{"id":186564,"date":"2025-01-25T09:23:59","date_gmt":"2025-01-25T09:23:59","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=186564"},"modified":"2025-01-25T09:24:01","modified_gmt":"2025-01-25T09:24:01","slug":"at-boulder-colorado-elevation-1650-m-the-raw-uncorrected-surface-pressure-measurement-is-84-kpa-while-the-surface-temperature-is-16-c","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/25\/at-boulder-colorado-elevation-1650-m-the-raw-uncorrected-surface-pressure-measurement-is-84-kpa-while-the-surface-temperature-is-16-c\/","title":{"rendered":"At Boulder, Colorado, elevation 1650 m, the raw (uncorrected) surface pressure measurement is 84 kPa while the surface temperature is 16 C"},"content":{"rendered":"\n<p>At Boulder, Colorado, elevation 1650 m, the raw (uncorrected) surface pressure measurement is 84 kPa while the surface temperature is 16 C. &#8220;Correct&#8221; the pressure to sea level using each of the following assumptions about the temperature in the &#8220;missing&#8221; atmosphere beneath the station.<br>a) The temperature is constant at its surface value.<br>b) The temperature increases with depth at the average lapse rate of 6.5 C\/km.<\/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 correct the atmospheric pressure at Boulder, Colorado (elevation 1,650 meters) to sea level, we can use the barometric formula, which relates pressure to altitude and temperature. The formula is:<\/p>\n\n\n\n<p>PSL=Pobs\u00d7(1+L\u00d7hTSL)g\u00d7MR\u00d7LP_{\\text{SL}} = P_{\\text{obs}} \\times \\left(1 + \\frac{L \\times h}{T_{\\text{SL}}}\\right)^{\\frac{g \\times M}{R \\times L}}<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>PSLP_{\\text{SL}} = sea-level pressure (Pa)\ue206<\/li>\n\n\n\n<li>PobsP_{\\text{obs}} = observed pressure at altitude (Pa)\ue206<\/li>\n\n\n\n<li>LL = temperature lapse rate (K\/m)\ue206<\/li>\n\n\n\n<li>hh = altitude (m)\ue206<\/li>\n\n\n\n<li>TSLT_{\\text{SL}} = standard sea-level temperature (K)\ue206<\/li>\n\n\n\n<li>gg = acceleration due to gravity (9.80665 m\/s\u00b2)\ue206<\/li>\n\n\n\n<li>MM = molar mass of Earth&#8217;s air (0.0289644 kg\/mol)\ue206<\/li>\n\n\n\n<li>RR = universal gas constant (8.3144598 J\/(mol\u00b7K))\ue206<\/li>\n<\/ul>\n\n\n\n<p>Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Pobs=84\u2009kPa=84,000\u2009PaP_{\\text{obs}} = 84 \\, \\text{kPa} = 84,000 \\, \\text{Pa}\ue206<\/li>\n\n\n\n<li>h=1,650\u2009mh = 1,650 \\, \\text{m}\ue206<\/li>\n\n\n\n<li>TSL=16\u2218C=289.15\u2009KT_{\\text{SL}} = 16^\\circ\\text{C} = 289.15 \\, \\text{K}\ue206<\/li>\n<\/ul>\n\n\n\n<p><strong>a) Assuming constant temperature at the surface value:<\/strong><\/p>\n\n\n\n<p>If the temperature is constant at 16\u00b0C, the lapse rate L=0L = 0. The formula simplifies to:<\/p>\n\n\n\n<p>PSL=Pobs\u00d7exp\u2061(g\u00d7M\u00d7hR\u00d7TSL)P_{\\text{SL}} = P_{\\text{obs}} \\times \\exp\\left(\\frac{g \\times M \\times h}{R \\times T_{\\text{SL}}}\\right)<\/p>\n\n\n\n<p>Calculating:<\/p>\n\n\n\n<p>PSL=84,000\u00d7exp\u2061(9.80665\u00d70.0289644\u00d71,6508.3144598\u00d7289.15)P_{\\text{SL}} = 84,000 \\times \\exp\\left(\\frac{9.80665 \\times 0.0289644 \\times 1,650}{8.3144598 \\times 289.15}\\right)<\/p>\n\n\n\n<p>PSL\u224884,000\u00d7exp\u2061(0.0565)P_{\\text{SL}} \\approx 84,000 \\times \\exp(0.0565)<\/p>\n\n\n\n<p>PSL\u224884,000\u00d71.0582P_{\\text{SL}} \\approx 84,000 \\times 1.0582<\/p>\n\n\n\n<p>PSL\u224888,900\u2009PaP_{\\text{SL}} \\approx 88,900 \\, \\text{Pa}<\/p>\n\n\n\n<p>PSL\u224888.9\u2009kPaP_{\\text{SL}} \\approx 88.9 \\, \\text{kPa}<\/p>\n\n\n\n<p><strong>b) Assuming a temperature lapse rate of 6.5\u00b0C\/km:<\/strong><\/p>\n\n\n\n<p>For a lapse rate of 6.5\u00b0C\/km (0.0065 K\/m), the formula becomes:<\/p>\n\n\n\n<p>PSL=Pobs\u00d7(1+0.0065\u00d71,650289.15)5.2561P_{\\text{SL}} = P_{\\text{obs}} \\times \\left(1 + \\frac{0.0065 \\times 1,650}{289.15}\\right)^{5.2561}<\/p>\n\n\n\n<p>Calculating:<\/p>\n\n\n\n<p>PSL=84,000\u00d7(1+0.0065\u00d71,650289.15)5.2561P_{\\text{SL}} = 84,000 \\times \\left(1 + \\frac{0.0065 \\times 1,650}{289.15}\\right)^{5.2561}<\/p>\n\n\n\n<p>PSL=84,000\u00d7(1+0.0370)5.2561P_{\\text{SL}} = 84,000 \\times \\left(1 + 0.0370\\right)^{5.2561}<\/p>\n\n\n\n<p>PSL=84,000\u00d7(1.0370)5.2561P_{\\text{SL}} = 84,000 \\times (1.0370)^{5.2561}<\/p>\n\n\n\n<p>PSL\u224884,000\u00d71.221P_{\\text{SL}} \\approx 84,000 \\times 1.221<\/p>\n\n\n\n<p>PSL\u2248102,300\u2009PaP_{\\text{SL}} \\approx 102,300 \\, \\text{Pa}<\/p>\n\n\n\n<p>PSL\u2248102.3\u2009kPaP_{\\text{SL}} \\approx 102.3 \\, \\text{kPa}<\/p>\n\n\n\n<p><strong>Explanation:<\/strong><\/p>\n\n\n\n<p>The barometric formula models how atmospheric pressure changes with altitude, considering temperature variations. In part (a), assuming a constant temperature at the surface value, the pressure decreases exponentially with altitude. In part (b), with a lapse rate of 6.5\u00b0C\/km, the temperature decreases linearly with altitude, leading to a different pressure correction. The lapse rate significantly influences the pressure correction, with a higher lapse rate resulting in a higher sea-level pressure.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>At Boulder, Colorado, elevation 1650 m, the raw (uncorrected) surface pressure measurement is 84 kPa while the surface temperature is 16 C. &#8220;Correct&#8221; the pressure to sea level using each of the following assumptions about the temperature in the &#8220;missing&#8221; atmosphere beneath the station.a) The temperature is constant at its surface value.b) The temperature increases [&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-186564","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/186564","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=186564"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/186564\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=186564"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=186564"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=186564"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}