{"id":1967,"date":"2016-03-12T19:03:59","date_gmt":"2016-03-12T19:03:59","guid":{"rendered":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/?p=1967"},"modified":"2016-03-12T19:03:59","modified_gmt":"2016-03-12T19:03:59","slug":"the-second-la-w-of-thermodynamicsthe-carnot-cycle","status":"publish","type":"post","link":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/the-second-la-w-of-thermodynamicsthe-carnot-cycle\/","title":{"rendered":"THE SECOND LA W OF THERMODYNAMICS:THE CARNOT CYCLE"},"content":{"rendered":"<div class=\"jxtsi6a0dcd5818240\" ><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.jxtsi6a0dcd5818240 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.jxtsi6a0dcd5818240 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.jxtsi6a0dcd5818240 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.jxtsi6a0dcd5818240 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.jxtsi6a0dcd5818240 {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n<p align=\"justify\"><font size=\"5\">\u25a0 <b>TH<\/b><b>E CARNOT CYCLE<\/b><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">We mentioned earlier that heat engines are cyclic devices and that the work<\/font><font size=\"5\">ing fluid of a heat engine returns to its initial state at the end of each cycle.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">Work is done by the working fluid during one part of the cycle and on the <\/font><font size=\"5\">working fluid during another part. The difference between these two is the net <\/font><font size=\"5\">work delivered by the heat engine. The efficiency of a heat-engine cycle greatly depends on how the individual processes that make up the cycle are executed. The net work, thus the cycle efficiency, can be maximized by using processes that require the least amount of work and deliver the most, that is, by using <i>r<\/i><i>eversibl<\/i><i>e processes. <\/i>Therefore, it is no surprise that the most efficient cycles are reversible cycles, that is, cycles that consist entirely of reversible processes.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">Reversible cycles cannot be achieved in practice because the irreversibilities associated with each process cannot be eliminated. However, reversible cycles provide upper limits on the performance of real cycles. Heat engines and refrigerators that work on reversible cycles serve as models to which ac<\/font><font size=\"5\">tual heat engines and refrigerators can be compared. Reversible cycles also serve as starting points in the development of actual cycles and are modified as needed to meet certain requirements.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">Probably the best known reversible cycle is the <b>Carno<\/b><b>t cycle, <\/b>first proposed in 1824 by French engineer Sadi Carnot. The theoretical heat engine that operates on the Carnot cycle is called the <b>Carno<\/b><b>t heat engine. <\/b>The Carnot <\/font><font size=\"5\">cycle is composed of four reversible processes\u2014two isothermal and two adiabatic\u2014and it can be executed either in a closed or a steady-flow system. Consider a closed system that consists of a gas contained in an adiabatic piston-cylinder device, as shown in Fig. 6\u201343. The insulation of the cylinder <\/font><font size=\"5\">head is such that it may be removed to bring the cylinder into contact with reservoirs to provide heat transfer. The four reversible processes that make up the Carnot cycle are as follows:<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><b>Reversibl<\/b><b>e Isothermal Expansion <\/b>(process 1-2, <i>T<\/i><i>H <\/i>= constant).<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">Initially (state 1), the temperature of the gas is <i>T<\/i><i>H <\/i>and the cylinder head <\/font><font size=\"5\">is in close contact with a source at temperature <i>T<\/i><i>H<\/i>. The gas is allowed <\/font><font size=\"5\">to expand slowly, doing work on the surroundings. As the gas expands, <\/font><font size=\"5\">the temperature of the gas tends to decrease. But as soon as the temperature drops by an infinitesimal amount <i>d<\/i><i>T<\/i>, some heat flows from the reservoir into the gas, raising the gas temperature to <i>T<\/i><i>H<\/i>. Thus, the gas temperature is kept constant at <i>T<\/i><i>H<\/i>. Since the temperature difference between the gas and the reservoir never exceeds a differential amount <i>d<\/i><i>T<\/i>, this is a reversible heat transfer process.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">It continues until the piston reaches position 2. The amount of total heat transferred to the gas during this process is <i>Q<\/i><i>H<\/i>.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><b>Reversibl<\/b><b>e Adiabatic Expansion <\/b>(process 2-3, temperature drops from <i>T<\/i><i>H <\/i>to <i>T<\/i><i>L<\/i>). At state 2, the reservoir that was in contact with the cylinder head is removed and replaced by insulation so that the system becomes adiabatic. The gas continues to expand slowly, doing work on the surroundings until its temperature drops from <i>T<\/i><i>H <\/i>to <i>T<\/i><i>L <\/i>(state 3).<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">The piston is assumed to be frictionless and the process to be quasi- equilibrium, so the process is reversible as well as adiabatic.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><b>Reversibl<\/b><b>e Isothermal Compression <\/b>(process 3-4, <i>T<\/i><i>L <\/i>= constant).<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">At state 3, the insulation at the cylinder head is removed, and the <\/font><font size=\"5\">cylinder is brought into contact with a sink at temperature <i>T<\/i><i>L<\/i>. Now the piston is pushed inward by an external force, doing work on the gas. As the gas is compressed, its temperature tends to rise. But as soon as it rises by an infinitesimal amount <i>d<\/i><i>T<\/i>, heat flows from the gas to the sink, causing the gas temperature to drop to <i>T<\/i><i>L<\/i>. Thus, the gas temperature is maintained constant at <i>T<\/i><i>L<\/i>. Since the temperature difference between the gas and the sink never exceeds a differential amount <i>d<\/i><i>T<\/i>, this is a reversible heat transfer process. It continues until the piston reaches state 4. The amount of heat rejected from the gas during this process is <i>Q<\/i><i>L<\/i>.<\/font> <\/p><div class=\"cydhr6a0dcd5818478\" ><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.cydhr6a0dcd5818478 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.cydhr6a0dcd5818478 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.cydhr6a0dcd5818478 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.cydhr6a0dcd5818478 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.cydhr6a0dcd5818478 {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n<div class=\"syftr6a0dcd5818360\" ><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.syftr6a0dcd5818360 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.syftr6a0dcd5818360 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.syftr6a0dcd5818360 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.syftr6a0dcd5818360 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.syftr6a0dcd5818360 {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n\n<p align=\"justify\"><font size=\"5\"><b>Reversibl<\/b><b>e Adiabatic Compression <\/b>(process 4-1, temperature rises from <i>T<\/i><i>L <\/i>to <i>T<\/i><i>H<\/i>). State 4 is such that when the low-temperature reservoir is removed, the insulation is put back on the cylinder head, and the gas is compressed in a reversible manner, the gas returns to its initial state (state 1). The temperature rises from <i>T<\/i><i>L <\/i>to <i>T<\/i><i>H <\/i>during this reversible adiabatic compression process, which completes the cycle.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">The <i>P-<\/i><i>V <\/i>diagram of this cycle is shown in Fig. 6\u201344. Remembering that on a <i>P-<\/i><i>V <\/i>diagram the area under the process curve represents the boundary work for quasi-equilibrium (internally reversible) processes, we see that the area un-<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/THE-SECOND-LAW-OF-THE-RMODYNAMICS-0116.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=\"THE SECOND LAW OF THE RMODYNAMICS-0116\" border=\"0\" alt=\"THE SECOND LAW OF THE RMODYNAMICS-0116\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/THE-SECOND-LAW-OF-THE-RMODYNAMICS-0116_thumb.jpg\" width=\"188\" height=\"183\"><\/a><\/font> <\/p>\n<p align=\"justify\">\n<p align=\"justify\"><i><font size=\"5\"><\/font><\/i><\/p>\n<p><font size=\"5\">der curve 1-2-3 is the work done by the gas during the expansion part of the cycle, and the area under curve 3-4-1 is the work done on the gas during the compression part of the cycle. The area enclosed by the path of the cycle (area 1-2-3-4-1) is the difference between these two and represents the net work&nbsp; <\/font><font size=\"5\">done during the cycle.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">Notice that if we acted stingily and compressed the gas at state 3 adiabatically instead of isothermally in an effort <i>t<\/i><i>o save Q<\/i><i>L<\/i>, we would end up back at state 2, retracing the process path 3-2. By doing so we would save <i>Q<\/i><i>L<\/i>, but we would not be able to obtain any net work output from this engine. This illustrates once more the necessity of a heat engine exchanging heat with at least two reservoirs at different temperatures to operate in a cycle and produce a net amount of work.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">The Carnot cycle can also be executed in a steady-flow system. It is dis- cussed in later chapters in conjunction with other power cycles.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">Being a reversible cycle, the Carnot cycle is the most efficient cycle operating between two specified temperature limits. Even though the Carnot cycle cannot be achieved in reality, the efficiency of actual cycles can be improved by attempting to approximate the Carnot cycle more closely.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><strong>The Reversed Carnot Cycle<\/strong><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">The Carnot heat-engine cycle just described is a totally reversible cycle.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">Therefore, all the processes that comprise it can be <i>r<\/i><i>eversed<\/i><i>, <\/i>in which case it becomes the <b>Carno<\/b><b>t refrigeration cycle. <\/b>This time, the cycle remains exactly the same, except that the directions of any heat and work interactions are reversed: Heat in the amount of <i>Q<\/i><i>L <\/i>is absorbed from the low-temperature reservoir, heat in the amount of <i>Q<\/i><i>H <\/i>is rejected to a high-temperature reservoir, and a work input of <i>W<\/i>net, in is required to accomplish all this.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">The <i>P-<\/i><i>V <\/i>diagram of the reversed Carnot cycle is the same as the one given for the Carnot cycle, except that the directions of the processes are reversed, as shown in Fig. 6\u201345.<\/font><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u25a0 THE CARNOT CYCLE We mentioned earlier that heat engines are cyclic devices and that the working fluid of a heat engine returns to its initial state at the end of each cycle. Work is done by the working fluid during one part of the cycle and on the working fluid during another part. The [&hellip;]<br \/><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/the-second-la-w-of-thermodynamicsthe-carnot-cycle\/\" 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\/1967"}],"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=1967"}],"version-history":[{"count":1,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/posts\/1967\/revisions"}],"predecessor-version":[{"id":1968,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/posts\/1967\/revisions\/1968"}],"wp:attachment":[{"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/media?parent=1967"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/categories?post=1967"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/tags?post=1967"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}