{"id":1626,"date":"2024-07-27T08:22:47","date_gmt":"2024-07-27T08:22:47","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=1626"},"modified":"2024-07-27T08:22:48","modified_gmt":"2024-07-27T08:22:48","slug":"clausius-statement","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/07\/27\/clausius-statement\/","title":{"rendered":"Clausius Statement"},"content":{"rendered":"\n

The efficiency of a heat engine cycle greatly depends on how the individual processes are executed. The net work can be maximized by using reversible processes. The best known reversible cycle is the Carnot cycle.<\/p>\n\n\n\n

Note that the reversible cycles cannot be achieved in practice because of irreversibilities associated with real processes. But, the reversible cycles provide upper limits on the performance of real cycles.<\/p>\n\n\n\n

Consider a gas in a cylinder\u2013piston (closed system). The Carnot cycle has four processes as <\/p>\n\n\n\n

\"Figure<\/figure>\n\n\n\n

\u00a0P\u2013V<\/em>\u00a0Diagram of Carnot Cycle<\/p>\n\n\n\n

1\u20132 Reversible Isothermal Expansion:<\/em><\/strong> The gas expands slowly; heat is added reversibly at constant temperature (T<\/em>H<\/sub>) to the system. Work is done on the surrounding.<\/p>\n\n\n\n

2\u20133 Reversible Adiabatic Expansion:<\/em><\/strong> The cylinder\u2013piston is now insulated (adiabatic) and gas continues to expand reversibly (slowly). So, the gas is doing work on the surroundings, and as a result of expansion the gas temperature reduces from T<\/em>H<\/sub> to T<\/em>L<\/sub>.<\/p>\n\n\n\n

3\u20134 Reversible Isothermal Compression:<\/em><\/strong> The gas is allowed to exchange heat with a sink at temperature T<\/em>L<\/sub> as the gas is being slowly compressed. So, the surrounding is doing work (reversibly) on the system, and heat is transferred from the system to the surroundings (reversibly) such that the gas temperature remains constant at T<\/em>L<\/sub>.<\/p>\n\n\n\n

<\/a>4\u20131 Reversible Adiabatic Compression:<\/em><\/strong> The gas temperature is increasing from T<\/em>L<\/sub> to T<\/em>H<\/sub> as a result of compression. Carnot cycle is the most efficient cycle operating between two specified temperature limits.<\/p>\n\n\n\n

The efficiency of all reversible heat engines operating between the two same reservoirs is the same. The thermal efficiency of a heat engine (reversible or irreversible) is<\/p>\n\n\n\n

\"Equation\"\/<\/figure>\n\n\n\n

The efficiency of an irreversible (real) cycle is always less than the efficiency of the Carnot cycle operating between the same two reservoirs.<\/p>\n\n\n\n

\"Equation\"\/<\/figure>\n\n\n\n

Carnot Corollaries<\/h4>\n\n\n\n

The two corollaries of the second law known as Carnot corollaries:<\/p>\n\n\n\n

    \n
  1. The thermal efficiency of an irreversible power cycle is always less than the thermal efficiency of a reversible power cycle when each operates between the same two thermal reservoirs.<\/li>\n\n\n\n
  2. All reversible power cycles operating between the same two thermal reservoirs have the same thermal efficiency.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

    The efficiency of a heat engine cycle greatly depends on how the individual processes are executed. The net work can be maximized by using reversible processes. The best known reversible cycle is the Carnot cycle. Note that the reversible cycles cannot be achieved in practice because of irreversibilities associated with real processes. But, the reversible […]<\/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-1626","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\/1626","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=1626"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/1626\/revisions"}],"predecessor-version":[{"id":1627,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/1626\/revisions\/1627"}],"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=1626"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=1626"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=1626"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}