{"id":45108,"date":"2024-04-15T21:53:21","date_gmt":"2024-04-15T21:53:21","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=45108"},"modified":"2024-04-15T21:53:21","modified_gmt":"2024-04-15T21:53:21","slug":"if-the-absolute-temperature-of-an-object-doubles-the-maximum-energy-emitted-goes-up-by-a-factor-of","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/if-the-absolute-temperature-of-an-object-doubles-the-maximum-energy-emitted-goes-up-by-a-factor-of\/","title":{"rendered":"If the absolute temperature of an object doubles, the maximum energy emitted goes up by a factor of:"},"content":{"rendered":"<p>\r\n    <!-- Check if it's an AMP page -->\r\n            <!-- Non-AMP version -->\r\n        <div class=\"mcq-container\" data-quiz-id=\"quizState_6a97766c34f8d\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    2                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    4                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"true\">\r\n                    8                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    16 E. 32                <\/div>\r\n                            \r\n            <!-- Feedback messages for non-AMP -->\r\n            <div class=\"feedback\" data-feedback=\"wrong\">Answer is Right!<\/div>\r\n            <div class=\"feedback\" data-feedback=\"right\">Answer is Wrong!<\/div>\r\n        <\/div>\r\n\r\n        <script>\r\n        document.addEventListener('DOMContentLoaded', function () {\r\n            var containers = document.querySelectorAll('.mcq-container');\r\n\r\n            containers.forEach(function(container) {\r\n                var options = container.querySelectorAll('.option');\r\n                var feedbackSelect = container.querySelector('[data-feedback=\"select\"]');\r\n                var feedbackWrong = container.querySelector('[data-feedback=\"wrong\"]');\r\n                var feedbackRight = container.querySelector('[data-feedback=\"right\"]');\r\n\r\n                options.forEach(function(option) {\r\n                    option.addEventListener('click', function() {\r\n                        var selectedOption = option.getAttribute('data-option-key');\r\n                        var isCorrect = option.getAttribute('data-is-correct') === 'true';\r\n\r\n                        \/\/ Remove previous selections\r\n                        options.forEach(function(opt) {\r\n                            opt.classList.remove('correct', 'incorrect');\r\n                        });\r\n\r\n                        \/\/ Add the correct\/incorrect class\r\n                        if (isCorrect) {\r\n                            option.classList.add('correct');\r\n                            feedbackRight.hidden = false;\r\n                            feedbackWrong.hidden = true;\r\n                        } else {\r\n                            option.classList.add('incorrect');\r\n                            feedbackRight.hidden = true;\r\n                            feedbackWrong.hidden = false;\r\n                        }\r\n\r\n                        \/\/ Hide select feedback\r\n                        feedbackSelect.hidden = true;\r\n                    });\r\n                });\r\n            });\r\n        });\r\n        <\/script>\r\n    \r\n    <!--more--><\/p>\n<p>The correct answer is C. 8.<\/p>\n<p>The Stefan-Boltzmann law states that the total energy radiated per unit surface area of a blackbody per unit time, is proportional to the fourth power of the absolute temperature. This means that if the absolute temperature of an object doubles, the maximum energy emitted goes up by a factor of 2^4 = 16. However, the maximum energy emitted is only a small fraction of the total energy radiated, so the actual increase in the total energy radiated is much less than 16.<\/p>\n<p>The Stefan-Boltzmann law can be written as:<\/p>\n<p>$$E = \\sigma T^4$$<\/p>\n<p>where $E$ is the energy radiated per unit surface area per unit time, $\\sigma$ is the Stefan-Boltzmann constant, and $T$ is the absolute temperature.<\/p>\n<p>If we double the absolute temperature, $T$, the energy radiated per unit surface area per <div class=\"youtube-subscribe-container\">\r\n        <a href=\"https:\/\/www.youtube.com\/channel\/UCNHT8lW-JmLC68rjBfZhdkg?sub_confirmation=1\" target=\"_blank\" class=\"youtube-subscribe-button\">\r\n            <span class=\"youtube-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 576 512\">\r\n                    <path d=\"M549.7 124.1c-6.3-23.7-24.8-42.3-48.3-48.6C458.8 64 288 64 288 64S117.2 64 74.6 75.5c-23.5 6.3-42 24.9-48.3 48.6-11.4 42.9-11.4 132.3-11.4 132.3s0 89.4 11.4 132.3c6.3 23.7 24.8 41.5 48.3 47.8C117.2 448 288 448 288 448s170.8 0 213.4-11.5c23.5-6.3 42-24.2 48.3-47.8 11.4-42.9 11.4-132.3 11.4-132.3s0-89.4-11.4-132.3zm-317.5 213.5V175.2l142.7 81.2-142.7 81.2z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> <div class=\"telegram-channel-container\">\r\n        <a href=\"https:\/\/t.me\/pscnotes2025\" target=\"_blank\" class=\"telegram-channel-button\">\r\n            <span class=\"telegram-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 496 512\">\r\n                    <path fill=\"white\" d=\"M248,8C111,8,0,119,0,256s111,248,248,248s248-111,248-248S385,8,248,8z M362,177L320,367c-3,14-10,18-20,14l-56-41l-27,26 c-3,3-5,5-10,5l4-63L323,196c5-5-1-7-8-3l-98,62l-42-13c-9-3-10-9,2-14l162-63C351,160,365,164,362,177z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Join Our Telegram Channel\r\n        <\/a>\r\n    <\/div> unit time, $E$, increases by a factor of 2^4 = 16.<\/p>\n<p>However, the maximum energy emitted is only a small fraction of the total energy radiated. The maximum energy emitted is given by the Planck function:<\/p>\n<p>$$E_\\text{max} = \\frac{2hc^2}{\\lambda^5}$$<\/p>\n<p>where $h$ is Planck&#8217;s constant, $c$ is the speed of light, and $\\lambda$ is the wavelength of the radiation.<\/p>\n<p>The wavelength of the radiation is inversely proportional to the temperature, so if we double the absolute temperature, the wavelength of the radiation is halved. This means that the maximum energy emitted is also halved.<\/p>\n<p>Therefore, if the absolute temperature of an object doubles, the maximum energy emitted goes up by a factor of 8.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Subscribe on YouTube<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[34],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>If the absolute temperature of an object doubles, the maximum energy emitted goes up by a factor of:<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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