{"id":185840,"date":"2025-01-23T08:17:00","date_gmt":"2025-01-23T08:17:00","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=185840"},"modified":"2025-01-23T08:17:02","modified_gmt":"2025-01-23T08:17:02","slug":"the-density-of-liquid-gallium-is-6-09-g-cm3-at-35c","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/23\/the-density-of-liquid-gallium-is-6-09-g-cm3-at-35c\/","title":{"rendered":"The density of liquid gallium is 6.09 g\/cm3 at 35\u00b0C"},"content":{"rendered":"\n<p>The density of liquid gallium is 6.09 g\/cm3 at 35\u00b0C. If this element is employed in a barometer instead of mercury, what is the height of a column of gallium sustained in the barometer at 1 atm pressure?<\/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<p>To solve this problem, we will use the concept that the pressure exerted by a column of liquid in a barometer is given by the equation: P=\u03c1\u22c5g\u22c5hP = \\rho \\cdot g \\cdot h<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>PP is the pressure exerted by the liquid column (1 atm = 101325 Pa),<\/li>\n\n\n\n<li>\u03c1\\rho is the density of the liquid (in kg\/m\u00b3),<\/li>\n\n\n\n<li>gg is the acceleration due to gravity (9.81 m\/s\u00b2),<\/li>\n\n\n\n<li>hh is the height of the liquid column (in meters).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Convert Density of Gallium to SI Units<\/h3>\n\n\n\n<p>The density of liquid gallium is given as 6.09 g\/cm\u00b3 at 35\u00b0C. We need to convert this density into kg\/m\u00b3 for use in the equation.<\/p>\n\n\n\n<p>1 g\/cm\u00b3 = 1000 kg\/m\u00b3<\/p>\n\n\n\n<p>Thus, the density of gallium: \u03c1=6.09\u2009g\/cm3=6.09\u00d71000\u2009kg\/m3=6090\u2009kg\/m3\\rho = 6.09 \\, \\text{g\/cm}^3 = 6.09 \\times 1000 \\, \\text{kg\/m}^3 = 6090 \\, \\text{kg\/m}^3<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Rearranging the Equation for Height<\/h3>\n\n\n\n<p>We can rearrange the pressure equation to solve for the height hh: h=P\u03c1\u22c5gh = \\frac{P}{\\rho \\cdot g}<\/p>\n\n\n\n<p>Substituting the known values: h=101325\u2009Pa6090\u2009kg\/m3\u22c59.81\u2009m\/s2h = \\frac{101325 \\, \\text{Pa}}{6090 \\, \\text{kg\/m}^3 \\cdot 9.81 \\, \\text{m\/s}^2}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Calculation<\/h3>\n\n\n\n<p>h=1013256090\u22c59.81\u224810132559758.9\u22481.695\u2009mh = \\frac{101325}{6090 \\cdot 9.81} \\approx \\frac{101325}{59758.9} \\approx 1.695 \\, \\text{m}<\/p>\n\n\n\n<p>Thus, the height of the column of gallium sustained in the barometer at 1 atm pressure is approximately <strong>1.695 meters<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>In a barometer, the height of the liquid column corresponds to the atmospheric pressure. Since mercury, which is commonly used in barometers, has a much higher density than gallium, the column of gallium will be taller for the same pressure. The density of gallium being much lower than mercury (which has a density of about 13,600 kg\/m\u00b3) results in a taller column to balance the same atmospheric pressure. Therefore, replacing mercury with gallium in a barometer results in a significant increase in the height of the liquid column.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The density of liquid gallium is 6.09 g\/cm3 at 35\u00b0C. If this element is employed in a barometer instead of mercury, what is the height of a column of gallium sustained in the barometer at 1 atm pressure? The Correct Answer and Explanation is : To solve this problem, we will use the concept that [&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-185840","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/185840","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=185840"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/185840\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=185840"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=185840"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=185840"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}