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href="../../../physics.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../252/thermal.html">Thermal</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../254/thermal-concepts.html">Thermal concepts</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">Latent heat</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="../../thermal/melt.jpg" style="float: left; width: 250px; height: 141px;">It is clear that, to melt ice and boil water, you need to add heat... but where does that energy go? </p> <p>It seems to be hidden, hence the name <strong>latent heat</strong>. This is in contrast to <strong>sensible heat</strong>, where a temperature change is observed with the addition of heat (as could reasonably be expected!). </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> <p>When a material is heated, it goes through several stages:</p> <p style="text-align: center;"><img alt="" src="../../thermal/heating-graph.png" style="width: 493px; height: 400px;"></p> <ul> <li><span class="math-tex">\(A \rightarrow B\)</span> is the heating of the solid. It increases in temperature. Specific heat capacity of the solid could be calculated for this region from the gradient as <span class="math-tex">\(\Delta Q=mc\Delta \theta \Rightarrow mc ={1\over gradient}\)</span>.</li> <li><span class="math-tex">\(B \rightarrow C\)</span> is the melting of the solid into liquid. This is the latent heat of fusion stage and the temperature remains constant: <span class="math-tex">\(\Delta Q= mL_f\)</span></li> <li><span class="math-tex">\(C \rightarrow D\)</span> is the heating of the liquid. It increases in temperature. I have shown this with a different gradient to the solid as the liquid with have a different specific heat capacity.</li> <li><span class="math-tex">\(D \rightarrow E\)</span> is the boiling of the liquid into gas. This is the latent heat of vaporisation stage and the temperature remains constant: <span class="math-tex">\(\Delta Q= mL_v\)</span></li> <li><span class="math-tex">\(E \rightarrow F\)</span> is the heating of the gas, which increases in temperature, again shown with a different gradient.</li> </ul> <p><img class="sibico" src="../../../img/sibico/exam-style.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="Exam-style question"> Notice that the unit on the horizontal axis is 'J' (Joules) indicating that heat is being added to the system. Graphs like this one will look the same even if the horiztonal axis is 'time', provided that heat is supplied at a constant rate.</p> <p>An electrical heater with constant power can provide this. To calculate the heat added from the <a href="../488/electrical-power.html" title="Electrical power">Electrical power</a>:</p> <div class="box"> <p style="text-align: center;"><span class="math-tex">\(\Delta Q = IV \Delta t\)</span></p> </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> <h4>Measuring latent heat of fusion of water</h4> <p><img alt="" src="../../thermal/boil.jpg" style="float: left; width: 180px; height: 120px;"><img class="sibico" src="../../../img/sibico/notes.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="Notes (summary/recap)"> The specific latent heat is the amount of heat required to change the state of one kilogram of a substance:</p> <div class="box"> <p style="text-align: center;"><span class="math-tex">\(Q = m L\)</span></p> </div> <p><img class="sibico" src="../../../img/sibico/tok.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="Theory if Knowledge"> We make the assumption that changes in state occur with no change in temperature.</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/163864674"></iframe></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="#35c89ed5"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="35c89ed5"> <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%;"> Change of state <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="6-62-257" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>When a solid changes to a liquid energy is required.</p><p>Which is the best description of where that energy goes.</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> to increase the PE of the molecules</label></p><p><label class="radio"><input type="radio"> to increase the KE of the molecules</label></p><p><label class="radio"><input type="radio"> to allow the molecules to move further apart</label></p><p><label class="radio"><input type="radio"> to break the bonds between atoms</label></p></div><div class="q-explanation"><p>Chemists talk about breaking bonds we talk about increasing PE, it would also be bonds between the molecules rather than atoms but I'd rather not get into that.</p><p>Temperature doesn't change so no change in KE</p><p>Water molecules actually get closer.</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>100g ice is melted at 0°C in 5 minutes by an electric heater.</p><p>The latent heat of fusion of ice is approximately 3 x 10<sup>5</sup> Jkg<sup>-1</sup></p></div><div class="q-answer"><p>The amount of heat required to melt the ice = <input type="text" style="height: auto;" data-c="30"> <span class="review"></span> kJ</p><p>The power of the heater = <input type="text" style="height: auto;" data-c="100"> <span class="review"></span> W</p></div><div class="q-explanation"><p>Q = mL, P = Q/t careful with units</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 temperature is measured as some water is boiled in a 2kW electric kettle.</p><p style="text-align: center;"><img alt="" src="../../images/lhq1.png" style="width: 340px; height: 292px;"></p><p>The latent heat of vaporisation of water is about 2 x 10<sup>6</sup> Jkg<sup>-1</sup></p></div><div class="q-answer"><p>Temperature T = <input type="text" style="height: auto;" data-c="100"> <span class="review"></span> °C</p><p>The heat required to boil the water = <input type="text" style="height: auto;" data-c="2000"> <span class="review"></span> kJ</p><p>The mass of water = <input type="text" style="height: auto;" data-c="1"> <span class="review"></span> kg</p></div><div class="q-explanation"><p>Q = Pt<br>m=Q/L</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 you get melted sugar on your skin it burns very badly.</p><p>Fill the gaps to give the explanation.</p><p>Word list: constant, energy, solid, liquid, temperature, release, state, power</p></div><div class="q-answer"><p>When sugar changes from <input type="text" style="height: auto;" data-c="liquid"> <span class="review"></span> to <input type="text" style="height: auto;" data-c="solid"> <span class="review"></span> it must release <input type="text" style="height: auto;" data-c="energy"> <span class="review"></span> , if in contact with your skin this <input type="text" style="height: auto;" data-c="energy"> <span class="review"></span> will be given to you. <input type="text" style="height: auto;" data-c="temperature"> <span class="review"></span> remains constant as the sugar changes <input type="text" style="height: auto;" data-c="state"> <span class="review"></span> so it remains at melting point until all the <input type="text" style="height: auto;" data-c="energy"> <span class="review"></span> is released. during this time the sugar will be damaging your skin.</p></div><div class="q-explanation"><p>It does too.</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>A type of salt is used to store solar energy collected in the day time so it can be used at night. The power station collects 1 MW. </p><p>The latent heat of fusion of the salt is 3 x 10<sup>6</sup> Jkg<sup>-1</sup></p></div><div class="q-answer"><p>The energy collected in 10 hours of sun light = <input type="text" style="height: auto;" data-c="36000"> <span class="review"></span> MJ (no commas)</p><p>The mass of salt melted in one day (10 hours of sunlight) = <input type="text" style="height: auto;" data-c="12000"> <span class="review"></span> kg</p></div><div class="q-explanation"><p>MJ is 10<sup>6</sup> J</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 btn-xs-block 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