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thermal energy transfer</a></label><ul class="side-nav level-1"><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../459/energy-from-the-sun.html">Energy from the Sun</a></label></li><li class="expanded parent selected"><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="energy-to-the-earth.html">Energy to the Earth</a></label></li></ul></li></ul></div> <div class="hidden-xs hidden-sm"> <button class="btn btn-default btn-block text-xs-center" data-toggle="modal" data-target="#modal-feedback" style="margin-bottom: 10px"><i class="fa fa-send"></i> Feedback</button> </div> </div> <div class="col-md-9" id="main-column"> <h1 class="page_title"> Energy to the Earth <a href="#" class="mark-page-favorite pull-right" data-pid="460" title="Mark as favorite" onclick="return false;"><i class="fa fa-star-o"></i></a> </h1> <ol class="breadcrumb"> <li><a href="../../../physics.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../446/energy-production.html">Energy production</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../458/global-thermal-energy-transfer.html">Global thermal energy transfer</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">Energy to the Earth</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 20 minutes"><i class="fa fa-clock-o"></i> 20'</span> </ol> <article id="main-article"> <p><img alt="" src="../../energy-production/1-earth.jpg" style="float: left; width: 244px; height: 250px;">The Subject Guide suggests that this is the best topic in which to learn about Conduction and Convection. However, we have these covered in the <a href="../256/heat-transfer.html" title="Heat transfer">heat transfer</a> section.</p> <p>This is where we take the energy that is incident on the Earth from the Sun and consider what happens to it.</p> <hr class="hidden-separator"> <div class="panel panel-turquoise panel-has-colored-body"> <div class="panel-heading"> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <div> <div class="panel panel-has-colored-body panel-has-border panel-turquoise"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Spheres and discs</p> </div> </div> <div class="panel-body"> <div> <p>The Earth absorbs like it's a disc but emits as a sphere. A way of thinking about this is to consider looking at a ball from a large distance - as far as you're concerned, it could be a pancake.</p> <p>Therefore:</p> <ol> <li>We can find the total power of the radiation incident on the Earth by multiplying the solar constant by the area of the silhouette of the Earth</li> <li>We can find the average intensity distributed across the Earth by dividing (1) by the total surface area of the Earth as a sphere</li> </ol> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/195179439"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-turquoise panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Emissivity and albedo</p> </div> </div> <div class="panel-body"> <div> <p>Emissivity is how well a body emits radiation, with a black body having <em>e</em> = 1. It is equal to the following ratio:</p> <div class="box"> <p style="text-align: center;"><span class="math-tex">\(e={E_{emitted}\over E_{absorbed}}\)</span></p> </div> <p>Albedo is how well a body scatters radiation:</p> <div class="box"> <p style="text-align: center;"><span class="math-tex">\(\alpha={E_{reflected}\over E_{incident}}\)</span></p> </div> <p>Global albedo is on average 0.3.</p> <p>Notice that from this ratio we can determine the amount of energy absorbed by the body, for subtitution into the emissivity equation:</p> <p style="text-align: center;"><span class="math-tex">\(E_{absorbed}=(1-\alpha )E_{incident}\)</span></p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/195179706"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-turquoise panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Energy flow</p> </div> </div> <div class="panel-body"> <div> <p>From conservation of energy (first law of thermodynamics), we recall that energy cannot be created or destroyed. Therefore:</p> <ul> <li>the quantity of radiation incident on a body will equal the sum of the radiation reflected or absorbed</li> <li>the radiation absorbed with then equal the sum of the radiation emitted or remaining</li> </ul> <p>In summary, energy in = energy out.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/195179561"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <div> <div class="panel panel-has-colored-body panel-has-border panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Electromagnetic radiation and the atmosphere</p> </div> </div> <div class="panel-body"> <div> <p>The atmosphere is made of many different gases that interact differently with electromagnetic radiation.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/195179662"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>The greenhouse effect</p> </div> </div> <div class="panel-body"> <div> <p>Radiation entering the Earth's atmosphere increases in wavelength (tending towards infrared) when it reflects off the Earth's surface.</p> <p>Greenhouse gases absorb this infrared radiation on its way back out to space:</p> <ul> <li>Carbon dioxide (CO<sub>2</sub>)</li> <li>Methane (CH<sub>4</sub>)</li> <li>Water (H<sub>2</sub>O)</li> <li>Nitrous oxide (N<sub>2</sub>O)</li> </ul> <p>However, gas molecules do not discriminate when re-emitting this radiation, and so a significant proportion returns to Earth. Statistically therefore, the Earth increases in thermal energy over time and global temperatures rise.</p> <p>This is beneficial for life on Earth, but there is scientific evidence that rising temperatures due to human emission of greenhouse gases are contributing to long-term global warming.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/195179577"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test Yourself</p> </div> </div> <div class="panel-body"> <div> <p><em>Use quizzes to practise application of theory.</em></p> <br><a class="btn btn-primary btn-block text-center" data-toggle="modal" href="#ba1855be"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="ba1855be"> <div class="modal-dialog" style="width: 95vw; max-width: 960px"> <div class="modal-content"> <div class="modal-header slide-quiz-title"> <h4 class="modal-title" style="width: 100%;"> Energy to the Earth <strong class="q-number pull-right"> <span class="counter">1</span>/<span class="total">1</span> </strong> </h4> </div> <div class="modal-body p-xs-3"> <div class="slide-quiz" data-stats="6-125-460" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>If the intensity of the suns radiation at earth's orbit is I and the radius of the earth is r the total power incident on the earth is the earth is:</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> I/πr<sup>2</sup></label></p><p><label class="radio"><input class="c" type="radio"> I x πr<sup>2</sup></label></p><p><label class="radio"><input type="radio"> I x 4πr<sup>2</sup></label></p><p><label class="radio"><input type="radio"> I/4πr<sup>2</sup></label></p></div><div class="q-explanation"><p>Radiation is absorbed over the area of a disk</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>If the intensity of the sun's radiation at the earths' orbit is I and the radius of the earth r. The power absorbed per m<sup>2</sup> of the earth will be:</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> I /4πr<sup>2</sup></label></p><p><label class="radio"><input class="c" type="radio"> I/4</label></p><p><label class="radio"><input type="radio"> I</label></p><p><label class="radio"><input type="radio"> I/πr<sup>2</sup></label></p></div><div class="q-explanation"><p>radiation absorbed = I x πr<sup>2</sup></p><p>power per m<sup>2</sup> = Iπr<sup>2</sup>/4πr<sup>2</sup></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Albedo is defined as</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> energy reflected / total incident energy</label></p><p><label class="radio"><input type="radio"> incident energy / energy reflected</label></p><p><label class="radio"><input type="radio"> energy absorbed / energy reflected</label></p><p><label class="radio"><input type="radio"> energy reflected / energy absorbed</label></p></div><div class="q-explanation"><p>one to remember</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Which surface would have an albedo close to 1?</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> grass</label></p><p><label class="radio"><input class="c" type="radio"> snow</label></p><p><label class="radio"><input type="radio"> sea</label></p><p><label class="radio"><input type="radio"> a road</label></p></div><div class="q-explanation"><p>snow reflects most of the radiation, it has an albedo = 0.9</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The spectrum below shows the absorption of different wavelengths by a gas.</p><p style="text-align: center;"><img alt="" height="120" src="../../mc-images/screen-shot-2017-01-06-at-12.50.42.png" width="497"></p><p>Which gas?</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> oxygen</label></p><p><label class="radio"><input type="radio"> carbon dioxide</label></p><p><label class="radio"><input type="radio"> water</label></p><p><label class="radio"><input class="c" type="radio"> ozone</label></p></div><div class="q-explanation"><p>ozone absorbs UV</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The diagram below represents energy flowing in and out of the earth.</p><p style="text-align: center;"><img alt="" height="222" src="../../mc-images/screen-shot-2017-01-06-at-13.02.20.png" width="263"></p><p>Here is a different scenario</p><p style="text-align: center;"><img alt="" height="213" src="../../mc-images/screen-shot-2017-01-06-at-13.04.31.png" width="277"></p><p>What changed</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> increased albedo</label></p><p><label class="radio"><input type="radio"> reduced emissivity</label></p><p><label class="radio"><input type="radio"> increased emissivity</label></p><p><label class="radio"><input class="c" type="radio"> reduction in albedo</label></p></div><div class="q-explanation"><p>less radiation reflected so more absorbed therefore more must be radiated</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The diagram below represents energy flowing in and out of the earth.</p><p style="text-align: center;"><img alt="" height="222" src="../../mc-images/screen-shot-2017-01-06-at-13.02.20.png" width="263"></p><p>Here is a different scenario</p><p style="text-align: center;"><img alt="" height="213" src="../../mc-images/screen-shot-2017-01-06-at-13.04.31.png" width="277"></p><p>What happened to the temperature of the Earth?</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> increased</label></p><p><label class="radio"><input type="radio"> constant</label></p><p><label class="radio"><input type="radio"> reduced</label></p><p><label class="radio"><input type="radio"> not possible to say</label></p></div><div class="q-explanation"><p>less radiation reflected so more absorbed therefore more must be radiated which means temp has increased</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Greenhouse gases</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> act like a blanket trapping the radiated energy</label></p><p><label class="radio"><input type="radio"> absorb all wavelengths of radiation</label></p><p><label class="radio"><input class="c" type="radio"> absorb then re-radiate the IR radiation from the Earth</label></p><p><label class="radio"><input type="radio"> absorb radiation and warm up the earth</label></p></div><div class="q-explanation"><p>some of the re-radiated radiation returns to the earth</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The radiated radiation is lower frequency than the absorbed radiation because compared to the sun the earth has a lower</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> albedo</label></p><p><label class="radio"><input type="radio"> emissivity </label></p><p><label class="radio"><input class="c" type="radio"> temperature </label></p><p><label class="radio"><input type="radio"> surface heat capacity</label></p></div><div class="q-explanation"><p>Stefan - Boltzmann law</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div> </div> </div> <div class="modal-footer slide-quiz-actions"> <div class=""> <div class="pull-left pull-xs-none mb-xs-3"> <button class="btn btn-default d-xs-none btn-prev"> <i class="fa fa-arrow-left"></i> Prev </button> </div> <div class="pull-right pull-xs-none"> <button class="btn btn-success 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