{"id":207789,"date":"2025-04-25T07:51:39","date_gmt":"2025-04-25T07:51:39","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=207789"},"modified":"2025-04-25T07:51:42","modified_gmt":"2025-04-25T07:51:42","slug":"humidity-from-wet-and-dry-bulb-temperatures","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/04\/25\/humidity-from-wet-and-dry-bulb-temperatures\/","title":{"rendered":"Humidity from Wet and Dry Bulb Temperatures"},"content":{"rendered":"\n

Humidity from Wet and Dry Bulb Temperatures. An air\u2013water vapor mixture has a dry bulb temperature of 65.6\u00b0C and a wet bulb temperature of 32.2\u00b0C. What is the humidity of the mixture?<\/p>\n\n\n\n

The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n

To find the humidity<\/strong> of an air\u2013water vapor mixture given the dry bulb<\/strong> and wet bulb<\/strong> temperatures, we need to determine the relative humidity (RH)<\/strong>. The dry bulb temperature<\/strong> (DBT) is the actual air temperature, and the wet bulb temperature<\/strong> (WBT) reflects the lowest temperature air can reach through evaporative cooling. The larger the difference between DBT and WBT, the drier the air is.<\/p>\n\n\n\n

\n\n\n\n

Given:<\/h3>\n\n\n\n
    \n
  • Dry Bulb Temperature (T_dry) = 65.6\u00b0C<\/strong><\/li>\n\n\n\n
  • Wet Bulb Temperature (T_wet) = 32.2\u00b0C<\/strong><\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    Step 1: Use an online psychrometric calculator or chart (or derive using equations), but for simplicity and precision at this high temperature range, we use a psychrometric equation<\/strong>:<\/h3>\n\n\n\n

    The formula for Relative Humidity (RH)<\/strong> (approximation method) is:<\/p>\n\n\n\n

    [
    RH = 100 \\times \\frac{e_w – \\gamma \\cdot (T_{dry} – T_{wet})}{e_s}
    ]<\/p>\n\n\n\n

    Where:<\/p>\n\n\n\n

      \n
    • ( e_s ) = saturation vapor pressure at dry bulb temp<\/li>\n\n\n\n
    • ( e_w ) = saturation vapor pressure at wet bulb temp<\/li>\n\n\n\n
    • ( \\gamma ) = psychrometric constant \u2248 0.00066 \u00d7 pressure (assuming atmospheric pressure of 101.325 kPa)<\/li>\n\n\n\n
    • ( T_{dry}, T_{wet} ) in \u00b0C<\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

      Step 2: Use saturated vapor pressure (from steam tables or Antoine equation):<\/h3>\n\n\n\n
        \n
      • At 65.6\u00b0C \u2192 ( e_s \\approx 25.05 ) kPa<\/li>\n\n\n\n
      • At 32.2\u00b0C \u2192 ( e_w \\approx 4.79 ) kPa<\/li>\n<\/ul>\n\n\n\n

        Assume standard pressure: ( \\gamma = 0.00066 \\times 101.325 \\approx 0.0669 )<\/p>\n\n\n\n

        \n\n\n\n

        Step 3: Plug into the formula:<\/h3>\n\n\n\n

        [
        RH = 100 \\times \\frac{4.79 – 0.0669 \\cdot (65.6 – 32.2)}{25.05}
        ]<\/p>\n\n\n\n

        [
        RH = 100 \\times \\frac{4.79 – 0.0669 \\cdot 33.4}{25.05}
        ]<\/p>\n\n\n\n

        [
        RH = 100 \\times \\frac{4.79 – 2.23446}{25.05} = 100 \\times \\frac{2.55554}{25.05}
        ]<\/p>\n\n\n\n

        [
        RH \\approx 10.2\\%
        ]<\/p>\n\n\n\n

        \n\n\n\n

        \u2705 Final Answer:<\/h3>\n\n\n\n

        Relative Humidity \u2248 10.2%<\/strong><\/p>\n\n\n\n

        \n\n\n\n

        \ud83d\udcd8 Explanation:<\/h3>\n\n\n\n

        Humidity measures how much water vapor is in the air compared to how much it could hold at that temperature. The dry bulb temperature<\/strong> represents the air’s thermal content, while the wet bulb<\/strong> includes cooling from evaporation. The bigger the gap between the two, the lower the moisture in the air.<\/p>\n\n\n\n

        In this case, the dry bulb is very high<\/strong> (65.6\u00b0C) and the wet bulb is significantly lower (32.2\u00b0C), indicating very dry air<\/strong>. The computed relative humidity of 10.2%<\/strong> confirms that this air mixture is extremely dry\u2014common in hot industrial settings or deserts.<\/p>\n\n\n\n

        This calculation is important in HVAC, meteorology, and thermal comfort applications.<\/p>\n","protected":false},"excerpt":{"rendered":"

        Humidity from Wet and Dry Bulb Temperatures. An air\u2013water vapor mixture has a dry bulb temperature of 65.6\u00b0C and a wet bulb temperature of 32.2\u00b0C. What is the humidity of the mixture? The correct answer and explanation is : To find the humidity of an air\u2013water vapor mixture given the dry bulb and wet bulb […]<\/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-207789","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/207789","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=207789"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/207789\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=207789"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=207789"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=207789"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}