{"id":224240,"date":"2025-06-02T19:38:50","date_gmt":"2025-06-02T19:38:50","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=224240"},"modified":"2025-06-02T19:38:52","modified_gmt":"2025-06-02T19:38:52","slug":"a-piston-has-an-external-pressure-of-12-0-atm","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/02\/a-piston-has-an-external-pressure-of-12-0-atm\/","title":{"rendered":"A piston has an external pressure of 12.0 atm."},"content":{"rendered":"\n

. A piston has an external pressure of 12.0 atm. How much work has been done in joules if the cylinder goes from a volume of 0.120 liters to 0.650 liters? Express your answer with the appropriate units.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Work done<\/strong> w=\u2212Pext\u2005\u200a\u0394V=\u221212.0 atm\u2005\u200a(0.650 L\u22120.120 L)=\u221212.0 atm\u2005\u200a(0.530 L)=\u22126.36 L\\cdotpatmw = -P_{\\text{ext}}\\;\\Delta V = -12.0\\ \\text{atm}\\;(0.650\\ \\text{L} – 0.120\\ \\text{L}) = -12.0\\ \\text{atm}\\;(0.530\\ \\text{L}) = -6.36\\ \\text{L\u00b7atm}<\/p>\n\n\n\n

Converting L\\cdotpatm\\text{L\u00b7atm} to joules ( 1 L\\cdotpatm=101.325 J1\\ \\text{L\u00b7atm} = 101.325\\ \\text{J} ): w=\u22126.36 L\\cdotpatm\u2005\u200a(101.325 J L\u22121atm\u22121)\u2248\u22126.44\u00d7102 Jw = -6.36\\ \\text{L\u00b7atm}\\;(101.325\\ \\text{J L}^{-1}\\text{atm}^{-1}) \\approx -6.44 \\times 10^{2}\\ \\text{J} w\u2248\u22126.44\u00d7102 J\\boxed{w \\approx -6.44 \\times 10^{2}\\ \\text{J}}<\/p>\n\n\n\n

\n\n\n\n

Why this result makes sense <\/h3>\n\n\n\n

In thermodynamics, the mechanical work associated with a gas pushing back an external force is defined (in chemistry) as
w=\u2212Pext\u0394Vw = -P_{\\text{ext}}\\Delta V.<\/p>\n\n\n\n

    \n
  • Sign convention.<\/strong> The negative sign reflects the \u201csystem\u201d point of view adopted in chemistry: if the gas expands, it spends energy doing work on its surroundings, and the system\u2019s internal energy decreases, so ww is negative. If the gas were compressed (\u0394V<0\\Delta V < 0), ww would be positive because energy is supplied to<\/strong> the gas.<\/li>\n\n\n\n
  • Constant external pressure.<\/strong> Because the problem states a single external pressure (12.0 atm), we do not need to integrate P(V)P(V) over the entire path. The work is simply the product of that constant pressure and the change in volume.<\/li>\n\n\n\n
  • Volume change.<\/strong> The cylinder grows from 0.120 L to 0.650 L, so \u0394V=+0.530\u00a0L\\Delta V = +0.530\\ \\text{L}. A positive \u0394V\\Delta V confirms this is an expansion.<\/li>\n\n\n\n
  • Unit conversion.<\/strong> Pressure\u2013volume work is naturally expressed in L\u00b7atm, but energy must be in joules to match SI. The experimentally determined equivalence 1\u00a0L\\cdotpatm=101.325\u00a0J1\\ \\text{L\u00b7atm} = 101.325\\ \\text{J} comes directly from the definition of the joule and the pascal (1 Pa = 1 N m\u22122^{-2}). By multiplying by this conversion factor, we translate macroscopic mechanical work into the SI energy unit.<\/li>\n\n\n\n
  • Magnitude.<\/strong> 644 J is roughly the energy required to lift a 6.6 kg mass one metre against Earth\u2019s gravity (because E=mgh\u22486.6\u00a0kg\u00d79.81\u00a0m\u00a0s\u22122\u00d71\u00a0m\u224865\u00a0JE = mgh \\approx 6.6\\ \\text{kg}\\times9.81\\ \\text{m s}^{-2}\\times1\\ \\text{m} \u2248 65\\ \\text{J} per kilogram\u2010metre). This comparison helps to visualize that high pressures acting over even modest laboratory volumes can involve hundreds of joules\u2014substantial on a human scale.<\/li>\n\n\n\n
  • Significant figures.<\/strong> Each measured quantity (12.0 atm, 0.120 L, 0.650 L) has three significant figures, so the final answer is reported to three significant figures: 6.44\u00d7102\u00a0J6.44 \\times 10^{2}\\ \\text{J}.<\/li>\n<\/ul>\n\n\n\n

    Thus, the expanding gas has done about \u22126.44 \u00d7 10\u00b2 J<\/strong> of work on its surroundings.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    . A piston has an external pressure of 12.0 atm. How much work has been done in joules if the cylinder goes from a volume of 0.120 liters to 0.650 liters? Express your answer with the appropriate units. The Correct Answer and Explanation is: Work done w=\u2212Pext\u2005\u200a\u0394V=\u221212.0 atm\u2005\u200a(0.650 L\u22120.120 L)=\u221212.0 atm\u2005\u200a(0.530 L)=\u22126.36 L\\cdotpatmw = -P_{\\text{ext}}\\;\\Delta V = -12.0\\ \\text{atm}\\;(0.650\\ \\text{L} – […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","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-5)","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-5)","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-5)","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":[25],"tags":[],"class_list":["post-224240","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224240","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=224240"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224240\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=224240"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=224240"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=224240"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}