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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="../258/modelling-gases.html">Modelling gases</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">Charles' law</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 10 minutes"><i class="fa fa-clock-o"></i> 10'</span> </ol> <article id="main-article"> <p><img alt="" src="../../thermal/gas-5.jpg" style="float: left; width: 150px; height: 205px;">Charles' law states that volume is proportional to absolute temperature, for a fixed amount of gas at constant pressure.</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="box"> <p style="text-align: center;"><span class="math-tex">\(V\propto T\)</span></p> <ul> <li><span class="math-tex">\(V\)</span> is volume (m<sup>3</sup>)</li> <li><span class="math-tex">\(T\)</span> is temperature (K)</li> </ul> </div> <p style="text-align: center;"><span class="math-tex">\({V_1\over T_1}={V_2\over T_2}\)</span></p> </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>Simulated experiment</p> </div> </div> <div class="panel-body"> <div> <p><img class="sibico" src="../../../img/sibico/video.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="Video"> If a piston is allowed to move freely, the pressure of the gas will equal the atmospheric pressure. If the temperature is increased the gas will expand.</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/163921200"></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>Kinetic theory explanation</p> </div> </div> <div class="panel-body"> <div> <p><img class="sibico" src="../../../img/sibico/video.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="Video"> If the temperature of a gas is increased, the kinetic energy of the molecules increases. In order for the total amount of force exerted on the walls of the container to remain constant, the time between collisions must increase. Therefore, the volume of the container increases such that pressure is constant.</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/163911771"></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="#cdc2751a"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="cdc2751a"> <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%;"> Charles' law <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="6-64-260" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>Fill in the gaps on this statement of Charles law</p><p>Word list: kelvin, celsius, directly, inversely, pressure volume. temperature</p></div><div class="q-answer"><p>For a fixed <input type="text" style="height: auto;" data-c=" mass "> <span class="review"></span> of gas at constant <input type="text" style="height: auto;" data-c=" pressure "> <span class="review"></span> , the <input type="text" style="height: auto;" data-c=" volume "> <span class="review"></span> is <input type="text" style="height: auto;" data-c=" directly"> <span class="review"></span> proportional to the <input type="text" style="height: auto;" data-c=" temperature "> <span class="review"></span> in <input type="text" style="height: auto;" data-c=" kelvin "> <span class="review"></span> .</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 temperature of a fixed mass of gas with volume 250 ml is raised form 300 K to 900 K at atmospheric pressure.</p><p>The new volume is:</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 500 ml</label></p><p><label class="radio"><input type="radio"> 50 ml</label></p><p><label class="radio"><input class="c" type="radio"> 750 ml</label></p><p><label class="radio"><input type="radio"> 83 ml</label></p></div><div class="q-explanation"><p>3 x temp must be 3 x volume.</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>300 ml of gas is at a temperature of 27°C. What would the temperature be if the gas expanded to 450 ml at constant pressure.</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 41°C</label></p><p><label class="radio"><input type="radio"> 450°C</label></p><p><label class="radio"><input class="c" type="radio"> 177°C</label></p><p><label class="radio"><input type="radio"> 54°C</label></p></div><div class="q-explanation"><p>The ratio V<sub>1</sub>/V<sub>2</sub> = T<sub>1</sub>/T<sub>2</sub> </p><p>Temp must be in K = 273 + 27 = 300K</p><p>300/450 = 300/T<sub>2</sub></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>Fill in the blanks in this explanation of why volume is proportional to temperature at constant pressure.</p><p>Word list: speed, outwards, inwards, temperature, pressure, KE, force</p></div><div class="q-answer"><p>When the <input type="text" style="height: auto;" data-c=" temperature "> <span class="review"></span> is increased the molecules have more <input type="text" style="height: auto;" data-c=" KE "> <span class="review"></span> so move with higher <input type="text" style="height: auto;" data-c=" speed "> <span class="review"></span> . This means that when they hit the piston they exert a larger <input type="text" style="height: auto;" data-c=" force "> <span class="review"></span> . If the opposing <input type="text" style="height: auto;" data-c=" force "> <span class="review"></span> is not increased then the piston will move <input type="text" style="height: auto;" data-c=" outwards "> <span class="review"></span> until the <input type="text" style="height: auto;" data-c=" pressure "> <span class="review"></span> on the inside again equals that on the outside.</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>Which of the following statements is true when a gas expands at constant pressure?</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> the density of molecules is constant</label></p><p><label class="radio"><input type="radio"> the number of molecules increases</label></p><p><label class="radio"><input class="c" type="radio"> heat was added</label></p><p><label class="radio"><input type="radio"> the average KE of gas molecules decreases</label></p></div><div class="q-explanation"><p>If P constant then the temp must rise so heat was added.</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 text-xs-center btn-results" style="display: none"> <i class="fa fa-bar-chart"></i> Check Results </button> <button class="btn btn-default d-xs-none btn-next"> Next <i class="fa fa-arrow-right"></i> </button> <button class="btn btn-default btn-xs-block text-xs-center btn-close" 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