Q. Consider a two-state system at thermal equilibrium having energies 0 and 2kBT for which the degeneracies are 1 and 2, respectively. The value of the partition function at the same absolute temperature T is\u00a0______.\u00a0 (Round off to two decimal places)<\/p>\n\n\n\n
(kB is the Boltzmann constant)<\/p>\n\n\n\n
Solution:<\/p>\n\n\n\n
General formula is\u00a0q = \u01a9 gi\u00a0e-Ei\u00a0\/ KT, <\/p>\n\n\n\n
For a two state system ,\u00a0<\/p>\n\n\n\n
q = \u01a9 gi\u00a0e-Ei\u00a0\/ KT\u00a0 <\/sup><\/p>\n\n\n\n \u21d2\u00a0q =\u00a0 g1\u00a0e-E1\u00a0\/ KT\u00a0+\u00a0\u00a0g2\u00a0e-E2 \/ KT\u00a0 <\/p>\n\n\n\n \u21d2\u00a0\u00a0q =\u00a0\u00a01\u00a0e0\u00a0\/ KT\u00a0+\u00a0\u00a02\u00a0e-2 \/ KT\u00a0 <\/p>\n\n\n\n \u21d2\u00a0q =\u00a0\u00a01\u00a0+\u00a0\u00a02\u00a0e-2\u00a0 <\/p>\n\n\n\n \u21d2\u00a0q = 1 + 0.27\u00a0 <\/p>\n\n\n\n \u21d2\u00a0 q = 1.27.<\/p>\n","protected":false},"excerpt":{"rendered":" Q. Consider a two-state system at thermal equilibrium having energies 0 and 2kBT for which the degeneracies are 1 and 2, respectively. The value of the partition function at the same absolute temperature T is\u00a0______.\u00a0 (Round off to two decimal places) (kB is the Boltzmann constant) Solution: General formula is\u00a0q = \u01a9 gi\u00a0e-Ei\u00a0\/ KT, For […]<\/p>\n","protected":false},"author":419,"featured_media":154319,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[5141],"tags":[5140],"class_list":["post-154318","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154318","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=154318"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154318\/revisions"}],"predecessor-version":[{"id":154320,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154318\/revisions\/154320"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/154319"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=154318"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=154318"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=154318"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}