{"id":2346,"date":"2016-03-14T12:39:19","date_gmt":"2016-03-14T12:39:19","guid":{"rendered":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/?p=2346"},"modified":"2016-03-14T12:39:19","modified_gmt":"2016-03-14T12:39:19","slug":"summary-of-entropy","status":"publish","type":"post","link":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/summary-of-entropy\/","title":{"rendered":"SUMMARY OF ENTROPY"},"content":{"rendered":"<div class=\"oarpz6a0dbcafde3ce\" ><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.oarpz6a0dbcafde3ce {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.oarpz6a0dbcafde3ce {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.oarpz6a0dbcafde3ce {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.oarpz6a0dbcafde3ce {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.oarpz6a0dbcafde3ce {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n<p align=\"justify\"><font size=\"5\"><b>SUMMA<\/b><b>R<\/b><b>Y<\/b><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">The second law of thermodynamics leads to the definition of a new property called <i>ent<\/i><i>r<\/i><i>op<\/i><i>y<\/i><i>, <\/i>which is a quantitative measure of microscopic disorder for a system. The definition of entropy is based on the <i>Clausius inequality, <\/i>given by<\/font><\/p>\n<p><i> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0284.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=\"ENTROPY-0284\" border=\"0\" alt=\"ENTROPY-0284\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0284_thumb.jpg\" width=\"106\" height=\"36\"><\/a><\/font><\/i><font size=\"5\">where the equality holds for internally or totally reversible <\/font><font size=\"5\">processes and the inequality for irreversible processes. Any <\/font><font size=\"5\">quantity whose cyclic integral is zero is a property, and entropy is defined as<\/font><\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0285.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=\"ENTROPY-0285\" border=\"0\" alt=\"ENTROPY-0285\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0285_thumb.jpg\" width=\"257\" height=\"173\"><\/a><\/font><\/p>\n<p align=\"justify\"><font size=\"5\">where <i>S<\/i>gen is the <i>ent<\/i><i>r<\/i><i>op<\/i><i>y generated <\/i>during the process. Entropy change is caused by heat transfer, mass flow, and irreversibili<\/font><font size=\"5\">ties. Heat transfer to a system increases the entropy, and heat <\/font><font size=\"5\">transfer from a system decreases it. The effect of irreversibili- ties is always to increase the entropy.<\/font><\/p>\n<p align=\"justify\"><font size=\"5\">Entropy is a property, and it can be expressed in terms of more familiar properties through the <i>T ds <\/i>relations, ex<\/font><font size=\"5\">pressed as<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0286.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=\"ENTROPY-0286\" border=\"0\" alt=\"ENTROPY-0286\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0286_thumb.jpg\" width=\"233\" height=\"68\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">These two relations have many uses in thermodynamics and <\/font><font size=\"5\">serve as the starting point in developing entropy-change relations for processes. The successful use of <i>T ds <\/i>relations de- pends on the availability of property relations. Such relations do not exist for a general pure substance but are available for <\/font><font size=\"5\">incompressible substances (solids, liquids) and ideal gases.<\/font> <\/p><div class=\"rhobk6a0dbcafde71f\" ><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.rhobk6a0dbcafde71f {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.rhobk6a0dbcafde71f {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.rhobk6a0dbcafde71f {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.rhobk6a0dbcafde71f {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.rhobk6a0dbcafde71f {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n<div class=\"ktdcc6a0dbcafde4eb\" ><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.ktdcc6a0dbcafde4eb {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.ktdcc6a0dbcafde4eb {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.ktdcc6a0dbcafde4eb {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.ktdcc6a0dbcafde4eb {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.ktdcc6a0dbcafde4eb {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n\n<p align=\"justify\"><font size=\"5\">The <i>entropy-change <\/i>and <i>isentropic relations <\/i>for a process <\/font><font size=\"5\">can be summarized as follows:<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0289.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=\"ENTROPY-0289\" border=\"0\" alt=\"ENTROPY-0289\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0289_thumb.jpg\" width=\"249\" height=\"484\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0290.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=\"ENTROPY-0290\" border=\"0\" alt=\"ENTROPY-0290\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0290_thumb.jpg\" width=\"277\" height=\"285\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">The work done during a steady-flow process is proportional to <\/font><font size=\"5\">the specific volume. Therefore, u should be kept as small as <\/font><font size=\"5\">possible during a compression process to minimize the work input and as large as possible during an expansion process to maximize the work output.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">The reversible work inputs to a compressor compressing an ideal gas from <i>T<\/i>1, <i>P<\/i>1 to <i>P<\/i>2 in an isentropic (<i>P<\/i>u<i>k <\/i>= constant), <\/font><font size=\"5\">polytropic (<i>P<\/i>u<i>n <\/i>= constant), or isothermal (<i>P<\/i>u = constant) <\/font><font size=\"5\">manner, are determined by integration for each case with the following results:<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0291.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=\"ENTROPY-0291\" border=\"0\" alt=\"ENTROPY-0291\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0291_thumb.jpg\" width=\"275\" height=\"155\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">The work input to a compressor can be reduced by using multistage compression with intercooling. For maximum savings from the work input, the pressure ratio across each stage of the compressor must be the same.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0292.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=\"ENTROPY-0292\" border=\"0\" alt=\"ENTROPY-0292\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0292_thumb.jpg\" width=\"277\" height=\"320\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><\/font><\/p>\n","protected":false},"excerpt":{"rendered":"<p>SUMMARY The second law of thermodynamics leads to the definition of a new property called entropy, which is a quantitative measure of microscopic disorder for a system. The definition of entropy is based on the Clausius inequality, given by where the equality holds for internally or totally reversible processes and the inequality for irreversible processes. 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