{"id":138,"date":"2018-11-14T07:29:33","date_gmt":"2018-11-14T07:29:33","guid":{"rendered":"http:\/\/phyp05.epgpbooks.inflibnet.ac.in\/?post_type=front-matter&#038;p=138"},"modified":"2019-04-29T11:07:24","modified_gmt":"2019-04-29T11:07:24","slug":"gibbs-paradox-and-indistinguishability-of-particles","status":"publish","type":"front-matter","link":"https:\/\/ebooks.inflibnet.ac.in\/phyp05\/front-matter\/gibbs-paradox-and-indistinguishability-of-particles\/","title":{"rendered":"Gibbs Paradox and Indistinguishability of Particles"},"content":{"raw":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/lrDbzEAWbrA\" target=\"_blank\" rel=\"noopener\"><img src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a>\r\n<\/span><\/div>\r\n<strong>1. Learning Outcomes<\/strong>\r\n\r\n&nbsp;\r\n\r\nAfter studying this module, you shall be able to\r\n<ul>\r\n \t<li style=\"text-align: justify\">Comprehend the logical consequences of violation of extensiveness of a thermodynamic physical quantity while applying statistical methods.<\/li>\r\n \t<li>Appreciate paradoxical situation which arises on mixing of same type of ideal gases together, namely Gibbs Paradox.<\/li>\r\n \t<li style=\"text-align: justify\">Infer the importance of indistinguishability of particles even in a classical system.<\/li>\r\n \t<li style=\"text-align: justify\">Correct the expression of entropy of an ideal gas by applying so called correct Boltzmann counting rule.<\/li>\r\n \t<li style=\"text-align: justify\">Learn that quantum statistical mechanics reduces to classical statistical mechanics results only when correct enumeration rules are applied in the classical limit.<\/li>\r\n<\/ul>\r\n<img class=\"aligncenter size-full wp-image-139\" src=\"http:\/\/phyp05.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/89\/2018\/11\/1-4.png\" alt=\"\" width=\"617\" height=\"682\" \/> <img class=\"aligncenter size-full wp-image-140\" src=\"http:\/\/phyp05.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/89\/2018\/11\/2-3.png\" alt=\"\" width=\"593\" height=\"690\" \/> <img class=\"aligncenter size-full wp-image-141\" src=\"http:\/\/phyp05.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/89\/2018\/11\/3-4.png\" alt=\"\" width=\"615\" height=\"709\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-142\" src=\"http:\/\/phyp05.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/89\/2018\/11\/4-3.png\" alt=\"\" width=\"613\" height=\"689\" \/> <img class=\"aligncenter size-full wp-image-143\" src=\"http:\/\/phyp05.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/89\/2018\/11\/5-3.png\" alt=\"\" width=\"612\" height=\"652\" \/> <img class=\"aligncenter size-full wp-image-144\" src=\"http:\/\/phyp05.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/89\/2018\/11\/6-3.png\" alt=\"\" width=\"619\" height=\"702\" \/>\r\n\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>you can view video on Gibbs Paradox and Indistinguishability of Particles<\/strong><\/td>\r\n<td><a href=\"https:\/\/youtu.be\/lrDbzEAWbrA\" target=\"_blank\" rel=\"noopener\"><img class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<strong>References:-<\/strong>\r\n<p class=\"no-indent\">1. Pathria R.K. and Beale P. D., Statistical Mechanics, 3rd ed. (Elsevier, 2011).\r\n2. Landau L.D., Lifshitz E.M., \u201c Statistical Physics Part 1,\u201d 3rd Edition, Oxford: Pergamon Press., 1982\r\n3. Pal P.B., \u201cAn Introductory Course of Statistical Mechanics\u201d, New Delhi: Narosa Publishing House Pvt. Ltd., 2008.\r\n4. Panat P.V., \u201cThermodynamics and Statistical Mechanics,\u201d New Delhi: Narosa Publishing House Pvt. Ltd., 2008\r\n5. Yoshioka D., \u201cStatistical Physics An Introduction,\u201d Berlin Heidelberg: Springer-Verlag, 2007<\/p>","rendered":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/lrDbzEAWbrA\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a><br \/>\n<\/span><\/div>\n<p><strong>1. Learning Outcomes<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>After studying this module, you shall be able to<\/p>\n<ul>\n<li style=\"text-align: justify\">Comprehend the logical consequences of violation of extensiveness of a thermodynamic physical quantity while applying statistical methods.<\/li>\n<li>Appreciate paradoxical situation which arises on mixing of same type of ideal gases together, namely Gibbs Paradox.<\/li>\n<li style=\"text-align: justify\">Infer the importance of indistinguishability of particles even in a classical system.<\/li>\n<li style=\"text-align: justify\">Correct the expression of entropy of an ideal gas by applying so called correct Boltzmann counting rule.<\/li>\n<li style=\"text-align: justify\">Learn that quantum statistical mechanics reduces to classical statistical mechanics results only when correct enumeration rules are applied in the classical limit.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-139\" src=\"http:\/\/phyp05.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/89\/2018\/11\/1-4.png\" alt=\"\" width=\"617\" height=\"682\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-content\/uploads\/sites\/89\/2018\/11\/1-4.png 617w, https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-content\/uploads\/sites\/89\/2018\/11\/1-4-271x300.png 271w, https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-content\/uploads\/sites\/89\/2018\/11\/1-4-65x72.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-content\/uploads\/sites\/89\/2018\/11\/1-4-225x249.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-content\/uploads\/sites\/89\/2018\/11\/1-4-350x387.png 350w\" sizes=\"auto, (max-width: 617px) 100vw, 617px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-140\" src=\"http:\/\/phyp05.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/89\/2018\/11\/2-3.png\" alt=\"\" width=\"593\" height=\"690\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-content\/uploads\/sites\/89\/2018\/11\/2-3.png 593w, https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-content\/uploads\/sites\/89\/2018\/11\/2-3-258x300.png 258w, https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-content\/uploads\/sites\/89\/2018\/11\/2-3-65x76.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-content\/uploads\/sites\/89\/2018\/11\/2-3-225x262.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-content\/uploads\/sites\/89\/2018\/11\/2-3-350x407.png 350w\" sizes=\"auto, (max-width: 593px) 100vw, 593px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-141\" src=\"http:\/\/phyp05.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/89\/2018\/11\/3-4.png\" alt=\"\" width=\"615\" height=\"709\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-content\/uploads\/sites\/89\/2018\/11\/3-4.png 615w, https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-content\/uploads\/sites\/89\/2018\/11\/3-4-260x300.png 260w, https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-content\/uploads\/sites\/89\/2018\/11\/3-4-65x75.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-content\/uploads\/sites\/89\/2018\/11\/3-4-225x259.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-content\/uploads\/sites\/89\/2018\/11\/3-4-350x403.png 350w\" sizes=\"auto, (max-width: 615px) 100vw, 615px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-142\" src=\"http:\/\/phyp05.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/89\/2018\/11\/4-3.png\" alt=\"\" width=\"613\" height=\"689\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-143\" src=\"http:\/\/phyp05.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/89\/2018\/11\/5-3.png\" alt=\"\" width=\"612\" height=\"652\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-144\" src=\"http:\/\/phyp05.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/89\/2018\/11\/6-3.png\" alt=\"\" width=\"619\" height=\"702\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-content\/uploads\/sites\/89\/2018\/11\/6-3.png 619w, https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-content\/uploads\/sites\/89\/2018\/11\/6-3-265x300.png 265w, https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-content\/uploads\/sites\/89\/2018\/11\/6-3-65x74.png 65w, https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-content\/uploads\/sites\/89\/2018\/11\/6-3-225x255.png 225w, https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-content\/uploads\/sites\/89\/2018\/11\/6-3-350x397.png 350w\" sizes=\"auto, (max-width: 619px) 100vw, 619px\" \/><\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>you can view video on Gibbs Paradox and Indistinguishability of Particles<\/strong><\/td>\n<td><a href=\"https:\/\/youtu.be\/lrDbzEAWbrA\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>References:-<\/strong><\/p>\n<p class=\"no-indent\">1. Pathria R.K. and Beale P. D., Statistical Mechanics, 3rd ed. (Elsevier, 2011).<br \/>\n2. Landau L.D., Lifshitz E.M., \u201c Statistical Physics Part 1,\u201d 3rd Edition, Oxford: Pergamon Press., 1982<br \/>\n3. Pal P.B., \u201cAn Introductory Course of Statistical Mechanics\u201d, New Delhi: Narosa Publishing House Pvt. Ltd., 2008.<br \/>\n4. Panat P.V., \u201cThermodynamics and Statistical Mechanics,\u201d New Delhi: Narosa Publishing House Pvt. Ltd., 2008<br \/>\n5. Yoshioka D., \u201cStatistical Physics An Introduction,\u201d Berlin Heidelberg: Springer-Verlag, 2007<\/p>\n","protected":false},"author":3,"menu_order":7,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["prof-p-k-ahluwalia"],"pb_section_license":""},"front-matter-type":[],"contributor":[58],"license":[],"class_list":["post-138","front-matter","type-front-matter","status-publish","hentry","contributor-prof-p-k-ahluwalia"],"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-json\/pressbooks\/v2\/front-matter\/138","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-json\/pressbooks\/v2\/front-matter"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-json\/wp\/v2\/types\/front-matter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":8,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-json\/pressbooks\/v2\/front-matter\/138\/revisions"}],"predecessor-version":[{"id":651,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-json\/pressbooks\/v2\/front-matter\/138\/revisions\/651"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-json\/pressbooks\/v2\/front-matter\/138\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-json\/wp\/v2\/media?parent=138"}],"wp:term":[{"taxonomy":"front-matter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-json\/pressbooks\/v2\/front-matter-type?post=138"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-json\/wp\/v2\/contributor?post=138"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp05\/wp-json\/wp\/v2\/license?post=138"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}