{"id":16891,"date":"2018-02-26T17:23:11","date_gmt":"2018-02-26T17:23:11","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=16891"},"modified":"2022-11-09T09:50:00","modified_gmt":"2022-11-09T09:50:00","slug":"second-law-of-thermodynamics","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/second-law-of-thermodynamics\/","title":{"rendered":"Second Law of Thermodynamics"},"content":{"rendered":"<div   id="8n9s8rpp6h"    class=\"sue-shadow-wrap sue-content-wrap sue-shadow-inline-no\"><div   id="8n9s8rpp6h"    class=\"sue-shadow sue-shadow-style-vertical\">\n<div   id="8n9s8rpp6h"    class=\"sue-panel\" data-url=\"\" data-target=\"self\" style=\"background-color:#ffffff;color:#333333;border-radius:0px;-moz-border-radius:0px;-webkit-border-radius:0px;box-shadow:none;-moz-box-shadow:none;-webkit-box-shadow:none;border:1px solid #cccccc\"><div   id="8n9s8rpp6h"    class=\"sue-panel-content sue-content-wrap\" style=\"padding:15px;text-align:left\">\n<div class=\"su-heading su-heading-style-modern-1-dark su-heading-align-left\" id=\"\" style=\"font-size:13px;margin-bottom:20px\"><div   id="8n9s8rpp6h"    class=\"su-heading-inner\">\n<h2>Article Summary &amp; FAQs<\/h2>\n<\/div><\/div>\n<h3>What states the second law of thermodynamics?<\/h3>\n<p>According to the second law of thermodynamics:<\/p>\n<p><em><strong><span style=\"font-size: 20px;\">The entropy of any isolated system never decreases. In a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems increases.<\/span><\/strong><\/em><\/p>\n<h3>Key Facts<\/h3>\n<p><strong><b><a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/second-law-of-thermodynamics\/carnots-principle-carnots-rule\/\">Carnot&#8217;s rule:<\/a><\/b><\/strong><\/p>\n<p>Before these statements, we have to remind <strong><b><a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/second-law-of-thermodynamics\/carnots-principle-carnots-rule\/\">Carnot&#8217;s rule<\/a><\/b><span style=\"font-weight: 400;\">\u00a0that specifies limits on the maximum efficiency any heat engine can obtain.<\/span><\/strong><\/p>\n<p><strong>Statements:<\/strong><\/p>\n<p>The <strong>second law of thermodynamics<\/strong> may be expressed in many specific ways. Each statement expresses the same law. Listed below are three that are often encountered.<\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li>Clausius Statement. <em>\u201cIt is impossible to construct a device which operates on a cycle and whose sole effect is the transfer of heat from a cooler body to a hotter body\u201d.<\/em><\/li>\n<li>Kelvin-Planck Statement. <em>\u201cIt is impossible to construct a device which operates on a cycle and produces no other effect than the production of work and the transfer of heat from a single body\u201d.<\/em><\/li>\n<li>Entropy and the Second Law. <em>The entropy of any isolated system never decreases. In a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems increases.<\/em><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>All conventional thermal power plants are <strong>heat engines<\/strong> subject to the efficiency limitations imposed by the <strong>second law of thermodynamics<\/strong>.<\/p>\n<p>A typical <strong>gasoline automotive engine<\/strong> operates at around <strong>25% to 30%<\/strong> of thermal efficiency. About 70-75% is rejected as waste heat without being converted into useful work, i.e., work delivered to wheels.<\/p>\n<p>In modern <a title=\"Nuclear Power Plant\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/\">nuclear power plants<\/a>, the overall thermodynamic efficiency is about <strong>one-third <\/strong>(33%), so <strong>3000 MWth<\/strong> of thermal power from the fission reaction is needed to generate <strong>1000 MWe<\/strong> of electrical power.<\/p>\n<p>This inefficiency can be attributed to three causes.<\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><strong>Irreversibility of Processes<\/strong>.<\/li>\n<li><strong>Presence of Friction and Heat Losses.<\/strong><\/li>\n<li><strong>Design Inefficiency<\/strong>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:10px 0;border-width:2px;border-color:#999999\"><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\">\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-modern-light su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>What are the four laws of thermodynamics?<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>What are the four laws of thermodynamics?<\/strong><\/p>\n<p>The laws are as follows:<\/p>\n<ol>\n<li><a title=\"Zeroth Law of Thermodynamics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-temperature-physics\/zeroth-law-of-thermodynamics\/\"><strong>Zeroth law of thermodynamics:<\/strong><\/a> <em>If two systems are both in thermal equilibrium with a third, then they are in thermal equilibrium with each other.<\/em><\/li>\n<li><strong><a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/\">The first<\/a><\/strong><a title=\"First Law of Thermodynamics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/\"><strong>\u00a0law of thermodynamics:<\/strong><\/a> <em>The increase in internal energy of a closed system is equal to the heat supplied to the system minus work done by it.\u00a0 <\/em><\/li>\n<li><a title=\"Second Law of Thermodynamics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/second-law-of-thermodynamics\/\"><strong>The second law of thermodynamics:<\/strong><\/a> <em>The entropy of any isolated system never decreases. In a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems increases. <\/em><\/li>\n<li><a title=\"Third Law of Thermodynamics \u2013 3rd Law\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/third-law-of-thermodynamics-3rd-law\/\"><strong>Third law of thermodynamics:<\/strong><\/a> <em>The entropy of a system approaches a constant value as the temperature approaches absolute zero.<\/em><\/li>\n<\/ol>\n<\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-modern-light su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>What limits all heat engines?<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<strong>What limits all heat engines?<\/strong><\/p>\n<p>As in the\u00a0<a title=\"Carnot Cycle \u2013 Carnot Heat Engine\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-cycles\/carnot-cycle-carnot-heat-engine\/\">Carnot<\/a>,\u00a0<a title=\"Otto Cycle \u2013 Otto Engine\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-cycles\/otto-cycle-otto-engine\/\">Otto<\/a>,\u00a0and\u00a0<a title=\"Brayton Cycle \u2013 Gas Turbine Engine\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-cycles\/brayton-cycle-gas-turbine-engine\/\">Brayton cycle<\/a>, the thermal efficiency tends to increase as the average temperature at which energy is added by heat transfer increases and\/or the average temperature at which energy is rejected decreases. This is the common feature of all thermodynamic cycles. This rule is known as the<strong><span style=\"font-weight: 400;\">\u00a0<\/span><b><a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/second-law-of-thermodynamics\/carnots-principle-carnots-rule\/\">Carnot&#8217;s rule.<\/a>\u00a0<\/b><\/strong><\/p>\n<\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-modern-light su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>What are typical thermal efficiencies of heat engines?<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<strong>What are the typical thermal efficiencies of heat engines?<\/strong><\/p>\n<ul>\n<li>A typical <strong>gasoline automotive engine<\/strong> operates at around <strong>25% to 30%<\/strong> of thermal efficiency. About 70-75% is rejected as waste heat without being converted into useful work, i.e., work delivered to wheels.<\/li>\n<li>A typical <strong>diesel automotive engine<\/strong> operates at around <strong>30% to 35%<\/strong>. In general, engines using the Diesel cycle are usually more efficient.<\/li>\n<li>Sub-critical fossil fuel power plants operated under <strong>critical pressure<\/strong> (i.e., lower than 22.1 MPa) can achieve 36\u201340% efficiency.<\/li>\n<li>In modern <a title=\"Nuclear Power Plant\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/\"><strong>nuclear power plants<\/strong><\/a>, the overall thermal efficiency is about <strong>one-third <\/strong>(33%), so <strong>3000 MWth<\/strong> of thermal power from the fission reaction is needed to generate <strong>1000 MWe<\/strong> of electrical power.<\/li>\n<\/ul>\n<p>Sometimes you can find comparisons between combustion engines and electric motors or conventional power plants and solar power plants. In these cases, comparisons are often made for incomparable characteristics. Sure electric vehicles have an efficiency of about 70%, but in this case, we are not talking about thermal efficiency because an electrical motor is not a heat engine.<\/p>\n<p>In electric cars, energy undergoes the following conversions: from stored <strong>chemical energy<\/strong> to <strong>electrical energy<\/strong> and from <strong>electrical energy<\/strong> to <strong>mechanical energy<\/strong>. But in this case, most of its chemical energy stored was produced by another heat engine (e.g.,, coal power plant), and you must include it.<\/p>\n<p>In gasoline cars, energy undergoes the following conversions: from stored <strong>chemical energy<\/strong> to <strong>thermal energy<\/strong> and from <strong>thermal energy<\/strong>\u00a0to <strong>mechanical energy<\/strong>. Automotive engines are heat engines that can consume primary energy sources.<\/p>\n<\/div><\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n<p>The<strong> second law of thermodynamics<\/strong> is a general principle that goes<strong> beyond the limitations<\/strong> imposed by the <a title=\"First Law of Thermodynamics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/\"><strong>first law of thermodynamics<\/strong><\/a>. The first law is used to relate and evaluate the various energies involved in a process. However, no information about the<strong> direction of the process<\/strong> can be obtained by applying the first law. The second law of thermodynamics places constraints upon the direction of heat transfer and sets an <strong>upper limit to the efficiency<\/strong> of conversion of heat to work in <strong>heat engines<\/strong>. So the second law is directly relevant for many important practical problems.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/Second-Law-of-Thermodynamics-Heat-Engines.png\"><img loading=\"lazy\" class=\"alignright wp-image-16894\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/Second-Law-of-Thermodynamics-Heat-Engines.png\" alt=\"Second Law of Thermodynamics - Heat Engines\" width=\"198\" height=\"719\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/Second-Law-of-Thermodynamics-Heat-Engines.png 227w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/Second-Law-of-Thermodynamics-Heat-Engines-83x300.png 83w\" sizes=\"(max-width: 198px) 100vw, 198px\" \/><\/a>The<strong> second law of thermodynamics<\/strong> law indicates the <strong>irreversibility<\/strong> of <strong>natural processes<\/strong>. Reversible processes are a useful and convenient theoretical fiction but do not occur in nature. From this law, it is impossible to construct a device that operates on a cycle and whose sole effect is the transfer of heat from a cooler body to a hotter body. It follows perpetual motion machines of the second kind are impossible.<\/p>\n<p>One of the areas of application of the<strong> second law of thermodynamics<\/strong> is the study of energy-conversion systems. For example, converting all the energy obtained from coal in a coal-fired power plant or from a nuclear reactor in a nuclear power plant into electrical energy is not possible. There must be<strong> losses<\/strong> in the conversion process.<\/p>\n<div   id="8n9s8rpp6h"    class=\"collapsible-container\">\n<h2>The direction of Thermodynamic Processes<\/h2>\n<p>Many thermodynamic processes proceed naturally in one direction but not the opposite. For example, when a <strong>temperature difference<\/strong> does exist, heat flows spontaneously <strong>from the warmer system to the colder system<\/strong>, never the reverse. In fact, such heat flow (from a colder body to a warmer system) would not violate the <a title=\"First Law of Thermodynamics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/\"><strong>first law of thermodynamics<\/strong><\/a>, i.e., energy would be conserved. But it doesn\u2019t happen in nature.<\/p>\n<p>For example, burning gasoline to power cars is an energy conversion process we rely on. The <a title=\"Enthalpy of Chemical Reaction\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/what-is-enthalpy\/enthalpy-of-chemical-reaction\/\"><strong>chemical energy<\/strong><\/a> in gasoline is<strong> converted<\/strong> to<a title=\"Internal Energy \u2013 Thermal Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/internal-energy-thermal-energy\/\"><strong> thermal energy<\/strong><\/a>, then converted to <a title=\"What is Mechanical Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/what-is-mechanical-energy\/\"><strong>mechanical energy<\/strong><\/a> that makes the car move. The <strong>mechanical energy<\/strong> has been converted to <a title=\"What is Kinetic Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/what-is-kinetic-energy\/\"><strong>kinetic energy<\/strong><\/a>. When we use the brakes to stop a car, that<strong> kinetic energy<\/strong> is converted by friction back to heat or <strong>thermal energy<\/strong>. In this reverse direction, there are plenty of devices that convert heat partially into mechanical energy. But you cannot build a machine that converts heat completely into mechanical energy. There will always be significant energy losses.<\/p>\n<p><strong> Directions of thermodynamic processes<\/strong> are subject to the second law of thermodynamics, especially of the <strong>Clausius Statement of the Second Law<\/strong>.<\/p>\n<h2>Various Statements of the Law<\/h2>\n<p>The <strong>second law of thermodynamics<\/strong> may be expressed in many specific ways. Each statement expresses the same law. Listed below are three that are often encountered.<\/p>\n<ul>\n<li>Clausius Statement<\/li>\n<li>Kelvin-Planck Statement<\/li>\n<li>Entropy and the Second Law<\/li>\n<\/ul>\n<p>Before these statements, we have to remind the <strong><span style=\"font-weight: 400;\">French engineer and physicist, <\/span><b>Nicolas L\u00e9onard Sadi Carnot<\/b><\/strong>, who <strong><span style=\"font-weight: 400;\">advanced the study of the second law by forming a principle (<\/span><span style=\"font-weight: 400;\">also called <\/span><b>Carnot&#8217;s rule<\/b><span style=\"font-weight: 400;\">) that specifies limits on the maximum efficiency of any heat engine can obtain.<\/span><\/strong><\/p>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Carnot's Principle<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">In 1824, a French engineer and physicist, <strong>Nicolas L\u00e9onard Sadi Carnot,<\/strong> advanced the study of the second law by forming a principle (also called <strong>Carnot&#8217;s rule<\/strong>) that specifies limits on the <strong>maximum efficiency any heat engine<\/strong> can obtain. In short, this principle states that the<strong> efficiency of a thermodynamic cycle<\/strong> depends solely on the difference between the hot and cold temperature reservoirs.<\/p>\n<p><strong>Carnot&#8217;s principle states:<\/strong><\/p>\n<ol>\n<li>No engine can be more efficient than a reversible engine (<strong>a Carnot heat engine<\/strong>) operating between the same high-temperature and low-temperature reservoirs.<\/li>\n<li>The efficiencies of all reversible engines (<strong>Carnot heat engines<\/strong>) operating between the same constant temperature reservoirs are the same, regardless of the working substance employed or the operation details.<\/li>\n<\/ol>\n<h2><strong><b>Carnot Efficiency<\/b><\/strong><\/h2>\n<p>The formula for this maximum efficiency is:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/carnot-efficiency-equation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-16897\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/carnot-efficiency-equation.png\" alt=\"Carnot Efficiency Formula\" width=\"369\" height=\"91\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/carnot-efficiency-equation.png 369w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/carnot-efficiency-equation-300x74.png 300w\" sizes=\"(max-width: 369px) 100vw, 369px\" \/><\/a><\/p>\n<p>where:<\/p>\n<ul>\n<li>is the efficiency of the Carnot cycle, i.e., it is the ratio <strong> = W\/Q<\/strong><strong><sub>H<\/sub><\/strong> of the work done by the engine to the heat energy entering the system from the hot reservoir.<\/li>\n<li><strong>T<sub>C<\/sub><\/strong> is the absolute temperature (Kelvins) of the cold reservoir,<\/li>\n<li>T<sub>H<\/sub> is the absolute temperature (Kelvins) of the hot reservoir.<\/li>\n<\/ul>\n<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Example: Carnot efficiency for coal-fired power plant <\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">In a modern <strong>coal-fired power plant<\/strong>, the temperature of <a title=\"What is Supercritical Steam\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/supercritical-fluid-supercritical-water\/what-is-supercritical-steam\/\"><strong>high-pressure steam<\/strong><\/a> (T<sub>hot<\/sub>) would be about 400\u00b0C (673K) and T<sub>cold<\/sub>, the cooling tower water temperature, would be about 20\u00b0C (293K). For this type of power plant, the maximum (ideal) efficiency will be:<\/p>\n<p>= 1 &#8211; T<sub>cold<\/sub>\/T<sub>hot<\/sub> = 1 &#8211; 293\/673 = 56%<\/p>\n<p>It must be added, and this is an<strong> idealized efficiency<\/strong>. The Carnot efficiency is valid for reversible processes. These processes cannot be achieved in real cycles of power plants. The Carnot efficiency dictates that higher efficiencies can be attained by increasing the temperature of the steam. This feature is also valid for real thermodynamic cycles. But this requires an increase in pressures inside boilers or <a title=\"Steam Generator\" href=\"http:\/\/sitepourvtc.com\/steam-generator\/\">steam generators<\/a>. However, metallurgical considerations place<strong> upper limits\u00a0<\/strong>on such pressures. Sub-critical fossil fuel power plants operated under <a title=\"Critical Pressure of Water\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/critical-pressure-of-water\/\"><strong>critical pressure<\/strong><\/a> (i.e., lower than 22.1 MPa) can achieve 36\u201340% efficiency. Supercritical designs operated at <a title=\"What is Supercritical Steam\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/supercritical-fluid-supercritical-water\/what-is-supercritical-steam\/\"><strong>supercritical pressure<\/strong><\/a> (i.e., greater than 22.1 MPa) have efficiencies of around 43%. Most efficient and complex coal-fired power plants operate at <strong>&#8220;ultra critical&#8221; <\/strong><strong>pressures <\/strong>(i.e., around 30 MPa) and use multiple stage reheat to reach about 48% efficiency.<\/p>\n<p>See also: <a title=\"Supercritical Water Reactor \u2013 SCWR\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/reactor-types\/supercritical-water-reactor-scwr\/\">Supercritical Reactor<\/a><\/p>\n<\/div><\/div><\/div>\n<h2>Clausius Statement of the Second Law<\/h2>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/clausius-statement-second-law.png\"><img loading=\"lazy\" class=\"alignright size-full wp-image-16898\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/clausius-statement-second-law.png\" alt=\"Clausius Statement of the Second Law\" width=\"223\" height=\"329\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/clausius-statement-second-law.png 223w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/clausius-statement-second-law-203x300.png 203w\" sizes=\"(max-width: 223px) 100vw, 223px\" \/><\/a>One of the earliest statements of the Second Law of Thermodynamics was made by <strong>R. Clausius in 1850<\/strong>. He stated the following.<\/p>\n<p><em>\u201cIt is impossible to construct a device which operates on a cycle and whose sole effect is the transfer of heat from a cooler body to a hotter body\u201d.<\/em><\/p>\n<p><strong>Heat cannot spontaneously flow<\/strong> from cold system to hot system without external work being performed on the system. This is exactly what refrigerators and heat pumps accomplish. In a refrigerator, heat flows from cold to hot, but only when forced by external work. Refrigerators are driven by electric motors requiring work from their surroundings to operate.<\/p>\n<p>The Clausius and the Kelvin-Planck statements are equivalent.<\/p>\n<h2>Kelvin-Planck Statement of the Second Law<\/h2>\n<p><em><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/kelvin-planck-statement-second-law.png\"><img loading=\"lazy\" class=\"alignright size-full wp-image-16899\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/kelvin-planck-statement-second-law.png\" alt=\"Kelvin-Planck Statement of the Second Law\" width=\"237\" height=\"364\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/kelvin-planck-statement-second-law.png 237w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/kelvin-planck-statement-second-law-195x300.png 195w\" sizes=\"(max-width: 237px) 100vw, 237px\" \/><\/a>\u201cIt is impossible to construct a device which operates on a cycle and produces no other effect than the production of work and the transfer of heat from a single body\u201d.<\/em><\/p>\n<p>This statement operates with the term \u201c<strong>thermal reservoir<\/strong>\u201d or \u201c<strong>single reservoir<\/strong>\u201d. \u00a0A reservoir is a large object in which the temperature remains constant while energy is extracted. Such a system can be approximated in many ways\u2014by the earth\u2019s atmosphere, large bodies of water like lakes, oceans, and so on.<\/p>\n<p>The <strong>Kelvin\u2013Planck statement<\/strong> does not exclude the existence of a system that develops a net amount of work from a heat transfer extracted from a thermal reservoir. According to this statement, a system undergoing a <strong>cycle<\/strong> cannot develop a positive net amount of work from a heat transfer extracted from a thermal reservoir.<\/p>\n<h2>Entropy and the Second Law<\/h2>\n<figure id=\"attachment_16713\" aria-describedby=\"caption-attachment-16713\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/Specific-Entropy-T-s-Diagram.png\"><img loading=\"lazy\" class=\"size-medium wp-image-16713\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/Specific-Entropy-T-s-Diagram-300x273.png\" alt=\"T-s diagram of a thermodynamic cycle\" width=\"300\" height=\"273\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/Specific-Entropy-T-s-Diagram-300x273.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/Specific-Entropy-T-s-Diagram.png 565w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-16713\" class=\"wp-caption-text\">T-s diagram of Rankine Cycle<\/figcaption><\/figure>\n<p>One consequence of the <strong>second law of thermodynamics<\/strong> is the development of the <strong>physical property<\/strong> of matter, which is known as the<a title=\"What is Entropy\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/what-is-entropy\/\"><strong> entropy (S)<\/strong><\/a>. The change in this property is used to determine the <strong>direction<\/strong> in which a given process will proceed. <strong>Entropy<\/strong> quantifies the <strong>energy<\/strong> of a substance that is <strong>no longer available to perform useful work<\/strong>. This relates to the<strong> second law<\/strong> since the second law predicts that not all heat provided to a cycle can be transformed into an equal amount of work. Some heat rejection must take place.<\/p>\n<p>See also: <a title=\"What is Entropy\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/what-is-entropy\/\">Entropy<\/a><\/p>\n<p>According to Clausius, the <strong>entropy<\/strong> was defined via the <strong>change in entropy S<\/strong> of a system. The change in entropy S, when an amount of heat Q is added to it by a reversible process at a constant temperature, is given by:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/Entropy-Equation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-16710\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/Entropy-Equation.png\" alt=\"Entropy- Equation\" width=\"102\" height=\"74\" \/><\/a><\/p>\n<p>Here <strong>Q<\/strong> is the energy transferred as <a title=\"Heat in Thermodynamics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/heat-in-thermodynamics\/\"><strong>heat<\/strong><\/a> to or from the system during the process, and <strong>T<\/strong> is the<strong> <a title=\"What is Temperature \u2013 Physics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-temperature-physics\/\">temperature<\/a><\/strong> of the system in <a title=\"Kelvin Scale \u2013 Absolute Temperature\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-temperature-physics\/kelvin-scale-absolute-temperature\/\">kelvins<\/a> during the process. The SI unit for entropy is <strong>J\/K<\/strong>.<\/p>\n<p>The <strong>second law of thermodynamics<\/strong> can also be expressed as <strong>\u2206S\u22650<\/strong> for a closed cycle.<\/p>\n<p>In words:<\/p>\n<p><em>The entropy of any isolated system never decreases. In a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems increases. <\/em><\/p>\n<p><strong>\u2206S\u22650<\/strong><\/p>\n<p>Because entropy tells so much about the usefulness of an amount of heat transferred in performing work, the <a title=\"Steam Tables \u2013 Specific Properties of Water and Steam\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/steam-tables\/\">steam tables<\/a> include values of <a title=\"Specific Entropy\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/what-is-entropy\/specific-entropy\/\">specific entropy<\/a> (s = S\/m) as part of the information tabulated.<\/p>\n<h2>Heat Engines<\/h2>\n<p><a title=\"Energy Sources\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/energy-sources\/\"><strong>Energy sources<\/strong><\/a> have always played a very important role in the development of human society. <strong><a title=\"What is Energy \u2013 Physics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/\">Energy<\/a><\/strong> is generally defined as the <strong>potential to do <a title=\"Work in Thermodynamics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/work-in-thermodynamics\/\">work<\/a><\/strong> <strong>or produce<a title=\"Heat in Thermodynamics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/heat-in-thermodynamics\/\"> heat<\/a><\/strong>. Sometimes it is like the \u201ccurrency\u201d for performing work. One of the most wonderful properties of the universe is that <strong>energy can be transformed from one type to another<\/strong> and <strong>transferred from one object to another<\/strong>.<\/p>\n<p>In general, it is easy to produce <a title=\"Internal Energy \u2013 Thermal Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/internal-energy-thermal-energy\/\"><strong>thermal energy<\/strong><\/a> <strong>by doing work<\/strong>, for example, by any frictional process. But to <strong>get work from thermal energy<\/strong> is more <strong>difficult<\/strong>. It is closely associated with the<a title=\"What is Entropy\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/what-is-entropy\/\"> concept of entropy<\/a>. For example, electricity is particularly useful since it has <strong>very<\/strong> <strong>low entropy<\/strong> (is highly ordered) and can be converted into other forms of energy<strong> very efficiently<\/strong>.<\/p>\n<p>Sometimes, <a title=\"What is Mechanical Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/what-is-mechanical-energy\/\">mechanical energy<\/a> is directly available, for example, wind power and hydropower. But most of our energy comes from burning <strong>fossil fuels<\/strong> (coal, oil, and gas) and <a title=\"Nuclear Reactions\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/nuclear-reactions\/\"><strong>nuclear reactions<\/strong><\/a>. At present, fossil fuel is still the world\u2019s predominant energy source. But the burning of fossil fuels generates <strong>only thermal energy<\/strong>. Therefore these energy sources are so-called \u201c<a title=\"Primary Energy Sources\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/primary-energy-sources\/\"><strong>primary energy sources<\/strong><\/a>\u201d, that must<strong> be converted<\/strong> to the <strong><a title=\"Secondary Energy Sources \u2013 Energy Carriers\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/secondary-energy-sources-energy-carriers\/\">secondary energy source<\/a><\/strong>, so-called <strong>energy carriers <\/strong>(<a title=\"Electrical Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/electrical-energy\/\">electrical energy<\/a>, etc.). To convert thermal energy into another form of energy, a <strong>heat engine<\/strong> must be used.<\/p>\n<p>In general, a <strong>heat engine<\/strong> is a device that converts chemical energy to heat or thermal energy and then to mechanical energy or electrical energy.<\/p>\n<figure id=\"attachment_16900\" aria-describedby=\"caption-attachment-16900\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/heat-engine-example.png\"><img loading=\"lazy\" class=\"size-medium wp-image-16900\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/heat-engine-example-300x224.png\" alt=\"Example of Heat Engine\" width=\"300\" height=\"224\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/heat-engine-example-300x224.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/heat-engine-example.png 449w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-16900\" class=\"wp-caption-text\">The Rankine cycle closely describes the processes in steam-operated heat engines commonly found in most thermal power plants.<\/figcaption><\/figure>\n<p>Many<strong> heat engines<\/strong>\u00a0operate in a cyclic manner, adding energy in the form of heat in one part of the cycle and using that energy to do useful work in another part of the cycle.<br \/>\nFor example, as is typical in all conventional <strong>thermal power plants,<\/strong>\u00a0the heat is used to generate <a title=\"Properties of Steam \u2013 What is Steam\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/\">steam<\/a> which drives a <strong>steam turbine<\/strong> connected to a generator that produces electricity. <a title=\"Steam Generator\" href=\"http:\/\/sitepourvtc.com\/steam-generator\/\">Steam generators<\/a>, steam turbines, condensers, and feedwater pumps constitute a <strong>heat engine<\/strong> subject to the efficiency limitations imposed by the <strong>second law of thermodynamics<\/strong>. In modern <a title=\"Nuclear Power Plant\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/\">nuclear power plants<\/a>, the overall thermodynamic efficiency is about <strong>one-third <\/strong>(33%), so <strong>3000 MWth<\/strong> of thermal power from the fission reaction is needed to generate <strong>1000 MWe<\/strong> of electrical power.<\/p>\n<h3>Types of Heat Engines<\/h3>\n<p>In general, heat engines are categorized according to a combustion location as:<\/p>\n<ul>\n<li><strong>External combustion engine.<\/strong> For example, steam engines are external combustion engines, where the working fluid is separate from the combustion products.<\/li>\n<li><strong>Internal combustion engine.<\/strong> A typical example of an internal combustion engine is an engine used in automobiles. The high temperature is achieved by burning the gasoline-air mixture in the cylinder itself.<\/li>\n<\/ul>\n<p>The detailed categorization is based on a working fluid used in a thermodynamic cycle:<\/p>\n<ul>\n<li><strong>Gas Cycles. <\/strong>In these cycles, the working fluid is always a gas. The Otto and Diesel cycles (used in automobiles) are also typical examples of gas-only cycles. Modern gas turbine engines and airbreathing jet engines are also based on the gas-only cycle, and they follow the Brayton cycle.<\/li>\n<li><strong>Liquid Cycles. <\/strong>Liquid-only cycles are rather exotic. In these cycles, the working fluid is always a liquid. The Malone liquid engine is an example of the liquid-only cycle. The Malone liquid engine modified the Stirling cycle, using water as the working fluid instead of gas.<\/li>\n<li><strong>Cycles with Phase Changes. <\/strong>Steam engines are typical examples of external engines with phase change of working fluid.<\/li>\n<\/ul>\n<h3>Example of Heat Engine<\/h3>\n<figure id=\"attachment_16026\" aria-describedby=\"caption-attachment-16026\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Thermodynamic-Cycles-min.png\"><img loading=\"lazy\" class=\"size-medium wp-image-16026\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Thermodynamic-Cycles-min-300x277.png\" alt=\"engineering thermodynamics\" width=\"300\" height=\"277\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Thermodynamic-Cycles-min-300x277.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/12\/Thermodynamic-Cycles-min.png 650w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-16026\" class=\"wp-caption-text\">Rankine Cycle &#8211; Thermodynamics as Energy Conversion Science<\/figcaption><\/figure>\n<p><strong>Steam engines<\/strong> and <strong>refrigerators<\/strong> are typical examples of external engines with phase change of working fluid. The typical thermodynamic cycle used to analyze this process is the <strong>Rankine cycle<\/strong>, which usually uses water as the working fluid.<\/p>\n<p>The<strong> Rankine cycle<\/strong> closely describes the processes in steam-operated heat engines commonly found in most <strong>thermal power plants<\/strong>. The heat sources used in these power plants are usually the combustion of fossil fuels such as coal, natural gas, or <strong>nuclear fission<\/strong>.<\/p>\n<p>A <a title=\"Nuclear Power Plant\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/\"><strong>nuclear power plant<\/strong><\/a> (nuclear power station) looks like a standard thermal power station with one exception. The heat source in the nuclear power plant is a <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/what-is-nuclear-reactor\/\"><strong>nuclear reactor<\/strong><\/a>. As is typical in all conventional thermal power stations, the heat is used to generate <a title=\"Properties of Steam \u2013 What is Steam\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/\">steam<\/a> which drives a steam turbine connected to a generator that produces electricity.<\/p>\n<p>Typically most <strong>nuclear power plants<\/strong> operate <strong>multi-stage condensing steam turbines<\/strong>. In these turbines, the high-pressure stage receives <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/\">steam<\/a> (this steam is nearly saturated steam \u2013 x = 0.995 \u2013 point C at the figure; <strong>6 MPa<\/strong>; 275.6\u00b0C) from a steam generator and exhausts it to moisture separator-reheater (point D). The steam must be reheated to avoid damages caused to the steam turbine blades by <a title=\"Vapor Quality \u2013 Dryness Fraction\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/vapor-quality-dryness-fraction\/\">low-quality steam<\/a>. The reheater heats the steam (point D), and then the steam is directed to the low-pressure stage of the steam turbine, where it expands (point E to F). The exhausted steam then condenses in the condenser. It is at a pressure well below atmospheric (absolute pressure of <strong>0.008 MPa<\/strong>) and is in a partially condensed state (point F), typically of a quality near 90%.<\/p>\n<p>In this case, steam generators, steam turbines, condensers, and feedwater pumps constitute a heat engine subject to the efficiency limitations imposed by the <strong>second law of thermodynamics<\/strong>. In an ideal case (no friction, reversible processes, perfect design), this heat engine would have a Carnot efficiency of<\/p>\n<p>= 1 &#8211; T<sub>cold<\/sub>\/T<sub>hot<\/sub> = 1 &#8211; 315\/549 = 42.6%<\/p>\n<p>where the temperature of the hot reservoir is 275.6\u00b0C (548.7K), the temperature of the cold reservoir is 41.5\u00b0C (314.7K). But the nuclear power plant is the <strong>real heat engine<\/strong>, in which thermodynamic processes are somehow irreversible. They are not done infinitely slowly. In real devices (turbines, pumps, and compressors), mechanical friction and heat losses cause further efficiency losses.<\/p>\n<p>Therefore nuclear power plants usually have an efficiency of about 33%. In modern nuclear power plants, the overall thermodynamic efficiency is about <strong>one-third <\/strong>(33%), so <strong>3000 MWth<\/strong> of thermal power from the fission reaction is needed to generate <strong>1000 MWe<\/strong> of electrical power.<\/p>\n<p>According to Carnot&#8217;s principle, higher efficiencies can be attained by increasing the <strong>temperature<\/strong> of the steam. But this requires an increase in pressures inside boilers or steam generators. However, metallurgical considerations place upper limits on such pressures. \u00a0From this point of view, <a title=\"Supercritical Water Reactor \u2013 SCWR\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/reactor-types\/supercritical-water-reactor-scwr\/\"><strong>supercritical water reactors<\/strong><\/a> are considered a promising advancement for <a title=\"Nuclear Power Plant\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/\">nuclear power plants <\/a>because of their <strong>high thermal efficiency<\/strong> (~45 % vs. ~33 % for current LWRs). SCWRs\u00a0are\u00a0operated at <strong>supercritical pressure<\/strong> (i.e., greater than 22.1 MPa).<\/p>\n<h2>Thermal Efficiency and the Second Law<\/h2>\n<p>An <strong>ideal heat engine<\/strong> is an imaginary engine in which energy extracted as heat from the high-temperature reservoir is converted completely to work. But according to the <strong>Kelvin-Planck statement<\/strong>, such an engine would violate the second law of thermodynamics because there must be losses in the conversion process. The net heat added to the system must be higher than the net work done by the system.<\/p>\n<p><strong>Kelvin-Planck statement:<\/strong><\/p>\n<p><em>\u201cIt is impossible to construct a device which operates on a cycle and produces no other effect than the production of work and the transfer of heat from a single body\u201d.<\/em><\/p>\n<h3>Thermal Efficiency Formula<\/h3>\n<p>As a result of this statement, we define the <strong>thermal efficiency<\/strong>, <strong><em>\u03b7<\/em><\/strong><strong><em><sub>th<\/sub><\/em><\/strong>, of any heat engine as the ratio of the <a title=\"Work in Thermodynamics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/work-in-thermodynamics\/\">work<\/a> it does, <strong>W<\/strong>, to the <a title=\"Heat in Thermodynamics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/heat-in-thermodynamics\/\">heat<\/a> input at the high temperature, Q<sub>H<\/sub>.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/thermal-efficiency-formula-1.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-16945\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/thermal-efficiency-formula-1.png\" alt=\"thermal efficiency formula - 1\" width=\"125\" height=\"82\" \/><\/a><\/p>\n<p>The <strong>thermal efficiency<\/strong>, <strong><em>\u03b7<\/em><\/strong><strong><em><sub>th<\/sub><\/em><\/strong>, represents the fraction of <strong>heat<\/strong>, <strong>Q<sub>H<\/sub><\/strong>, converted <strong>to work<\/strong>. It is a dimensionless performance measure of a heat engine that uses thermal energy, such as a steam turbine, an internal combustion engine, or a refrigerator. For refrigeration or heat pumps, thermal efficiency indicates the extent to which the energy added by work is converted to net heat output. Since it is a dimensionless number, we must always express W, Q<sub>H<\/sub>, and Q<sub>C<\/sub> in the same units.<\/p>\n<p>Since energy is conserved according to the <a title=\"First Law of Thermodynamics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/\"><strong>first law of thermodynamics<\/strong> <\/a>and energy cannot be converted to work completely, the heat input, Q<sub>H<\/sub>, must equal the work done, W, plus the heat that must be dissipated as <strong>waste heat Q<sub>C<\/sub><\/strong> into the environment. Therefore we can rewrite the formula for thermal efficiency as:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/thermal-efficiency-formula-2.png\"><img loading=\"lazy\" class=\"aligncenter size-medium wp-image-16944\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/thermal-efficiency-formula-2-300x71.png\" alt=\"thermal efficiency formula - 2\" width=\"300\" height=\"71\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/thermal-efficiency-formula-2-300x71.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/02\/thermal-efficiency-formula-2.png 352w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>To give the efficiency as a percent, we multiply the previous formula by 100. Note that <strong><em>\u03b7<\/em><\/strong><strong><em><sub>th<\/sub><\/em><\/strong> could be 100% only if the waste heat Q<sub>C <\/sub>is zero.<\/p>\n<p>In general, the efficiency of even the <strong>best heat engines<\/strong> is quite low. In short, it is<strong> very difficult<\/strong> to convert<a title=\"Internal Energy \u2013 Thermal Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/internal-energy-thermal-energy\/\"> thermal energy<\/a> to <a title=\"What is Mechanical Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/what-is-mechanical-energy\/\">mechanical energy<\/a>. The thermal efficiencies are usually <strong>below 50%<\/strong> and often far below. Be careful when you compare it with efficiencies of wind or hydropower (wind turbines are not heat engines). There is no energy conversion between thermal and mechanical energy.<\/p>\n<h2>Causes of Inefficiency<\/h2>\n<p>As was discussed, an efficiency can range between 0 and 1. Each heat engine is somehow inefficient. This inefficiency can be attributed to three causes.<\/p>\n<ul>\n<li><strong>Irreversibility of Processes<\/strong>. There is an overall theoretical upper limit to the efficiency of conversion of heat to work in any heat engine. This upper limit is called the <strong>Carnot efficiency<\/strong>. According to the <strong>Carnot principle<\/strong>, no engine can be more efficient than a reversible engine (<strong>a Carnot heat engine<\/strong>) operating between the same high temperature and low-temperature reservoirs. For example, when the hot reservoir has T<sub>hot<\/sub> of 400\u00b0C (673K) and T<sub>cold<\/sub> of about 20\u00b0C (293K), the maximum (ideal) efficiency will be: = 1 &#8211; T<sub>cold<\/sub>\/T<sub>hot<\/sub> = 1 &#8211; 293\/673 = 56%. But all real thermodynamic processes are somehow <strong>irreversible<\/strong>. They are not done infinitely slowly. Therefore, heat engines must have lower efficiencies than limits on their efficiency due to the inherent irreversibility of the heat engine cycle they use.<\/li>\n<li><strong>Presence of Friction and Heat Losses.<\/strong> In real thermodynamic systems or real heat engines, a part of the overall cycle inefficiency is due to the losses by the individual components. In real devices (such as turbines, pumps, and compressors), <strong>mechanical friction<\/strong>, <strong>heat losses,<\/strong> and losses in the combustion process cause further efficiency losses.<\/li>\n<li><strong>Design Inefficiency<\/strong>. Finally, the last and important source of inefficiencies is the <strong>compromises<\/strong> made by <strong>engineers<\/strong> when designing a heat engine (e.g.,, power plant). They must consider cost and other factors in the design and operation of the cycle. As an example, consider the design of the <strong>condenser<\/strong> in the thermal power plants. \u00a0Ideally, the steam exhausted into the condenser would have <strong>no subcooling<\/strong>. But real condensers are designed to subcool the liquid by a few degrees Celsius to avoid the <a title=\"Suction Cavitation\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/centrifugal-pumps\/cavitation\/suction-cavitation\/\"><strong>suction cavitation<\/strong><\/a> in the condensate pumps. But, this subcooling increases the inefficiency of the cycle because more energy is needed to reheat the water.<\/li>\n<\/ul>\n<h2>Thermal Efficiency of Heat Engines<\/h2>\n<p>In general, the efficiency of even the best heat engines is quite low. In short, it is <strong>very difficult to convert thermal energy to mechanical energy<\/strong>. The thermal efficiencies are usually below 50% and often far below.<\/p>\n<figure id=\"attachment_16961\" aria-describedby=\"caption-attachment-16961\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/03\/thermal-efficiency-engines-turbines-min.png\"><img loading=\"lazy\" class=\"size-medium wp-image-16961\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/03\/thermal-efficiency-engines-turbines-min-300x222.png\" alt=\"Takaishi, Tatsuo; Numata, Akira; Nakano, Ryouji; Sakaguchi, Katsuhiko (March 2008). \" width=\"300\" height=\"222\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/03\/thermal-efficiency-engines-turbines-min-300x222.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/03\/thermal-efficiency-engines-turbines-min.png 541w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-16961\" class=\"wp-caption-text\">Takaishi, Tatsuo; Numata, Akira; Nakano, Ryouji; Sakaguchi, Katsuhiko (March 2008). &#8220;Approach to High-Efficiency Diesel and Gas Engines&#8221; (PDF). Mitsubishi Heavy Industries Technical Review. 45 (1). Retrieved 2012-02-04.<\/figcaption><\/figure>\n<p>It is easy to produce thermal energy by doing work, for example, by any frictional process. But to get work from thermal energy is more difficult. It is closely associated with the <a title=\"What is Entropy\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/what-is-entropy\/\"><strong>concept of entropy<\/strong><\/a>, which quantifies the energy of a substance that is no longer available to perform useful work. For example, electricity is particularly useful since it has <strong>very<\/strong> <strong>low entropy<\/strong> (is highly ordered) and can be converted into other forms of energy<strong> very efficiently<\/strong>. Be careful when you compare it with efficiencies of wind or hydropower (wind turbines are not heat engines). There is no energy conversion between thermal and mechanical energy.<\/p>\n<p>The thermal efficiency of various heat engines designed or used today has a large range:<\/p>\n<p><strong>For example:<\/strong><\/p>\n<p><strong>Transportation<\/strong><\/p>\n<ul>\n<li>In the middle of the twentieth century, a typical <strong>steam locomotive<\/strong> had a thermal efficiency of about <strong>6%<\/strong>. That means for every 100 MJ of coal burned, 6 MJ of mechanical power were produced.<\/li>\n<li>A typical <strong>gasoline automotive engine<\/strong> operates at around <strong>25% to 30%<\/strong> of thermal efficiency. About 70-75% is rejected as waste heat without being converted into useful work, i.e., work delivered to wheels.<\/li>\n<li>A typical <strong>diesel automotive engine<\/strong> operates at around <strong>30% to 35%<\/strong>. In general, engines using the Diesel cycle are usually more efficient.<\/li>\n<li>In 2014, new regulations were introduced for <strong>Formula 1 cars<\/strong>. These motorsport regulations have pushed teams to develop highly efficient power units. According to Mercedes, their power unit is now achieving <strong>more than 45%<\/strong> and close to 50% thermal efficiency, i.e., 45 &#8211; 50% of the potential energy in the fuel is delivered to wheels.<\/li>\n<li>The diesel engine has the highest thermal efficiency of any practical combustion engine. <strong>Low-speed diesel engines<\/strong> (as used in ships) can have a thermal efficiency that exceeds <strong>50%<\/strong>. The largest diesel engine in the world peaks at 51.7%.<\/li>\n<\/ul>\n<p><strong>Power Engineering<\/strong><\/p>\n<ul>\n<li><strong>Ocean thermal energy conversion (OTEC). \u00a0OTEC<\/strong> is a sophisticated heat engine that uses the temperature difference between cooler deep and warmer surface seawaters to run a low-pressure turbine. Since the <strong>temperature difference is low<\/strong>, about 20\u00b0C, its thermal efficiency is also very low, <strong>about 3%<\/strong>.<\/li>\n<li>In modern <a title=\"Nuclear Power Plant\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/\"><strong>nuclear power plants<\/strong><\/a>, the overall thermal efficiency is about <strong>one-third <\/strong>(33%), so <strong>3000 MWth<\/strong> of thermal power from the fission reaction is needed to generate <strong>1000 MWe<\/strong> of electrical power. Higher efficiencies can be attained by increasing the <strong>temperature<\/strong> of the <a title=\"Properties of Steam \u2013 What is Steam\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/\">steam<\/a>. But this requires an increase in pressures inside boilers or <a title=\"Steam Generator\" href=\"http:\/\/sitepourvtc.com\/steam-generator\/\">steam generators<\/a>. However, metallurgical considerations place upper limits on such pressures. In comparison to other energy sources, the thermal efficiency of 33% is not much. But it must be noted that nuclear power plants are much more complex than fossil fuel power plants, and it is much easier to burn fossil fuel than to generate energy from <a title=\"Nuclear Fuel\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/\">nuclear fuel<\/a>.<\/li>\n<li>Sub-critical fossil fuel power plants operated under <strong>critical pressure<\/strong> (i.e., lower than 22.1 MPa) can achieve 36\u201340% efficiency.<\/li>\n<li><strong><a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/reactor-types\/supercritical-water-reactor-scwr\/\">Supercritical<\/a><\/strong><a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/reactor-types\/supercritical-water-reactor-scwr\/\"><strong>\u00a0water reactors<\/strong><\/a> are considered a promising advancement for <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/\">nuclear power plants <\/a>because of their <strong>high thermal efficiency<\/strong> (~45 % vs. ~33 % for current LWRs).<\/li>\n<li>Supercritical fossil fuel power plants operated at <strong>supercritical pressure<\/strong> (i.e., greater than 22.1 MPa) have efficiencies of around <strong>43%<\/strong>. Most efficient and complex coal-fired power plants operate at <strong>&#8220;ultra critical&#8221; <\/strong><strong>pressures <\/strong>(i.e., around 30 MPa) and use multiple stage reheat to reach about <strong>48%<\/strong> efficiency.<\/li>\n<li>Modern <strong>Combined Cycle Gas Turbine<\/strong> (CCGT) plants, in which the thermodynamic cycle consists of <strong>two power plant cycles<\/strong> (e.g.,, the Brayton cycle and the Rankine cycle), can achieve a thermal efficiency of around<strong> 55%<\/strong>, in contrast to a single cycle steam power plant which is limited to efficiencies of around 35-45%.<\/li>\n<\/ul>\n<\/div>\n<div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:20px 0;border-width:2px;border-color:#999999\"><\/div>\n<div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\u00a0 <div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>References:<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>Nuclear and Reactor Physics:<\/strong>\n<ol>\n<li>J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading,\u00a0MA (1983).<\/li>\n<li>J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.<\/li>\n<li>W. M. Stacey, Nuclear Reactor Physics, John Wiley &amp; Sons, 2001, ISBN: 0- 471-39127-1.<\/li>\n<li>Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering,\u00a0Springer; 4th edition, 1994, ISBN:\u00a0978-0412985317<\/li>\n<li>W.S.C. Williams. Nuclear and Particle Physics.\u00a0Clarendon Press; 1 edition, 1991, ISBN:\u00a0978-0198520467<\/li>\n<li>Kenneth S. Krane. Introductory Nuclear Physics, 3rd Edition, Wiley, 1987,\u00a0ISBN:\u00a0978-0471805533<\/li>\n<li>G.R.Keepin. Physics of Nuclear Kinetics.\u00a0Addison-Wesley Pub. Co; 1st edition, 1965<\/li>\n<li>Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.<\/li>\n<li>U.S. Department of Energy, Nuclear Physics and Reactor Theory.\u00a0DOE Fundamentals Handbook,\u00a0Volume 1 and 2.\u00a0January\u00a01993.<\/li>\n<\/ol>\n<p><strong><\/strong><strong>Advanced Reactor Physics:<\/strong><\/p>\n<ol>\n<li>K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.<\/li>\n<li>K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.<\/li>\n<li><span style=\"font-weight: 400;\">D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.\u00a0<\/span><\/li>\n<li>E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.<\/li>\n<\/ol>\n<\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-default\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\n<h2>See previous:<\/h2>\n<p>First Law<a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/\" class=\"su-button su-button-style-flat\" style=\"color:#606060;background-color:#ffffff;border-color:#cccccc;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px\" target=\"_self\"><span style=\"color:#606060;padding:7px 20px;font-size:16px;line-height:24px;border-color:#ffffff;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px;text-shadow:0px 0px 0px #000000;-moz-text-shadow:0px 0px 0px #000000;-webkit-text-shadow:0px 0px 0px #000000\"><i class=\"sui sui-link\" style=\"font-size:16px;color:#5d5d5d\"><\/i> <\/span><\/a><\/p><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\n<h2>See above:<\/h2>\n<p>Thermodynamics<a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/\" class=\"su-button su-button-style-flat\" style=\"color:#606060;background-color:#ffffff;border-color:#cccccc;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px\" target=\"_self\"><span style=\"color:#606060;padding:7px 20px;font-size:16px;line-height:24px;border-color:#ffffff;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px;text-shadow:0px 0px 0px #000000;-moz-text-shadow:0px 0px 0px #000000;-webkit-text-shadow:0px 0px 0px #000000\"><i class=\"sui sui-link\" style=\"font-size:16px;color:#5d5d5d\"><\/i> <\/span><\/a><\/p><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\n<h2>See next:<\/h2>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>The second law of thermodynamics is a general principle that goes beyond the limitations imposed by the first law of thermodynamics. The first law is used to relate and evaluate the various energies involved in a process. However, no information about the direction of the process can be obtained by applying the first law. The &#8230; <a title=\"Second Law of Thermodynamics\" class=\"read-more\" href=\"https:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/second-law-of-thermodynamics\/\" aria-label=\"More on Second Law of Thermodynamics\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":16176,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"generate_page_header":""},"_links":{"self":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/16891"}],"collection":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/comments?post=16891"}],"version-history":[{"count":5,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/16891\/revisions"}],"predecessor-version":[{"id":34937,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/16891\/revisions\/34937"}],"up":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/16176"}],"wp:attachment":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/media?parent=16891"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}