{"id":2081,"date":"2016-03-13T11:43:11","date_gmt":"2016-03-13T11:43:11","guid":{"rendered":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/?p=2081"},"modified":"2016-03-13T11:43:11","modified_gmt":"2016-03-13T11:43:11","slug":"entropythe-increase-of-entropy-principle","status":"publish","type":"post","link":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/entropythe-increase-of-entropy-principle\/","title":{"rendered":"ENTROPY:THE INCREASE OF ENTROPY PRINCIPLE"},"content":{"rendered":"<div class=\"eegnq6a0dc92d39adc\" ><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.eegnq6a0dc92d39adc {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.eegnq6a0dc92d39adc {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.eegnq6a0dc92d39adc {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.eegnq6a0dc92d39adc {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.eegnq6a0dc92d39adc {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n<h4 align=\"justify\"><font size=\"5\"><b>TH<\/b><b>E INCREASE OF ENTROPY PRINCIPLE<\/b><\/font><\/h4>\n<p align=\"justify\"><font size=\"5\">Consider a cycle that is made up of two processes: process 1-2, which is arbitrary (reversible or irreversible), and process 2-1, which is internally reversible, as shown in Fig. 7\u20135. From the Clausius inequality,<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0159.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-0159\" border=\"0\" alt=\"ENTROPY-0159\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0159_thumb.jpg\" width=\"64\" height=\"33\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0160.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-0160\" border=\"0\" alt=\"ENTROPY-0160\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0160_thumb.jpg\" width=\"418\" height=\"239\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">where the equality holds for an internally reversible process and the inequality for an irreversible process. We may conclude from these equations that the entropy change of a closed system during an irreversible process is greater than the integral of d<i>Q<\/i>\/<i>T <\/i>evaluated for that process. In the limiting case of a reversible process, these two quantities become equal. We again emphasize that <i>T <\/i>in these relations is the <i>absolute temperature <\/i>at the <i>boundary <\/i>where the differential heat d<i>Q <\/i>is transferred between the system and the surroundings.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">The quantity !::<i>S <\/i>= <i>S<\/i>2 &#8211; <i>S<\/i>1 represents the <i>entropy change <\/i>of the system. For a reversible process, it becomes equal to f21 d<i>Q<\/i>\/<i>T<\/i>, which represents the <i>ent<\/i><i>r<\/i><i>op<\/i><i>y transfer <\/i>with heat.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">The inequality sign in the preceding relations is a constant reminder that the entropy change of a closed system during an irreversible process is always greater than the entropy transfer. That is, some entropy is <i>generated <\/i>or <i>created <\/i>during an irreversible process, and this generation is due entirely to the pres- ence of irreversibilities. The entropy generated during a process is called <b>entropy generation <\/b>and is denoted by <i>S<\/i>gen. Noting that the difference between the entropy change of a closed system and the entropy transfer is equal to entropy generation, Eq. 7\u20137 can be rewritten as an equality as<\/font><\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0161.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-0161\" border=\"0\" alt=\"ENTROPY-0161\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0161_thumb.jpg\" width=\"262\" height=\"35\"><\/a><\/font><\/p>\n<p align=\"justify\"><font size=\"5\">Note that the entropy generation <i>S<\/i>gen is always a <i>positive <\/i>quantity or zero. Its value depends on the process, and thus it is <i>not <\/i>a property of the system. Also, in the absence of any entropy transfer, the entropy change of a system is equal to the entropy generation.<\/font><\/p>\n<p align=\"justify\"><font size=\"5\">Equation 7\u20137 has far-reaching implications in thermodynamics. For an iso- lated system (or simply an adiabatic closed system), the heat transfer is zero, and Eq. 7\u20137 reduces to<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0162.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-0162\" border=\"0\" alt=\"ENTROPY-0162\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0162_thumb.jpg\" width=\"210\" height=\"26\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">This equation can be expressed as <i>the entropy of an isolated system during a process always increases or, in the limiting case of a reversible process, re- mains constant. <\/i>In other words, it <i>never <\/i>decreases. This is known as the <b>in- crease of entropy principle. <\/b>Note that in the absence of any heat transfer, <\/font><font size=\"5\">entropy change is due to irreversibilities only, and their effect is always to in- crease entropy.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">Entropy is an extensive property, and thus the total entropy of a system is equal to the sum of the entropies of the parts of the system. An isolated system may consist of any number of subsystems (Fig. 7\u20136). A system and its sur- roundings, for example, constitute an isolated system since both can be en-<\/font><font size=\"5\">closed by a sufficiently large arbitrary boundary across which there is no heat, work, or mass transfer (Fig. 7\u20137). Therefore, a system and its surroundings can be viewed as the two subsystems of an isolated system, and the entropy change of this isolated system during a process is the sum of the entropy changes of the system and its surroundings, which is equal to the entropy gen<font size=\"5\">eration since an isolated system involves no entropy transfer. That is,<\/font><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0163.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-0163\" border=\"0\" alt=\"ENTROPY-0163\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0163_thumb.jpg\" width=\"127\" height=\"484\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0164.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-0164\" border=\"0\" alt=\"ENTROPY-0164\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0164_thumb.jpg\" width=\"265\" height=\"31\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">where the equality holds for reversible processes and the inequality for ir- reversible ones. Note that !::<i>S<\/i>surr refers to the change in the entropy of the surroundings as a result of the occurrence of the process under consideration.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">Since no actual process is truly reversible, we can conclude that some en- tropy is generated during a process, and therefore the entropy of the universe, which can be considered to be an isolated system, is continuously increasing. The more irreversible a process, the larger the entropy generated during that process. No entropy is generated during reversible processes (<i>S<\/i>gen = 0).<\/font> <\/p><div class=\"wgiah6a0dc92d39da0\" ><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.wgiah6a0dc92d39da0 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.wgiah6a0dc92d39da0 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.wgiah6a0dc92d39da0 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.wgiah6a0dc92d39da0 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.wgiah6a0dc92d39da0 {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n<div class=\"fxibu6a0dc92d39c2c\" ><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.fxibu6a0dc92d39c2c {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.fxibu6a0dc92d39c2c {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.fxibu6a0dc92d39c2c {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.fxibu6a0dc92d39c2c {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.fxibu6a0dc92d39c2c {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n\n<p align=\"justify\"><font size=\"5\">Entropy increase of the universe is a major concern not only to engineers but also to philosophers, theologians, economists, and environmentalists since entropy is viewed as a measure of the disorder (or \u201cmixed-up-ness\u201d) in the universe.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">The increase of entropy principle does not imply that the entropy of a sys<\/font><font size=\"5\">tem cannot decrease. The entropy change of a system <i>can <\/i>be negative during a process (Fig. 7\u20138), but entropy generation cannot. The increase of entropy principle 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-0165.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-0165\" border=\"0\" alt=\"ENTROPY-0165\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0165_thumb.jpg\" width=\"194\" height=\"52\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">This relation serves as a criterion in determining whether a process is reversible, irreversible, or impossible.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">Things in nature have a tendency to change until they attain a state of equilibrium. The increase of entropy principle dictates that the entropy of an isolated system will increase until the entropy of the system reaches a <i>maximum <\/i>value. At that point, the system is said to have reached an equilibrium state since the increase of entropy principle prohibits the system from undergoing any change of state that will result in a decrease in entropy.<\/font> <\/p>\n<h4 align=\"justify\"><font size=\"5\"><font style=\"font-weight: bold\">Some Remarks about Entropy<\/font><\/font><\/h4>\n<p align=\"justify\"><font size=\"5\">In light of the preceding discussions, we can draw these conclusions:<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><b>1. <\/b>Processes can occur in a <i>certain <\/i>direction only, not in <i>any <\/i>direction.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">A process must proceed in the direction that complies with the increase of entropy principle, that is, <i>S<\/i>gen &gt; 0. A process that violates this principle is impossible. This principle often forces chemical reactions to come to a halt before reaching completion.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><b>2. <\/b>Entropy is a <i>nonconserved property, <\/i>and there is <i>no <\/i>such thing as<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">the <i>conservation of entropy principle. <\/i>Entropy is conserved during the idealized reversible processes only and increases during <i>all <\/i>actual processes. Therefore, the entropy of the universe is continuously increasing.<\/font> <\/p>\n<p align=\"justify\"><b><font size=\"5\">3. <\/font><\/b><font size=\"5\">The performance of engineering systems is degraded by the presence of irreversibilities, and <i>ent<\/i><i>ropy generation <\/i>is a measure of the magnitudes of the irreversibilities present during that process. The greater the extent of irreversibilities, the greater the entropy generation. Therefore, entropy generation can be used as a quantitative measure of irreversibilities associated with a process. It is also used to establish criteria for the performance of engineering devices. This point is illustrated further in Example 7\u20132.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0166.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-0166\" border=\"0\" alt=\"ENTROPY-0166\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0166_thumb.jpg\" width=\"556\" height=\"398\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0167.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-0167\" border=\"0\" alt=\"ENTROPY-0167\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0167_thumb.jpg\" width=\"369\" height=\"347\"><\/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>THE INCREASE OF ENTROPY PRINCIPLE Consider a cycle that is made up of two processes: process 1-2, which is arbitrary (reversible or irreversible), and process 2-1, which is internally reversible, as shown in Fig. 7\u20135. From the Clausius inequality, where the equality holds for an internally reversible process and the inequality for an irreversible process. 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