{"id":207581,"date":"2025-04-24T21:29:03","date_gmt":"2025-04-24T21:29:03","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=207581"},"modified":"2025-04-24T21:29:06","modified_gmt":"2025-04-24T21:29:06","slug":"the-output-power-of-the-sun-is-1-0-times-1026-w-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/04\/24\/the-output-power-of-the-sun-is-1-0-times-1026-w-2\/","title":{"rendered":"The output power of the Sun is 1.0 times 1026 W"},"content":{"rendered":"\n<p>The output power of the Sun is 1.0 times 1026 W. Calculate, at 8 cents per kWh, the cost of running the sun for 1 hour.<\/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 calculate the cost of running the Sun for 1 hour, given its output power and the cost per kilowatt-hour (kWh), let&#8217;s break down the steps.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Understand the problem<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Power output of the Sun<\/strong>: ( P = 1.0 \\times 10^{26} ) W (watts).<\/li>\n\n\n\n<li><strong>Cost per kWh<\/strong>: 8 cents per kWh = $0.08 per kWh.<\/li>\n\n\n\n<li><strong>Time duration<\/strong>: 1 hour.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Convert the Sun&#8217;s power to kilowatts<\/h3>\n\n\n\n<p>1 watt (W) is equal to ( 1\/1000 ) kilowatts (kW), so we first need to convert the Sun\u2019s power from watts to kilowatts.<\/p>\n\n\n\n<p>[<br>P_{\\text{kW}} = 1.0 \\times 10^{26} \\, \\text{W} \\times \\frac{1 \\, \\text{kW}}{1000 \\, \\text{W}} = 1.0 \\times 10^{23} \\, \\text{kW}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Calculate energy produced in 1 hour<\/h3>\n\n\n\n<p>Energy is power multiplied by time. Since 1 hour is 1 hour, or 3600 seconds, we can compute the energy output of the Sun in 1 hour:<\/p>\n\n\n\n<p>[<br>E = P_{\\text{kW}} \\times \\text{time} = 1.0 \\times 10^{23} \\, \\text{kW} \\times 1 \\, \\text{hour} = 1.0 \\times 10^{23} \\, \\text{kWh}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Calculate the cost<\/h3>\n\n\n\n<p>Now, to find the cost of running the Sun for 1 hour, we multiply the energy output by the cost per kWh:<\/p>\n\n\n\n<p>[<br>\\text{Cost} = E \\times \\text{Cost per kWh} = 1.0 \\times 10^{23} \\, \\text{kWh} \\times 0.08 \\, \\text{dollars\/kWh}<br>]<\/p>\n\n\n\n<p>[<br>\\text{Cost} = 8.0 \\times 10^{21} \\, \\text{dollars}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>The cost of running the Sun for 1 hour at 8 cents per kWh is:<\/p>\n\n\n\n<p>[<br>8.0 \\times 10^{21} \\, \\text{dollars}.<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>The calculation involves understanding the immense scale of the Sun\u2019s energy output. The Sun releases an astronomical amount of energy every second. By converting that to kilowatt-hours and multiplying by the given cost per unit of energy (kWh), we arrive at an enormous figure that highlights the sheer scale of energy the Sun generates. This number, ( 8.0 \\times 10^{21} ) dollars, is so large it underscores just how much energy is being radiated by the Sun, far beyond the scope of any human-run energy system. The comparison gives an appreciation for the vastness of the Sun\u2019s power, which is far beyond what we use on Earth in energy consumption.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The output power of the Sun is 1.0 times 1026 W. Calculate, at 8 cents per kWh, the cost of running the sun for 1 hour. The correct answer and explanation is : To calculate the cost of running the Sun for 1 hour, given its output power and the cost per kilowatt-hour (kWh), let&#8217;s [&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-207581","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/207581","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=207581"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/207581\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=207581"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=207581"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=207581"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}