{"id":157312,"date":"2023-09-05T14:24:08","date_gmt":"2023-09-05T08:54:08","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=157312"},"modified":"2023-09-05T14:24:08","modified_gmt":"2023-09-05T08:54:08","slug":"consider-a-one-dimensional-gas-of-%f0%9d%91%81-non-interacting-particles-of-mass-%f0%9d%91%9a-with-the-hamiltonian-for-a-single-particle-given-by","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/consider-a-one-dimensional-gas-of-%f0%9d%91%81-non-interacting-particles-of-mass-%f0%9d%91%9a-with-the-hamiltonian-for-a-single-particle-given-by\/","title":{"rendered":"Consider a one-dimensional gas of \ud835\udc41 non-interacting particles of mass \ud835\udc5a with the Hamiltonian for a single particle given by"},"content":{"rendered":"\n<p>Q. Consider a one-dimensional gas of \ud835\udc41 non-interacting particles of mass \ud835\udc5a with the Hamiltonian for a single particle given by ,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"235\" height=\"41\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/image-18.png\" alt=\"\" class=\"wp-image-157315\"\/><\/figure>\n\n\n\n<p>The high temperature specific heat in units of \ud835\udc45 = \ud835\udc41\ud835\udc58<sub>\ud835\udc35<\/sub> (\ud835\udc58<sub>\ud835\udc35<\/sub> is the Boltzmann constant) is<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>(A) 1<\/td><\/tr><tr><td>(B) 1.5<\/td><\/tr><tr><td>(C) 2<\/td><\/tr><tr><td>(D) 2.5<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Ans: 1<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Q. Consider a one-dimensional gas of \ud835\udc41 non-interacting particles of mass \ud835\udc5a with the Hamiltonian for a single particle given by , The high temperature specific heat in units of \ud835\udc45 = \ud835\udc41\ud835\udc58\ud835\udc35 (\ud835\udc58\ud835\udc35 is the Boltzmann constant) is (A) 1 (B) 1.5 (C) 2 (D) 2.5 Ans: 1<\/p>\n","protected":false},"author":419,"featured_media":157320,"comment_status":"open","ping_status":"","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-157312","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\/157312","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=157312"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/157312\/revisions"}],"predecessor-version":[{"id":157321,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/157312\/revisions\/157321"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/157320"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=157312"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=157312"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=157312"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}