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thermal energy transfer</a></label><ul class="side-nav level-1"><li class="expanded parent selected"><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="energy-from-the-sun.html">Energy from the Sun</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../460/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 from the Sun <a href="#" class="mark-page-favorite pull-right" data-pid="459" 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 from the Sun</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 15 minutes"><i class="fa fa-clock-o"></i> 15'</span> </ol> <article id="main-article"> <p><img alt="" src="../../astro/sun-1.jpg" style="float: left; width: 225px; height: 225px;">20% of the world's deserts covered with solar panels would supply enough energy for present needs. Here we will learn the first half of a means to calculate this energy: the intensity of the light emitted from the Sun upon the Earth's surface.</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>Fusion in the Sun</p> </div> </div> <div class="panel-body"> <div> <p>The fusion of hydrogen to helium is what provides the energy to keep the Sun hot. The Sun remains in equilibrium between the force of the radiation exerted outwards and the force of gravitation inwards.</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/195073281"></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>The black body spectrum</p> </div> </div> <div class="panel-body"> <div> <p>A black body is a perfect absorber and emitter of radiation, which means that a full emission spectrum is released. We can visualise this spectrum on a graph of power (or intensity or energy) against wavelength.</p> <p>The hotter the object, the more power will be produced and the shorter the peak wavelength will be. The sun is a good example.</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/195073312"></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-yellow panel-has-colored-body panel-has-border"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Stefan Boltzmann law</p> </div> </div> <div class="panel-body"> <div> <p>The higher the temperature, the larger the area of the black body curve above the axis, as this is proportional to the total power emitted. The Stefan Boltzmann law gives the relationship between temperature and power emitted per unit area:</p> <div class="box"> <p style="text-align: center;"><span class="math-tex">\(P=e\sigma AT^4\)</span></p> <ul> <li>P = power released (W)</li> <li>e = emissivity (dimensionless quantity = 1 for a black body)</li> <li>σ = constant of proportionality</li> <li>A = surface area (m<sup>2</sup>)</li> <li>T = absolute temperature (K)</li> </ul> </div> <p>NB: It is worth taking note of the power of 4, making the temperature of the body much more significant in determining the power than the area.</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/195073327"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-yellow panel-has-colored-body panel-has-border panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Wien's law</p> </div> </div> <div class="panel-body"> <div> <p>The higher the temperature, the lower the wavelength of the peak of the black body curve. This is intuitive, as shorter wavelengths correspond with higher freqencies and energies. However, it does have the effect that the very hottest stars in terms of temperature actually release much more gamma and X-ray radiation than infrared (thermal).</p> <p>Remarkably, the product of this peak wavelength and the absolute temperature is a constant. Wien's law relates the peak wavelength and temperature:</p> <div class="box"> <p style="text-align: center;"><span class="math-tex">\(\lambda_{\text{peak}}={0.00289\over T}\)</span></p> </div> <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/195073335"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-yellow panel-has-colored-body panel-has-border panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Inverse square law</p> </div> </div> <div class="panel-body"> <div> <p>The further from the sun you go the less the power per square meter becomes. This can be measured as the physical quantity <strong>intensity</strong>, which is the power arriving per unit area.</p> <p style="text-align: center;"><span class="math-tex">\(I={P\over 4\pi r^2}\)</span></p> <p>NB: The bottom line of this fraction is the surface area of the 'sphere' of radiation being emitted from the Sun. If you were interested in finding the intensity of the Sun's radiation landing on the Earth, you would substitute <em>r</em> as the distance from the Sun to the Earth. This value, 1388 Wm<sup>-2</sup>, is known as the <strong>solar constant</strong>.</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/195179419"></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-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="#a5d3dc9e"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="a5d3dc9e"> <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 from the sun <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="6-124-459" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>The time taken for light to travel from the sun to the earth is about</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 1 hour</label></p><p><label class="radio"><input type="radio"> 3 days</label></p><p><label class="radio"><input type="radio"> 5 seconds</label></p><p><label class="radio"><input class="c" type="radio"> 8 minutes</label></p></div><div class="q-explanation"><p>The distance is 1.5 x 10<sup>11</sup> m and the speed of light is 3 x 10<sup>8</sup> ms<sup>-1</sup> so thats 500 s about 8 mins</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 energy source in the core of the sun is</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> hydrogen burning</label></p><p><label class="radio"><input type="radio"> fission of helium to form hydrogen</label></p><p><label class="radio"><input type="radio"> helium fusing to form hydrogen</label></p><p><label class="radio"><input class="c" type="radio"> hydrogen fusing to form helium</label></p></div><div class="q-explanation"></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 condition for fusion is that the gas must be:</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> neither dense nor hot</label></p><p><label class="radio"><input class="c" type="radio"> dense and hot</label></p><p><label class="radio"><input type="radio"> hot but not dense</label></p><p><label class="radio"><input type="radio"> dense but not hot</label></p></div><div class="q-explanation"><p>hot so they get close, dense so they meet each other</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 sun radiates 4 x 10<sup>26</sup> W. If its temperature was half what it is now how much power would be radiated?</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 1 x 10 <sup>26</sup> W</label></p><p><label class="radio"><input class="c" type="radio"> 2.5 x 10<sup>25 </sup>W</label></p><p><label class="radio"><input type="radio"> 5 x 10<sup>25</sup> W</label></p><p><label class="radio"><input type="radio"> 2 x 10<sup>26</sup> W</label></p></div><div class="q-explanation"><p>P is proportional tp T<sup>4</sup> so if T is 1/2 P will be (1/2)<sup>4</sup> = 1/16</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 emissivity of the sun is taken to be</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 0.3</label></p><p><label class="radio"><input class="c" type="radio"> 1</label></p><p><label class="radio"><input type="radio"> 2</label></p><p><label class="radio"><input type="radio"> 0.6</label></p></div><div class="q-explanation"><p>The sun, and all stars are taken to be perfect black body radiators</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>Below is a graph showing the intensity of radiation against wavelength for a black body radiator.</p><p style="text-align: center;"><img alt="" height="231" src="../../mc-images/screen-shot-2017-01-06-at-11.20.22.png" width="334"></p><p>How are power and temperature related to ABC and D</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> OD is proportional to T and B to T<sup>4</sup></label></p><p><label class="radio"><input class="c" type="radio"> D is proportional to T<sup>4</sup> and B to 1/T</label></p><p><label class="radio"><input type="radio"> C is proportional to T and B to 1/T</label></p><p><label class="radio"><input type="radio"> A is proportional to T and D to T<sup>4</sup></label></p></div><div class="q-explanation"><p>The area is proportional ot the total power which is proportional to T<sup>4</sup></p><p>The peak wavelength is inversely proportioanl to T</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 peak in the black body spectrum of the sun is</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> red</label></p><p><label class="radio"><input type="radio"> blue</label></p><p><label class="radio"><input class="c" type="radio"> green</label></p><p><label class="radio"><input type="radio"> infra red</label></p></div><div class="q-explanation"><p>It looks yellow but peak is green</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 best estimate of the temperature of a star that had a peak wavelength of 250 nm is</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 6000 K</label></p><p><label class="radio"><input type="radio"> 200 K</label></p><p><label class="radio"><input class="c" type="radio"> 12,000 K</label></p><p><label class="radio"><input type="radio"> 3000 K</label></p></div><div class="q-explanation"><p>The sun's temp is about 6000 K and the wavelength of green light is about 500 nm.</p><p>Temp is inversely proportional to wavelength</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 intensity of radiation reaching the Earth from the sun is 1400 Wm<sup>-2</sup>. If you were to travel to a point half way between the sun and the Earth what would the intensity be ?</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 12800 Wm<sup>-2</sup></label></p><p><label class="radio"><input type="radio"> 700 Wm<sup>-2</sup></label></p><p><label class="radio"><input class="c" type="radio"> 5600 Wm<sup>-2</sup></label></p><p><label class="radio"><input type="radio"> 2800 Wm<sup>-2</sup></label></p></div><div class="q-explanation"><p>Intensity is proportional to 1/r<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> </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 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