{"id":190193,"date":"2025-02-11T17:57:26","date_gmt":"2025-02-11T17:57:26","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=190193"},"modified":"2025-02-11T17:57:29","modified_gmt":"2025-02-11T17:57:29","slug":"the-air-gas-constant-is-53-34-ft-lbf-ibmr","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/11\/the-air-gas-constant-is-53-34-ft-lbf-ibmr\/","title":{"rendered":"The air gas constant is 53.34 ft.lbf\/Ibm\u00b0R"},"content":{"rendered":"\n<p>a. 1. The air gas constant is 53.34 ft.lbf\/Ibm\u00b0R. Convert this constant to Btu\/Ibm.oR, joules\/kg.K, and kcallkg.K.<\/p>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li>The universal gas constant is 1.986 Btu\/lb mole. OR. Convert this constant to kcal\/kg mole.K, ft.lbf\/ lIb mole. oR, and joules\/kg mole K.<\/li>\n<\/ol>\n\n\n\n<p>b. 1. The thermal conductivity of aluminum is 200 W\/m.oC. Convert this value to Btu\/hr.ft.oP and kcaVsec.m.oC<\/p>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li>The thermal conductivity of copper is 50 Btu\/h.ft. oF. Convert this value to W\/m.oC and cal\/sec.m.\u00b0c.<\/li>\n<\/ol>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>Let&#8217;s tackle the conversions one at a time.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Part a.1: Convert the air gas constant (53.34 ft.lbf\/Ibm.\u00b0R) to other units.<\/h3>\n\n\n\n<p>Given the air gas constant:<br><strong>R = 53.34 ft.lbf\/Ibm.\u00b0R<\/strong><\/p>\n\n\n\n<p>We need to convert this to:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Btu\/Ibm.\u00b0R<\/strong><\/li>\n\n\n\n<li><strong>Joules\/kg.K<\/strong><\/li>\n\n\n\n<li><strong>kcal\/kg.K<\/strong><\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading\">Conversion Factors:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1 Btu = 1.35582 ft.lbf<\/li>\n\n\n\n<li>1 Joule = 0.73756 ft.lbf<\/li>\n\n\n\n<li>1 kcal = 4184 Joules<\/li>\n\n\n\n<li>1 lbm (pound mass) = 0.453592 kg<\/li>\n\n\n\n<li>1 \u00b0R = 5\/9 \u00b0C<\/li>\n\n\n\n<li>1 \u00b0R = 1 \u00b0F (for practical purposes in this case)<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Step-by-step conversion:<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Convert ft.lbf\/Ibm.\u00b0R to Btu\/Ibm.\u00b0R<\/strong>:<br>[<br>R = 53.34 \\, \\text{ft.lbf\/Ibm.\u00b0R} \\times \\frac{1 \\, \\text{Btu}}{1.35582 \\, \\text{ft.lbf}} = 39.38 \\, \\text{Btu\/Ibm.\u00b0R}<br>]<\/li>\n\n\n\n<li><strong>Convert ft.lbf\/Ibm.\u00b0R to Joules\/kg.K<\/strong>:<br>[<br>R = 53.34 \\, \\text{ft.lbf\/Ibm.\u00b0R} \\times \\frac{0.73756 \\, \\text{Joules}}{1 \\, \\text{ft.lbf}} \\times \\frac{1}{0.453592 \\, \\text{kg}} = 85.16 \\, \\text{Joules\/kg.K}<br>]<\/li>\n\n\n\n<li><strong>Convert ft.lbf\/Ibm.\u00b0R to kcal\/kg.K<\/strong>:<br>[<br>R = 53.34 \\, \\text{ft.lbf\/Ibm.\u00b0R} \\times \\frac{0.73756 \\, \\text{Joules}}{1 \\, \\text{ft.lbf}} \\times \\frac{1}{0.453592 \\, \\text{kg}} \\times \\frac{1 \\, \\text{kcal}}{4184 \\, \\text{Joules}} = 0.0204 \\, \\text{kcal\/kg.K}<br>]<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Part a.2: Convert the universal gas constant (1.986 Btu\/lb mole.\u00b0R) to other units.<\/h3>\n\n\n\n<p>Given the universal gas constant:<br><strong>R = 1.986 Btu\/lb mole.\u00b0R<\/strong><\/p>\n\n\n\n<p>We need to convert this to:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>kcal\/kg mole.K<\/strong><\/li>\n\n\n\n<li><strong>ft.lbf\/lb mole.\u00b0R<\/strong><\/li>\n\n\n\n<li><strong>Joules\/kg mole.K<\/strong><\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading\">Conversion Factors:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1 Btu = 1.35582 ft.lbf<\/li>\n\n\n\n<li>1 kcal = 4184 Joules<\/li>\n\n\n\n<li>1 lbm = 0.453592 kg<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Step-by-step conversion:<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Convert Btu\/lb mole.\u00b0R to kcal\/kg mole.K<\/strong>:<br>[<br>R = 1.986 \\, \\text{Btu\/lb mole.\u00b0R} \\times \\frac{1 \\, \\text{kcal}}{3.9683 \\, \\text{Btu}} \\times \\frac{1}{0.453592 \\, \\text{kg}} = 4.42 \\, \\text{kcal\/kg mole.K}<br>]<\/li>\n\n\n\n<li><strong>Convert Btu\/lb mole.\u00b0R to ft.lbf\/lb mole.\u00b0R<\/strong>:<br>[<br>R = 1.986 \\, \\text{Btu\/lb mole.\u00b0R} \\times 1.35582 \\, \\text{ft.lbf\/Btu} = 2.69 \\, \\text{ft.lbf\/lb mole.\u00b0R}<br>]<\/li>\n\n\n\n<li><strong>Convert Btu\/lb mole.\u00b0R to Joules\/kg mole.K<\/strong>:<br>[<br>R = 1.986 \\, \\text{Btu\/lb mole.\u00b0R} \\times 1.35582 \\, \\text{ft.lbf\/Btu} \\times 0.73756 \\, \\text{Joules\/ft.lbf} \\times \\frac{1}{0.453592 \\, \\text{kg}} = 830.3 \\, \\text{Joules\/kg mole.K}<br>]<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Part b.1: Convert the thermal conductivity of aluminum (200 W\/m.\u00b0C) to other units.<\/h3>\n\n\n\n<p>Given the thermal conductivity of aluminum:<br><strong>K = 200 W\/m.\u00b0C<\/strong><\/p>\n\n\n\n<p>We need to convert this to:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Btu\/hr.ft.\u00b0F<\/strong><\/li>\n\n\n\n<li><strong>kcal\/sec.m.\u00b0C<\/strong><\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading\">Conversion Factors:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1 W = 3.41214 Btu\/hr<\/li>\n\n\n\n<li>1 W = 0.8598 cal\/sec<\/li>\n\n\n\n<li>1 meter = 3.28084 feet<\/li>\n\n\n\n<li>1 \u00b0C = 1.8 \u00b0F (temperature difference is equivalent)<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Step-by-step conversion:<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Convert W\/m.\u00b0C to Btu\/hr.ft.\u00b0F<\/strong>:<br>[<br>K = 200 \\, \\text{W\/m.\u00b0C} \\times \\frac{3.41214 \\, \\text{Btu\/hr}}{1 \\, \\text{W}} \\times \\frac{1}{3.28084 \\, \\text{ft}} \\times \\frac{1}{1.8 \\, \\text{\u00b0C\/\u00b0F}} = 1.28 \\, \\text{Btu\/hr.ft.\u00b0F}<br>]<\/li>\n\n\n\n<li><strong>Convert W\/m.\u00b0C to kcal\/sec.m.\u00b0C<\/strong>:<br>[<br>K = 200 \\, \\text{W\/m.\u00b0C} \\times 0.8598 \\, \\text{cal\/sec} \\times \\frac{1}{1000} = 0.17196 \\, \\text{kcal\/sec.m.\u00b0C}<br>]<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Part b.2: Convert the thermal conductivity of copper (50 Btu\/h.ft.\u00b0F) to other units.<\/h3>\n\n\n\n<p>Given the thermal conductivity of copper:<br><strong>K = 50 Btu\/h.ft.\u00b0F<\/strong><\/p>\n\n\n\n<p>We need to convert this to:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>W\/m.\u00b0C<\/strong><\/li>\n\n\n\n<li><strong>cal\/sec.m.\u00b0C<\/strong><\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading\">Conversion Factors:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1 Btu = 1055.06 J<\/li>\n\n\n\n<li>1 hour = 3600 seconds<\/li>\n\n\n\n<li>1 foot = 0.3048 meters<\/li>\n\n\n\n<li>1 \u00b0F = 5\/9 \u00b0C (temperature difference)<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Step-by-step conversion:<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Convert Btu\/h.ft.\u00b0F to W\/m.\u00b0C<\/strong>:<br>[<br>K = 50 \\, \\text{Btu\/h.ft.\u00b0F} \\times \\frac{1055.06 \\, \\text{J\/Btu}}{1 \\, \\text{Btu}} \\times \\frac{1 \\, \\text{h}}{3600 \\, \\text{s}} \\times \\frac{1}{0.3048^2 \\, \\text{m}^2} \\times \\frac{1}{5\/9 \\, \\text{\u00b0F\/\u00b0C}} = 235.87 \\, \\text{W\/m.\u00b0C}<br>]<\/li>\n\n\n\n<li><strong>Convert Btu\/h.ft.\u00b0F to cal\/sec.m.\u00b0C<\/strong>:<br>[<br>K = 50 \\, \\text{Btu\/h.ft.\u00b0F} \\times 0.8598 \\, \\text{cal\/sec} \\times \\frac{1}{0.3048^2 \\, \\text{m}^2} \\times \\frac{1}{5\/9 \\, \\text{\u00b0F\/\u00b0C}} = 0.02847 \\, \\text{cal\/sec.m.\u00b0C}<br>]<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Final Results:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Air gas constant:<\/li>\n\n\n\n<li><strong>39.38 Btu\/Ibm.\u00b0R<\/strong><\/li>\n\n\n\n<li><strong>85.16 Joules\/kg.K<\/strong><\/li>\n\n\n\n<li><strong>0.0204 kcal\/kg.K<\/strong><\/li>\n\n\n\n<li>Universal gas constant:<\/li>\n\n\n\n<li><strong>4.42 kcal\/kg mole.K<\/strong><\/li>\n\n\n\n<li><strong>2.69 ft.lbf\/lb mole.\u00b0R<\/strong><\/li>\n\n\n\n<li><strong>830.3 Joules\/kg mole.K<\/strong><\/li>\n\n\n\n<li>Thermal conductivity of aluminum:<\/li>\n\n\n\n<li><strong>1.28 Btu\/hr.ft.\u00b0F<\/strong><\/li>\n\n\n\n<li><strong>0.17196 kcal\/sec.m.\u00b0C<\/strong><\/li>\n\n\n\n<li>Thermal conductivity of copper:<\/li>\n\n\n\n<li><strong>235.87 W\/m.\u00b0C<\/strong><\/li>\n\n\n\n<li><strong>0.02847 cal\/sec.m.\u00b0C<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>These conversions are necessary when dealing with various units in thermodynamics, particularly when working with different measurement systems (e.g., Imperial vs. SI units). It&#8217;s important to use proper conversion factors to ensure consistency in calculations, as thermodynamic properties like gas constants and thermal conductivity can differ in their expression depending on the unit system. Understanding these conversions is fundamental to accurately analyzing and applying thermodynamic principles in real-world engineering applications.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>a. 1. The air gas constant is 53.34 ft.lbf\/Ibm\u00b0R. Convert this constant to Btu\/Ibm.oR, joules\/kg.K, and kcallkg.K. b. 1. The thermal conductivity of aluminum is 200 W\/m.oC. Convert this value to Btu\/hr.ft.oP and kcaVsec.m.oC The Correct Answer and Explanation is : Let&#8217;s tackle the conversions one at a time. Part a.1: Convert the air gas [&hellip;]<\/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-190193","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/190193","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=190193"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/190193\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=190193"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=190193"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=190193"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}