{"id":1630,"date":"2024-07-27T08:30:16","date_gmt":"2024-07-27T08:30:16","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=1630"},"modified":"2024-07-27T08:30:16","modified_gmt":"2024-07-27T08:30:16","slug":"entropy-and-entropy-generation","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/07\/27\/entropy-and-entropy-generation\/","title":{"rendered":"\u00a0ENTROPY AND ENTROPY GENERATION"},"content":{"rendered":"\n<h4 class=\"wp-block-heading\" id=\"h4-029\">&nbsp;Entropy<\/h4>\n\n\n\n<p id=\"para-230\">Defining entropy in an exact word or line is impossible. It can be viewed as a measure of molecular disorder or molecular randomness. As a system becomes more disordered, the positions of the molecules become less predictable and the entropy increases. Thus, the entropy of a substance is lowest in the solid phase and highest in the gas phase. Heat is, in essence, a form of disorganized energy, and some disorganization (entropy) will flow with heat. Work instead is an organized form of energy and is free of disorder or randomness, and thus free of entropy. There is no entropy transfer associated with energy transfer as work. Unlike energy, entropy is a non-conserved property.<\/p>\n\n\n\n<p id=\"para-231\">According to Clausius inequality,&nbsp;<img loading=\"lazy\" decoding=\"async\" alt=\"equation\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page25a.png\" width=\"58\" height=\"35\">&nbsp;is a cyclic integral of differential heat flow&nbsp;<em>\u03b4Q<\/em>&nbsp;at absolute temperature&nbsp;<em>T<\/em>. For a process change in entropy is defined by,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page25b.png\" alt=\"Equation\"\/><\/figure>\n\n\n\n<p id=\"para-232\">Entropy always increases. For all process&nbsp;<img loading=\"lazy\" decoding=\"async\" alt=\"equation\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page25c.png\" width=\"129\" height=\"40\"><\/p>\n\n\n\n<p id=\"para-233\">To make it equality, add entropy generation term<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page25d.png\" alt=\"Equation\"\/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h4-030\">1.9.2&nbsp;&nbsp;Entropy Generation<\/h4>\n\n\n\n<ul class=\"wp-block-list\" id=\"ul-008\">\n<li><em>S<\/em><sub>GEN<\/sub>&nbsp;&gt; 0 for an irreversible (real) process<\/li>\n\n\n\n<li><em>S<\/em><sub>GEN<\/sub>&nbsp;= 0 for a reversible (ideal) process<\/li>\n\n\n\n<li><em>S<\/em><sub>GEN<\/sub>&nbsp;&lt; 0 for an impossible process<\/li>\n<\/ul>\n\n\n\n<p id=\"para-234\"><em>S<\/em><sub>GEN<\/sub>&nbsp;includes the change in&nbsp;<em>S<\/em>&nbsp;of the substance in the system, and the heat transfer,&nbsp;<em>Q<\/em>, to\/from the surroundings. Entropy always increases. It cannot be conserved (does not balance or return to zero, i.e., there is no law of conservation of entropy). The amount of entropy increase gives a measure of the magnitude of irreversibility in a process.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h4-031\">1.9.3&nbsp;&nbsp;Entropy Balance<\/h4>\n\n\n\n<ul class=\"wp-block-list\" id=\"ul-009\">\n<li>\u0394<em>S<\/em><sub>system<\/sub>&nbsp;=&nbsp;<em>S<\/em><sub>transfer<\/sub>&nbsp;+&nbsp;<em>S<\/em><sub>GEN<\/sub><\/li>\n\n\n\n<li>\u0394<em>S<\/em><sub>system<\/sub>&nbsp;=&nbsp;<em>S<\/em><sub>final<\/sub>&nbsp;\u2212&nbsp;<em>S<\/em><sub>initial<\/sub><\/li>\n\n\n\n<li>\u0394<em>S<\/em><sub>system<\/sub>&nbsp;=&nbsp;<em>m<\/em>(<em>s<\/em><sub>final<\/sub>&nbsp;\u2212&nbsp;<em>s<\/em><sub>initial<\/sub>) using specific entropy<em>s<\/em><sub>transfer<\/sub>&nbsp;comes from heat transfer,&nbsp;<em>Q<\/em>, or from mass flow&nbsp;<em>&nbsp;<\/em>,If heat transfer occurs,&nbsp;<em>s<\/em><sub>transfer<\/sub>&nbsp;=&nbsp;<em>Q\/T<\/em>If mass flow occurs,<\/li>\n\n\n\n<li><em>S<\/em><sub>transfer<\/sub>&nbsp;=&nbsp;<em>m<\/em>&nbsp;\u00d7&nbsp;<em>s<\/em>&nbsp;(for mass entering the system)<\/li>\n\n\n\n<li><em>S<\/em><sub>transfer<\/sub>&nbsp;= \u2212<em>m<\/em>&nbsp;\u00d7&nbsp;<em>s<\/em>&nbsp;(for mass leaving the system)<\/li>\n\n\n\n<li><em>S<\/em><sub>GEN<\/sub>&nbsp;= 0 for an internally reversible process<\/li>\n\n\n\n<li><em>S<\/em><sub>GEN<\/sub>&nbsp;&gt; 0 for a real, irreversible process<\/li>\n<\/ul>\n\n\n\n<p id=\"para-238\"><a><\/a>For a closed system (no mass flow):<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page26a.png\" alt=\"Equation\"\/><\/figure>\n\n\n\n<p id=\"para-239\">In terms of rate:<\/p>\n\n\n\n<p id=\"para-240\">For an adiabatic system (when&nbsp;<em>dQ<\/em>&nbsp;= 0):<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page026_1.png\" alt=\"Equation\"\/><\/figure>\n\n\n\n<p id=\"para-243\">For an open system steady flow process:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page26b.png\" alt=\"Equation\"\/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h4-032\">1.9.4&nbsp;&nbsp;Evaluation of Entropy Change<\/h4>\n\n\n\n<p id=\"para-244\">From equation:<\/p>\n\n\n\n<ol class=\"wp-block-list\" id=\"ol-006\">\n<li>&nbsp;&nbsp;<img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page26c.png\" alt=\"equation\" width=\"350\"><\/li>\n\n\n\n<li>&nbsp;&nbsp;<img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page26e.png\" alt=\"equation\" width=\"350\"><\/li>\n<\/ol>\n\n\n\n<p id=\"para-253\"><strong>Example 1.18:<\/strong>\u00a0A heat engine having an efficiency of 35% is used to run a refrigerator of COP of 4, what is the heat input into the each MJ removed from the cold body by the refrigerator? If this system is used as a heat pump (Figure 1.16), how many MJ of heat would be available for heating for each MJ of heat input to the engine?<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page26h.png\" alt=\"Figure 1.16\"\/><\/figure>\n\n\n\n<p id=\"para-254\"><strong>Figure 1.16<\/strong>&nbsp;Heat Reservoir and Sink<\/p>\n\n\n\n<p id=\"para-255\"><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page26g.png\" alt=\"Equation\"\/><\/figure>\n\n\n\n<p id=\"para-256\"><strong><a><\/a>Example 1.19:<\/strong>&nbsp;A heat pump working on a Carnot cycle takes in heat from a reservoir at 8\u00b0C and delivers heat to the reservoir at 50\u00b0C. The heat pump is driven by a reversible heat engine taking heat from a reservoir at 850\u00b0C and rejecting heat to reservoir at 50\u00b0C (<a href=\"https:\/\/learning.oreilly.com\/library\/view\/basic-mechanical-engineering\/9789332524415\/xhtml\/chapter001.xhtml#img-080\">Figure 1.17<\/a>). The reversible heat engine also drives a machine of input required of 25 kW. If the heat pump extracts 15 kJ\/sec from the 8\u00b0C reservoir, determine (a) the rate of heat supply from the 850\u00b0C source, and (b) the rate of heat rejection to 50\u00b0C sink.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page27a.png\" alt=\"Figure 1.17\"\/><\/figure>\n\n\n\n<p id=\"para-257\"><strong>Figure 1.17<\/strong>&nbsp;Heat Pump and Heat Engine<\/p>\n\n\n\n<p id=\"para-258\"><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page27b.png\" alt=\"Equation\"\/><\/figure>\n\n\n\n<p id=\"para-261\"><strong>Example 1.20:<\/strong>&nbsp;A reversible heat engine as shown in&nbsp;<a href=\"https:\/\/learning.oreilly.com\/library\/view\/basic-mechanical-engineering\/9789332524415\/xhtml\/chapter001.xhtml#img-083\">Figure 1.18&nbsp;<\/a>during a cycle of operation draws 5 MJ from the 400 K reservoir and does 840 kJ work. Find the amount and direction of heat interaction with other reservoirs.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page27d.png\" alt=\"Figure 1.18\"\/><\/figure>\n\n\n\n<p id=\"para-262\"><strong>Figure 1.18<\/strong>&nbsp;Reversible Heat Engine<\/p>\n\n\n\n<p id=\"para-263\"><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page27e.png\" alt=\"Equation\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page28a.png\" alt=\"Equation\"\/><\/figure>\n\n\n\n<p id=\"para-264\">Solving&nbsp;<a href=\"https:\/\/learning.oreilly.com\/library\/view\/basic-mechanical-engineering\/9789332524415\/xhtml\/chapter001.xhtml#img-084\">Eqs (1.1)<\/a>&nbsp;and&nbsp;<a href=\"https:\/\/learning.oreilly.com\/library\/view\/basic-mechanical-engineering\/9789332524415\/xhtml\/chapter001.xhtml#img-085\">(1.2),<\/a>&nbsp;we get<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page028_1.png\" alt=\"Equation\"\/><\/figure>\n\n\n\n<p id=\"para-267\"><strong>Example 1.21:<\/strong>&nbsp;Two blocks of metal each of mass&nbsp;<em>M<\/em>&nbsp;and specific heat&nbsp;<em>C<\/em>, initially at absolute temperature&nbsp;<em>T<\/em><sub>1<\/sub>&nbsp;and&nbsp;<em>T<\/em><sub>2<\/sub>, respectively, brought to the same final temperature&nbsp;<em>T<\/em><sub>f<\/sub>&nbsp;by means of reversible process. Derive an expression for the amount of work obtained during the process in terms of&nbsp;<em>M, C, T<\/em><sub>1<\/sub>&nbsp;and&nbsp;<em>T<\/em><sub>2<\/sub>.<\/p>\n\n\n\n<p id=\"para-268\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p id=\"para-269\">Let&nbsp;<em>T<\/em><sub>1<\/sub>&nbsp;&gt;&nbsp;<em>T<\/em><sub>2<\/sub>&nbsp;and final temperature be&nbsp;<em>T<\/em><sub>f<\/sub>.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page28b.png\" alt=\"Equation\"\/><\/figure>\n\n\n\n<p id=\"para-270\">For reversible process, total entropy = 0<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page28c.png\" alt=\"Equation\"\/><\/figure>\n\n\n\n<p id=\"para-271\"><strong>Example 1.22:<\/strong>&nbsp;An insulated tank of 1 m<sup>3<\/sup>&nbsp;volume contains air at 0.1 MPa and 300 K. The tank is connected to high pressure line in which air at 1 MPa and 600 K flows. The tank is quickly filled with air by opening the valve between the tank and high pressure line. If the final pressure of air in tank is 1 MPa (<a href=\"https:\/\/learning.oreilly.com\/library\/view\/basic-mechanical-engineering\/9789332524415\/xhtml\/chapter001.xhtml#img-089\">Figure 1.19<\/a>), determine the mass of air which enters the tank and the entropy change associated with filling process. Take universal gas constant&nbsp;<img loading=\"lazy\" decoding=\"async\" alt=\"equation\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page28e.png\" width=\"12\" height=\"15\">&nbsp;= 8.314 kJ\/kg mole K.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page28d.png\" alt=\"Figure 1.19\"\/><\/figure>\n\n\n\n<p id=\"para-272\"><strong>Figure 1.19<\/strong>&nbsp;Insulated Tank<\/p>\n\n\n\n<p id=\"para-273\"><strong><a><\/a>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page29a.png\" alt=\"Equation\"\/><\/figure>\n\n\n\n<p id=\"para-276\">Let final mass of air inside the cylinder =&nbsp;<em>m<\/em><sub>2<\/sub><\/p>\n\n\n\n<p id=\"para-277\">Final temperature of air inside the cylinder =&nbsp;<em>T<\/em><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page29c.png\" alt=\"Equation\"\/><\/figure>\n\n\n\n<p id=\"para-278\">From&nbsp;<a href=\"https:\/\/learning.oreilly.com\/library\/view\/basic-mechanical-engineering\/9789332524415\/xhtml\/chapter001.xhtml#img-092\">Eqs (1.3)<\/a>&nbsp;and&nbsp;<a href=\"https:\/\/learning.oreilly.com\/library\/view\/basic-mechanical-engineering\/9789332524415\/xhtml\/chapter001.xhtml#img-092\">(1.4)<\/a><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page29d.png\" alt=\"Equation\"\/><\/figure>\n\n\n\n<p id=\"para-279\">Entropy change associated with the process = \u0394<em>S<\/em><sub>1<\/sub>&nbsp;+ \u0394<em>S<\/em><sub>2<\/sub>&nbsp;= 0.88261 kJ\/K<\/p>\n\n\n\n<p id=\"para-280\">Ten kilograms of water at 0\u00b0C is brought into contact of a heat reservoir at 100\u00b0C, where water temperature becomes 100\u00b0C. Find the entropy change of water, reservoir and universe.<\/p>\n\n\n\n<p id=\"para-281\"><a><\/a><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page30a.png\" alt=\"Equation\"\/><\/figure>\n\n\n\n<p id=\"para-282\"><strong>Example 1.24:<\/strong>&nbsp;Calculate the entropy change when 5 kg of water at 20\u00b0C is mixed with 5 kg of water at 100\u00b0C. The specific heat of water is 4.18 kJ\/kg.<\/p>\n\n\n\n<p id=\"para-283\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p id=\"para-284\">Let&nbsp;<em>T<\/em><sub>f<\/sub>&nbsp;is final temperature<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332524415\/files\/images\/page30b.png\" alt=\"Equation\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>&nbsp;Entropy Defining entropy in an exact word or line is impossible. It can be viewed as a measure of molecular disorder or molecular randomness. As a system becomes more disordered, the positions of the molecules become less predictable and the entropy increases. Thus, the entropy of a substance is lowest in the solid phase and [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":1601,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1630","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-blog"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/07\/thermodynamics-1-3.png","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/1630","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/comments?post=1630"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/1630\/revisions"}],"predecessor-version":[{"id":1631,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/1630\/revisions\/1631"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/1601"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=1630"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=1630"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=1630"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}