{"id":187430,"date":"2025-02-04T18:41:32","date_gmt":"2025-02-04T18:41:32","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=187430"},"modified":"2025-02-04T18:41:34","modified_gmt":"2025-02-04T18:41:34","slug":"which-of-the-following-are-dimensionless-physical-quantities","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/04\/which-of-the-following-are-dimensionless-physical-quantities\/","title":{"rendered":"Which of the following are dimensionless physical quantities"},"content":{"rendered":"\n<p>Which of the following are dimensionless physical quantities?<br>Thermal conductivity<br>Temperature<br>Amount of substance<br>Density<br>Dynamic viscosity<br>Reynolds No. (<br>Dryness fraction<br>Specific enthalpy<br>Ratio of specific heat capacities<br>Mach No. ( Ma)<br>Frequency<br>Specific heat transfer<br>Entropy (S)<br>Strain<\/p>\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<h3 class=\"wp-block-heading\"><strong>Dimensionless Physical Quantities from the Given List:<\/strong><\/h3>\n\n\n\n<p>The following quantities are <strong>dimensionless<\/strong>:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Reynolds Number (Re)<\/strong><\/li>\n\n\n\n<li><strong>Dryness Fraction (x)<\/strong><\/li>\n\n\n\n<li><strong>Ratio of Specific Heat Capacities (\u03b3 = Cp\/Cv)<\/strong><\/li>\n\n\n\n<li><strong>Mach Number (Ma)<\/strong><\/li>\n\n\n\n<li><strong>Strain<\/strong><\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation:<\/strong><\/h3>\n\n\n\n<p>Dimensionless physical quantities are those that <strong>do not have any physical units<\/strong> and are represented as pure numbers. They are often formed by the <strong>ratio of similar physical quantities<\/strong>, canceling out the units.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Reynolds Number (Re)<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Defined as ( Re = \\frac{\\rho vL}{\\mu} ), where ( \\rho ) is density, ( v ) is velocity, ( L ) is characteristic length, and ( \\mu ) is dynamic viscosity.<\/li>\n\n\n\n<li>Since it is a ratio of forces (inertial to viscous), all units cancel out, making it <strong>dimensionless<\/strong>.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Dryness Fraction (x)<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Defined as ( x = \\frac{\\text{Mass of vapor}}{\\text{Total mass}} ).<\/li>\n\n\n\n<li>Since it is a <strong>ratio of masses<\/strong>, it has <strong>no dimensions<\/strong>.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Ratio of Specific Heat Capacities (\u03b3 = Cp\/Cv)<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Specific heats (( C_p ) and ( C_v )) have the same unit (J\/kg\u00b7K).<\/li>\n\n\n\n<li>Their ratio is <strong>dimensionless<\/strong>.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Mach Number (Ma)<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Defined as ( Ma = \\frac{v}{c} ), where ( v ) is the speed of the object and ( c ) is the speed of sound.<\/li>\n\n\n\n<li>Since it is a <strong>ratio of two velocities<\/strong>, it has <strong>no dimensions<\/strong>.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Strain<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Defined as ( \\text{Strain} = \\frac{\\Delta L}{L} ), where ( \\Delta L ) is change in length and ( L ) is original length.<\/li>\n\n\n\n<li>Since it is a <strong>ratio of lengths<\/strong>, it has <strong>no dimensions<\/strong>.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Physical Quantities that are NOT Dimensionless:<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Thermal Conductivity<\/strong> (W\/m\u00b7K) \u2192 Has dimensions<\/li>\n\n\n\n<li><strong>Temperature<\/strong> (K) \u2192 Has dimensions<\/li>\n\n\n\n<li><strong>Amount of Substance<\/strong> (mol) \u2192 Has dimensions<\/li>\n\n\n\n<li><strong>Density<\/strong> (kg\/m\u00b3) \u2192 Has dimensions<\/li>\n\n\n\n<li><strong>Dynamic Viscosity<\/strong> (Pa\u00b7s or kg\/m\u00b7s) \u2192 Has dimensions<\/li>\n\n\n\n<li><strong>Specific Enthalpy<\/strong> (J\/kg) \u2192 Has dimensions<\/li>\n\n\n\n<li><strong>Frequency<\/strong> (Hz or s\u207b\u00b9) \u2192 Has dimensions<\/li>\n\n\n\n<li><strong>Specific Heat Transfer<\/strong> (J\/kg\u00b7K) \u2192 Has dimensions<\/li>\n\n\n\n<li><strong>Entropy (S)<\/strong> (J\/K) \u2192 Has dimensions<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Conclusion:<\/strong><\/h3>\n\n\n\n<p>Only <strong>Reynolds Number, Dryness Fraction, Ratio of Specific Heats, Mach Number, and Strain<\/strong> are <strong>dimensionless<\/strong> quantities in the given list. These are typically formed as <strong>ratios of similar properties<\/strong> where the units cancel out, making them independent of measurement systems.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Which of the following are dimensionless physical quantities?Thermal conductivityTemperatureAmount of substanceDensityDynamic viscosityReynolds No. (Dryness fractionSpecific enthalpyRatio of specific heat capacitiesMach No. ( Ma)FrequencySpecific heat transferEntropy (S)Strain The Correct Answer and Explanation is : Dimensionless Physical Quantities from the Given List: The following quantities are dimensionless: Explanation: Dimensionless physical quantities are those that do not have [&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-187430","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187430","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=187430"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187430\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=187430"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=187430"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=187430"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}