{"id":112656,"date":"2015-08-11T03:00:00","date_gmt":"2015-08-11T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=5a7f035a683349c08b4e8a7e1d278d23"},"modified":"2015-08-11T03:00:00","modified_gmt":"2015-08-11T00:00:00","slug":"finite-size-effect-on-classical-ideal-gas-revisited","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=112656","title":{"rendered":"Finite size effect on classical ideal gas revisited"},"content":{"rendered":"<p>Finite size effects on classical ideal gas are revisited. The micro-canonical partition function for<br \/>\na collection of ideal particles confined in a box is evaluated using Euler?Maclaurin?s as well as<br \/>\nPoisson&#8217;s summation formula. In Poisson&#8217;s summation formula there are some exponential terms which<br \/>\nare absent in Euler?Maclaurin?s formula. In the thermodynamic limit the exponential correction is<br \/>\nnegligibly small but in the macro\/nano dimensions and at low temperatures they may have a great<br \/>\nsignificance. The consequences of finite size effects have been illustrated by redoing the<br \/>\ncalculations in one and three dimensions keeping the exponential corrections. Global and local<br \/>\nthermodynamic properties, diffusion driven by the finite size effect, and effect on speed of sound<br \/>\nhave been discussed. Thermo-size effects, similar to thermoelectric effects, have been described in<br \/>\ndetail and may be a theoretical basis with which to design nano-scaled devices. This paper can also<br \/>\nbe very helpful f&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Finite size effects on classical ideal gas are revisited. The micro-canonical partition function for<br \/>\na collection of ideal particles confined in a box is evaluated using Euler?Maclaurin?s as well as<br \/>\nPoisson&#8217;s summation formula. In Poisson&#8217;s summation&#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-112656","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\/112656","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=112656"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/112656\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=112656"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=112656"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=112656"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}