{"id":154312,"date":"2023-08-03T17:06:56","date_gmt":"2023-08-03T11:36:56","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=154312"},"modified":"2023-08-03T17:06:58","modified_gmt":"2023-08-03T11:36:58","slug":"an-ideal-gas-occupies-an-unknown-volume-v-liters-l-at-a-pressure-of-12-atm-the-gas-is-expanded-isothermally-against-a-constant","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/an-ideal-gas-occupies-an-unknown-volume-v-liters-l-at-a-pressure-of-12-atm-the-gas-is-expanded-isothermally-against-a-constant\/","title":{"rendered":"An ideal gas occupies an unknown volume V liters (L) at a pressure of 12 atm. The gas is expanded isothermally against a constant"},"content":{"rendered":"\n<p>Q. An ideal gas occupies an unknown volume <strong>V <\/strong>liters (L) at a pressure of 12 atm. The gas is expanded isothermally against a constant external pressure of 2 atm so that its final volume becomes 3 L. The work involved for this expansion process is______cal. (Round off to two decimal places)<\/p>\n\n\n\n<p>(Gas constant R = 0.082 L atm mol<sup>\u20131<\/sup> K<sup>\u20131<\/sup> = 2 cal mol<sup>\u20131<\/sup> K<sup>\u20131<\/sup>)<\/p>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<p>Ideal Gas Equation-\u00a0PV= n RT,\u00a0 where P = Pressure, V = Volume, n = No. of moles, R = Gas constant, T = Temperature.\u00a0 <\/p>\n\n\n\n<p>Given, P1\u00a0= 12 atm , V1\u00a0= V (L), Pext\u00a0= 2 atm, V = 2L .<\/p>\n\n\n\n<p> Using, <\/p>\n\n\n\n<p>PV = n RT, <\/p>\n\n\n\n<p>V = RT\/ P where n is unity and T = 298 K .\u00a0 <\/p>\n\n\n\n<p>W = -Pext\u00a0(V2\u00a0&#8211; V1)\u00a0, <\/p>\n\n\n\n<p>W = -2 atm\u00a0 (3L &#8211; RT1\u00a0\/ P1),\u00a0\u00a0 <\/p>\n\n\n\n<p>W = -2 atm (3L &#8211; 0.082Latm K-1mol-1\u00a0x 298 K\u00a0\/ 12 atm\u00a0),\u00a0\u00a0 <\/p>\n\n\n\n<p>W = -1.927\u00a0atm L, Using 1 atm L = 101.32 J,\u00a0\u00a0 <\/p>\n\n\n\n<p>W = -1.927 x 101.32 \/ 4.184\u00a0 calories.\u00a0\u00a0 <\/p>\n\n\n\n<p>W = -46.66 calories.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Q. An ideal gas occupies an unknown volume V liters (L) at a pressure of 12 atm. The gas is expanded isothermally against a constant external pressure of 2 atm so that its final volume becomes 3 L. The work involved for this expansion process is______cal. (Round off to two decimal places) (Gas constant R [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":154313,"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-154312","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\/154312","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=154312"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154312\/revisions"}],"predecessor-version":[{"id":154314,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154312\/revisions\/154314"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/154313"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=154312"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=154312"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=154312"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}