{"id":120428,"date":"2015-08-28T02:00:00","date_gmt":"2015-08-27T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=2bb821911e86c25e833ea2fbb3c5d697"},"modified":"2015-08-28T02:00:00","modified_gmt":"2015-08-27T23:00:00","slug":"increase-of-entropy-in-the-thermalization-of-two-blocks-a-simpler-proof","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=120428","title":{"rendered":"Increase of entropy in the thermalization of two blocks: a simpler proof"},"content":{"rendered":"<p>The thermalization of two blocks with distinct initial temperatures put inside an insulated<br \/>\nrecipient is an irreversible process to which the entropic version of the second law of<br \/>\nthermodynamics applies, so the entropy of this system must increase. In a very recent note in this<br \/>\njournal, Mungan (2015 Eur. J. Phys. 36 [http:\/\/dx.doi.org\/10.1088\/0143-0807\/36\/4\/048004] 048004 )<br \/>\nhas presented a proof of such an increase in the more general case of distinct blocks, but his<br \/>\napproach involves the analysis of some series expansions, which sounds mathematically complex for<br \/>\nfirst year undergraduates. His approach also has the disadvantage of demanding the analysis of<br \/>\ndistinct cases, according to the values of the initial temperatures and thermal capacities of the<br \/>\nblocks. In this short note, I make use of the concavity of the logarithm function to present a<br \/>\nsimpler, elementary proof which is more suitable for introductory physics classes.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The thermalization of two blocks with distinct initial temperatures put inside an insulated<br \/>\nrecipient is an irreversible process to which the entropic version of the second law of<br \/>\nthermodynamics applies, so the entropy of this system must increase. I&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-120428","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/120428","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=120428"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/120428\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=120428"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=120428"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=120428"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}