6\" ><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.ciaxe6a0dce4f14ea6 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.ciaxe6a0dce4f14ea6 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.ciaxe6a0dce4f14ea6 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.ciaxe6a0dce4f14ea6 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.ciaxe6a0dce4f14ea6 {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n\n<p align=\"justify\"><font size=\"5\"><b>1. <\/b>At very low pressures (<i>P<\/i><i>R <\/i> 1), the gases behave as an ideal gas <\/font><font size=\"5\">regardless of temperature (Fig. 3\u201352),<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><b>2. <\/b>At high temperatures (<i>T<\/i><i>R <\/i>&gt; 2), ideal-gas behavior can be assumed with good accuracy regardless of pressure (except when <i>P<\/i><i>R <\/i>\ufffd1).<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><b>3. <\/b>The deviation of a gas from ideal-gas behavior is greatest in the vicinity of the critical point (Fig. 3\u201353).<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/PROPERTIES-OF-PURE-SUBSTANCES-0153.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=\"PROPERTIES OF PURE SUBSTANCES-0153\" border=\"0\" alt=\"PROPERTIES OF PURE SUBSTANCES-0153\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/PROPERTIES-OF-PURE-SUBSTANCES-0153_thumb.jpg\" width=\"362\" height=\"453\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">When <i>P <\/i>and \u03c5, or <i>T <\/i>and \u03c5, are given instead of <i>P <\/i>and <i>T<\/i>, the generalized compressibility chart can still be used to determine the third property, but it would involve tedious trial and error. Therefore, it is necessary to define one <\/font><font size=\"5\">more reduced property called the <b>pseudo-reduced specific volume <\/b>\u03c5<i>R <\/i>as<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/PROPERTIES-OF-PURE-SUBSTANCES-0154.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=\"PROPERTIES OF PURE SUBSTANCES-0154\" border=\"0\" alt=\"PROPERTIES OF PURE SUBSTANCES-0154\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/PROPERTIES-OF-PURE-SUBSTANCES-0154_thumb.jpg\" width=\"220\" height=\"33\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">Note that \u03c5<i>R <\/i>is defined differently from <i>P<\/i><i>R <\/i>and <i>T<\/i><i>R<\/i>. It is related to <i>T<\/i>cr and <i>P<\/i>cr <\/font><font size=\"5\">instead of \u03c5cr. Lines of constant \u03c5<i>R <\/i>are also added to the compressibility <\/font><font size=\"5\">charts, and this enables one to determine <i>T <\/i>or <i>P <\/i>without having to resort to <\/font><font size=\"5\">time-consuming iterations (Fig. 3\u201354).<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/PROPERTIES-OF-PURE-SUBSTANCES-0155.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=\"PROPERTIES OF PURE SUBSTANCES-0155\" border=\"0\" alt=\"PROPERTIES OF PURE SUBSTANCES-0155\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/PROPERTIES-OF-PURE-SUBSTANCES-0155_thumb.jpg\" width=\"183\" height=\"267\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/PROPERTIES-OF-PURE-SUBSTANCES-0156.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=\"PROPERTIES OF PURE SUBSTANCES-0156\" border=\"0\" alt=\"PROPERTIES OF PURE SUBSTANCES-0156\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/PROPERTIES-OF-PURE-SUBSTANCES-0156_thumb.jpg\" width=\"372\" height=\"464\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/PROPERTIES-OF-PURE-SUBSTANCES-0157.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=\"PROPERTIES OF PURE SUBSTANCES-0157\" border=\"0\" alt=\"PROPERTIES OF PURE SUBSTANCES-0157\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/PROPERTIES-OF-PURE-SUBSTANCES-0157_thumb.jpg\" width=\"349\" height=\"132\"><\/a><\/font> <\/p>\n<p align=\"justify\">\n<p align=\"justify\"><font size=\"5\"><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><\/font><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>COMPRESSIBILITY FACTOR\u2014A MEASURE OF DEVIATION FROM IDEAL-GAS BEHAVIOR The ideal-gas equation is very simple and thus very convenient to use. But, as illustrated in Fig. 3\u201349, gases deviate from ideal-gas behavior significantly at states near the saturation region and the critical point. This deviation from for most substances, but not for air. Air (or nitrogen) [&hellip;]<br \/><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/properties-of-pure-substancescompressibility-factora-measure-of-deviation-from-ideal-gas-behavior\/\" 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\/1463"}],"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=1463"}],"version-history":[{"count":1,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/posts\/1463\/revisions"}],"predecessor-version":[{"id":1464,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/posts\/1463\/revisions\/1464"}],"wp:attachment":[{"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/media?parent=1463"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/categories?post=1463"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/tags?post=1463"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}