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<h2>SL Paper 2</h2><div class="specification">
<p>A sample of vegetable oil, initially in the liquid state, is placed in a freezer that transfers thermal energy from the sample at a constant rate. The graph shows how temperature <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> of the sample varies with time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>.</p>
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" width="515" height="299"></p>
<p>The following data are available.</p>
<p style="padding-left: 30px;">Mass of the sample <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>32</mn><mo> </mo><mi>kg</mi></math><br>Specific latent heat of fusion of the oil <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>130</mn><mo> </mo><mi>kJ</mi><mo> </mo><msup><mi>kg</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math><br>Rate of thermal energy transfer <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>15</mn><mo> </mo><mi mathvariant="normal">W</mi></math></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the thermal energy transferred from the sample during the first <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> minutes.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the specific heat capacity of the oil in its liquid phase. State an appropriate unit for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The sample begins to freeze during the thermal energy transfer. Explain, in terms of the molecular model of matter, why the temperature of the sample remains constant during freezing.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the mass of the oil that remains unfrozen after <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn></math> minutes.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A mass of 1.0 kg of water is brought to its boiling point of 100 °C using an electric heater of power 1.6 kW.</p>
</div>
<div class="specification">
<p>A mass of 0.86 kg of water remains after it has boiled for 200 s.</p>
</div>
<div class="specification">
<p>The electric heater has two identical resistors connected in parallel.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAREAAACeCAYAAAAVBT43AAANoUlEQVR4Ae2dMW/cRhbH/T0Cl0HuZB1ySHMWVF2Ag2OVjhPEh1QXA3F5TgCri3OF1cWd1cSlVcStBVxqC1BvQaUbxV9Agj8Ag/8ab03RXO5KHM7jPP4GWMzuDjlv3u/N/DUz5FJXKhIEIACBHgSu9DiXUyEAgRYCJycn1dWrH81e+/svWo6I9RUiEiueeDMCAjs7j6r19bVqc3Ojunfv+xG0aNgmICLD8qX2CRIw8TAxOT09DU0BEQkdXpzLTUDLFy1l9vaeVQcHL2fvd3ef5G5GVnuISFbcGBsDgYcPf5oN7rOzs+TN0fJFSxlLmpXoFTkhIpGji2/nCEg0vvrqy5mAfPfdf86VpfigZYsEZHv7wbw6zUI0M9GsJGpCRKJGFr/OETg+Pq7W1v4yG9CPH/9yrizVhzbBsCs1dWFJZW8s9SAiY4kE7RiMwPPnv83EQyJyeHg4mB0tW+zSbjPXDCXqBisiMliXouIxELh//7+zgX3jxr+qN2/+GKxJXZuo2mSVqETdYEVEButWVOxJQPsfEg4NXgnJEJuodf+0XOmabWiWsrV1s35KmPeISJhQ4ogRqO9/PH36q309aN7cUG0a0z0jErSjo1fNouI/IyLFhxAH6gRy7X/UbbZtqNbL9V7iIRGRmERLiEi0iE7UHy1Xcu1/TBTxQrcRkYVoKCiFgDZMc+5/lMIlVzuLERFNBXl9yCBXRxmrHV2ytfs/tJQh5SeAiBQuTvm7zHgsatNUf1gkItpMJfkQKE5EfDCNz6rNysbXsuFb1Nz/GPry7fAelW0BESk0flMVkeb+R6HhC9VsRKTQcE5RRNj/GGdnRUTGGZelrYouIlqiSDRsr0M/mpPPqfY/mvUvBc4BCwkgIgvRjLsgsojYDWPm42ef/X0mIPoZf4r9j/odrbKhy8Mp6h13jxmudYjIcGwHrdkG2KBGHCrXnof5Vs9v376VrDV2Sbhev25UI12OQBYRqQer7/vLuRnvrL4cSztfs5AUSUskb99T+DGmOhCRMUXjAm3xHgi57ad6EtmimU5Ofy4Q5iIOzSoifYhYkPvUEencqDy0N3H9+j8+mC1oBpEq2SMSjaHyHL/2NXup/BhLPYjIWCJxwXZE7ZDCoNmC9ig02PX6/ff/X5BO9+ESKj2s2erPdbt81JghIt39bbSlUTvkaIEnaFjUmBUnIhYI8nc/xkvQt6kiEwHrs5nMZTODiPADvGydbeqGEJEePSAqvB5IOHWCBKKOg2JmIhPsc7gcjAAi0iOgUeH1QMKpEyQQdRwwE5lgZ8ZlHwKISA/uUeH1QMKpEyQQdRwwE5lgZ8ZlHwKISA/uUeH1QMKpEyQQdRwwE5lgZ8ZlHwKISA/uUeH1QMKpEyQQdRwwE5lgZ8ZlHwKISA/uUeH1QMKpEyOgXyLbONCzUSI9jpGZyMQ6M+7mJ9D2ICQ9hiBKQkSiRBI/RkvAnlRvM5Hc+dBgEJGhCU+s/q2tm/Npe32wrK+vVbu7T9xpaBmhBx6pbbmWFM2n19e55Hg/NHREZGjCE6tfIiLBaKa9vWezgbuz86hZlO2zlhX69xAauDmf7i6xMrsmGpqdDJ3M1tB2EJGhCU+s/kUiIgx37nzTKjA5EHn/9zwJiQ3qlM+L7WJn9rqOSVGGiKSgSB1zAstEROW5kx7CrAGV6r/nXbb9uQa1tS+XPUTEiJMnIbBIRLQfsrm5UR0dvUpiZ5VK6vsfY/gvd7kGtbHJZQ8RMeLkSQhIRKzzNnOJyP7+iyR2llXitf/R1S7j0XVMyrJc9hCRlFGjrmrRTETiIRHRpuvp6emgpLz3PxY5l2tQm/1c9hARI06ehMAiEVHlWtKoY+tKzVDJ7snw3v9o8y/XoDbbuewhIkacPAmBVURkiPtFtP+h28k1cHQ3qD6PLeUa1OZ3LnuIiBEnT0KgS0S2tx/MBvnBwcsktqyS4+Pj+X0Y+s92Y025BrX5n8seImLEyZMQWCQi2hPRfojuFUmZ9MM2LV30yvXvMC/b/lyD2tqXy14xImJAyN/95zvjYB1mLLlExNpWzyUgqe9Wtf0P/QNwzUbGnoxHrnbmsoeI8B/wcvXpZHZK2P9oczbXoDbbuewVJyIGaOp5rg4yNs6l7H+0ccsds1z2EJG2aBfwXa4OMiYU2vMoZf+jjVvumOWyh4i0RbuA73J1EC8UuuNUN43ZXoeuushn3b5u3/Vpm5ZEqj/Xj+HU1twxy2VvcBGxza++HSAXkD4dM+e5kXk0n79x7dpfZwMw1WMFbUZjDCVMEq2hk9kb2o7Vn8veoCIilTdHLL/sY+HsfAM09TwqD80yzLd6/u23/04Wci2J6nXrvQRq6GQ2h7Zj9eey1yki1ogx5QZo6vmYYpKjLZf949PsJ21/2HK0v26j2aahPtdt9n3f1UZEpIvOiMv6dorSzk/1JDItW7x9z9WtUvrZ1eaVRKSrgmVlzcfCXfauQgOyzN5UyiPzaPYZ+ZpiM9X6hv3Gxhgq152vpA8JGKMPS95/M7iIyJQCpKdL9dm8WsWZ927FfxeZh66caOahJYwGfOorKKpfG/6qXy8EZPF4WaWfZRGRxU1cvWQVZ1avrfwj4VF+DEvwYJV+hoiUEMmWNq4S3JbT+AoCFyKwSj8rTkTMKfJ3P8S7UI/gYAhckICNs67TEBF+gNfVPyibOIFQIjLxWOI+BFwIICIu2DEKgTgEEJE4scQTCLgQQERcsGMUAnEIICJxYoknEHAhgIi4YMcoBOIQQETixBJPIOBCABFxwY5RCMQhgIjEiSWeQMCFACLigh2jEIhDABGJE0s8gYALAUTEBTtGIRCHACISJ5Z4AgEXAoiIC3aMQiAOAUQkTizxBAIuBBARF+wYhUAcAohInFjiCQRcCCAiLtgxCoE4BBCROLHEEwi4EEBEXLBjFAJxCCAicWKJJxBwIYCIuGDHKATiEEBE4sQSTyDgQgARccGOUQjEIYCIxIklnkDAhQAi4oIdoxCIQwARiRNLPIGACwFExAU7RiEQhwAiEieWeAIBFwKIiAt2jEIgDgFEJE4s8QQCLgQQERfsGIVAHAKISJxY4gkEXAggIi7YMQqBOAQQkTixxBMIuBBARFywYxQCcQggInFiiScQcCGAiLhgxygE4hBAROLEEk8g4EIAEXHBjlEIxCGAiMSJJZ5AwIUAIuKCHaMQiEMAEYkTSzyBgAsBRMQFO0YhEIcAIhInlngCARcCiIgLdoxCIA4BRCROLPEEAi4EEBEX7BiFQBwCiEicWOIJBFwIICIu2DEKgTgEEJE4scQTCLgQQERcsGMUAnEIICJxYoknEHAhgIi4YMcoBOIQQETixBJPIOBCABFxwY5RCMQhgIjEiSWeQMCFACLigh2jEIhDABGJE0s8gYALAUTEBTtGIRCHACISJ5Z4AgEXAoiIC/bhjZ6dnVVv3vwxmKHj4+PB6qbisgggImXFa2lrJR5ff327ssBubFyvUg74589/q9bX1+b1P3z409I2cUBsAtbXury80lW4SgVd51OWlsDdu3dnA/zTT/9WfXnr1uy9Br3EpW86PDyci8cP9+9Xein+jx//0rdqzi+YwCoasJKIWEXkH80HmhcLCcjr16+rt2/fzoVEAtA3SSzk0/9+/nle1eef/7P65JOP3X32Yo3d9/193ila3iAiV9+DKqHT5BQRzXauXXu/vCmBD20cpj+3aMf8q04RmR/Fm1EQsP2QoZczmo2wnBlFyItoBCJSRJjeNVJ7H198cWO+vNB+SIqljCF4+vTXed36i/7jjz9YETkEFhJARBaiGW+BrsikFI+6pxIq1T3kJeS6Pd6XTwARKT+GeAABVwKIiCt+jEOgfAKISPkxxAMIuBJARFzxYxwC5RNAREYcw93dJ+duQ79z55tqf//FuRbv7T2rtrZuzq+qbG5uVDqvmba3H8yP0ZWXe/e+r05OTpqHzT/LlurqSjs7j2bt6zqGsvgEEJGRxliDXpdwJRKWNLAlAAcHL2dfqUyfNZgtSUD0XV1IbLBbXRIPCU+XSEis6ras/nqu9tVt18t4Px0CiMgIY316ejobwBKSZtLA1SxCaZEQNGcREotmXSZAXbMRnWe2mu2w84+OXjWL+DwxAohIYQGXiEg8upIGvmYREiOJRHNmonMXfV+v15ZTqqeZJFR6kSCAiBTUB2zgN2cVTRc0g7Clii1LmnspNtvpWo7oGIlWfWkkW5p9SJiadTbbwedpEEBECoqzxEODt2sJYcsMG/jLRGTRcsWwqLw585HwmEjZceTTJYCIFBJ7iULbsqTefIlLfc9EZX1FRJu4smubuapTAmIiVbfP+2kSQEQKiLsJQdfSQ0sdDe7mPoWdq7yeVlnO2PGaidgSSvVIqNr2Sex48mkRQERGHm+bgXQJiAZ2m4DINdtHac4cFn3fhkPnSjiUJFLLlkBtdfBdXAKIyEhjq7/0GrDLljC2T9I1sCUwNpMwd23vpL5MsbK23DZYm0ubtmP5bloEEJGRxltLiBQCIvc0i1FdEg4lzUJUf3PDtAuF6pCQXOScrvooi0MAERlhLG0fQwO/7WV7Em1l9e/sKo5mNTZjsXLNciQmqya7rNtcFq16PsfFJYCIxI0tnkEgCwFEJAtmjEAgLgFEJG5s8QwCWQggIlkwYwQCcQn8CXIrg7hImhXnAAAAAElFTkSuQmCC"></p>
<p>The circuit transfers 1.6 kW when switch A only is closed. The external voltage is 220 V.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The molar mass of water is 18 g mol<sup>−1</sup>. Estimate the average speed of the water molecules in the vapor produced. Assume the vapor behaves as an ideal gas.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State <strong>one</strong> assumption of the kinetic model of an ideal gas.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the specific latent heat of vaporization of water. State an appropriate unit for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why the temperature of water remains at 100 °C during this time.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The heater is removed and a mass of 0.30 kg of pasta at −10 °C is added to the boiling water.</p>
<p>Determine the equilibrium temperature of the pasta and water after the pasta is added. Other heat transfers are negligible.</p>
<p style="padding-left:180px;">Specific heat capacity of pasta = 1.8 kJ kg<sup>−1</sup> K<sup>−1</sup><br>Specific heat capacity of water = 4.2 kJ kg<sup>−1</sup> K<sup>−1</sup></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that each resistor has a resistance of about 30 Ω.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the power transferred by the heater when both switches are closed.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Cold milk enters a small sterilizing unit and flows over an electrical heating element.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The temperature of the milk is raised from 11 °C to 84 °C. A mass of 55 g of milk enters the sterilizing unit every second.</p>
<p style="padding-left: 210px;">Specific heat capacity of milk = 3.9 kJ kg<sup>−1 </sup>K<sup>−1</sup></p>
</div>
<div class="specification">
<p>The milk flows out through an insulated metal pipe. The pipe is at a temperature of 84 °C. A small section of the insulation has been removed from around the pipe.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the power input to the heating element. State an appropriate unit for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline whether your answer to (a) is likely to overestimate or underestimate the power input.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Discuss, with reference to the molecules in the liquid, the difference between milk at 11 °C and milk at 84 °C.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State how energy is transferred from the inside of the metal pipe to the outside of the metal pipe.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The missing section of insulation is 0.56 m long and the external radius of the pipe is 0.067 m. The emissivity of the pipe surface is 0.40. Determine the energy lost every second from the pipe surface. Ignore any absorption of radiation by the pipe surface.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe <strong>one</strong> other method by which significant amounts of energy can be transferred from the pipe to the surroundings.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.iii.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Define <em>internal energy.</em></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>0.46 mole of an ideal monatomic gas is trapped in a cylinder. The gas has a volume of 21 m<sup>3</sup> and a pressure of 1.4 Pa.</p>
<p>(i) State how the internal energy of an ideal gas differs from that of a real gas.</p>
<p>(ii) Determine, in kelvin, the temperature of the gas in the cylinder.</p>
<p>(iii) The kinetic theory of ideal gases is one example of a scientific model. Identify <strong>one</strong> reason why scientists find such models useful.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A large cube is formed from ice. A light ray is incident from a vacuum at an angle of 46˚ to the normal on one surface of the cube. The light ray is parallel to the plane of one of the sides of the cube. The angle of refraction inside the cube is 33˚.</p>
<p><img 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"></p>
</div>
<div class="specification">
<p>Each side of the ice cube is 0.75 m in length. The initial temperature of the ice cube is –20 °C.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the speed of light inside the ice cube.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that no light emerges from side AB.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch, on the diagram, the subsequent path of the light ray.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the energy required to melt all of the ice from –20 °C to water at a temperature of 0 °C.</p>
<p>Specific latent heat of fusion of ice = 330 kJ kg<sup>–1</sup><br>Specific heat capacity of ice = 2.1 kJ kg<sup>–1</sup> k<sup>–1</sup><br>Density of ice = 920 kg m<sup>–3</sup></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline the difference between the molecular structure of a solid and a liquid.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The first scientists to identify alpha particles by a direct method were Rutherford and Royds. They knew that radium-226 (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{86}^{226}{\text{Ra}}">
<msubsup>
<mrow>
</mrow>
<mrow>
<mn>86</mn>
</mrow>
<mrow>
<mn>226</mn>
</mrow>
</msubsup>
<mrow>
<mtext>Ra</mtext>
</mrow>
</math></span>) decays by alpha emission to form a nuclide known as radon (Rn).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the missing values in the nuclear equation for this decay.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Rutherford and Royds put some pure radium-226 in a small closed cylinder A. Cylinder A is fixed in the centre of a larger closed cylinder B.</p>
<p><img src="data:image/png;base64,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"></p>
<p>At the start of the experiment all the air was removed from cylinder B. The alpha particles combined with electrons as they moved through the wall of cylinder A to form helium gas in cylinder B.</p>
<p>The wall of cylinder A is made from glass. Outline why this glass wall had to be very thin.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Rutherford and Royds expected 2.7 x 10<sup>15</sup> alpha particles to be emitted during the experiment. The experiment was carried out at a temperature of 18 °C. The volume of cylinder B was 1.3 x 10<sup>–5</sup> m<sup>3</sup> and the volume of cylinder A was negligible. Calculate the pressure of the helium gas that was collected in cylinder B.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Rutherford and Royds identified the helium gas in cylinder B by observing its emission spectrum. Outline, with reference to atomic energy levels, how an emission spectrum is formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The work was first reported in a peer-reviewed scientific journal. Outline why Rutherford and Royds chose to publish their work in this way.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A closed box of fixed volume 0.15 m<sup>3</sup> contains 3.0 mol of an ideal monatomic gas. The temperature of the gas is 290 K.</p>
</div>
<div class="specification">
<p>When the gas is supplied with 0.86 kJ of energy, its temperature increases by 23 K. The specific heat capacity of the gas is 3.1 kJ kg<sup>–1</sup> K<sup>–1</sup>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the pressure of the gas.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, in kg, the mass of the gas.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the average kinetic energy of the particles of the gas.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain, with reference to the kinetic model of an ideal gas, how an increase in temperature of the gas leads to an increase in pressure.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram below shows part of a downhill ski course which starts at point A, 50 m above level ground. Point B is 20 m above level ground.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>A skier of mass 65 kg starts from rest at point A and during the ski course some of the gravitational potential energy transferred to kinetic energy.</p>
</div>
<div class="specification">
<p>At the side of the course flexible safety nets are used. Another skier of mass 76 kg falls normally into the safety net with speed 9.6 m s<sup>–1</sup>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>From A to B, 24 % of the gravitational potential energy transferred to kinetic energy. Show that the velocity at B is 12 m s<sup>–1</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Some of the gravitational potential energy transferred into internal energy of the skis, slightly increasing their temperature. Distinguish between internal energy and temperature.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The dot on the following diagram represents the skier as she passes point B.<br>Draw and label the vertical forces acting on the skier.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The hill at point B has a circular shape with a radius of 20 m. Determine whether the skier will lose contact with the ground at point B.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The skier reaches point C with a speed of 8.2 m s<sup>–1</sup>. She stops after a distance of 24 m at point D.</p>
<p>Determine the coefficient of dynamic friction between the base of the skis and the snow. Assume that the frictional force is constant and that air resistance can be neglected.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the impulse required from the net to stop the skier and state an appropriate unit for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain, with reference to change in momentum, why a flexible safety net is less likely to harm the skier than a rigid barrier.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>An ideal monatomic gas is kept in a container of volume 2.1 × 10<sup>–4</sup> m<sup>3</sup>, temperature 310 K and pressure 5.3 × 10<sup>5</sup> Pa.</p>
</div>
<div class="specification">
<p>The volume of the gas in (a) is increased to 6.8 × 10<sup>–4</sup> m<sup>3</sup> at constant temperature.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by an ideal gas.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the number of atoms in the gas.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, in J, the internal energy of the gas.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, in Pa, the new pressure of the gas.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain, in terms of molecular motion, this change in pressure.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Liquid oxygen at its boiling point is stored in an insulated tank. Gaseous oxygen is produced from the tank when required using an electrical heater placed in the liquid.</p>
<p>The following data are available.</p>
<p style="padding-left: 60px;">Mass of 1.0 mol of oxygen = 32 g</p>
<p style="padding-left: 60px;">Specific latent heat of vaporization of oxygen = 2.1 × 10<sup>5</sup> J kg<sup>–1</sup></p>
</div>
<div class="specification">
<p>An oxygen flow rate of 0.25 mol s<sup>–1</sup> is needed.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Distinguish between the internal energy of the oxygen at the boiling point when it is in its liquid phase and when it is in its gas phase.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, in kW, the heater power required.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the volume of the oxygen produced in one second when it is allowed to expand to a pressure of 0.11 MPa and to reach a temperature of 260 K.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State <strong>one</strong> assumption of the kinetic model of an ideal gas that does not apply to oxygen.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The graph shows the variation with temperature <em>T</em> of the pressure <em>P</em> of a fixed mass of helium gas trapped in a container with a fixed volume of 1.0 × 10<sup>−3 </sup>m<sup>3</sup>.</p>
<p style="text-align: center;"><img 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a7P+zsoy//s+tVyr4WNkGqhYmcfhBQhVUtBq0h67bMX2dr1Ywbl/R1UzT/6bXb9arnXwkZItVCxsw9ASgYC1qO9MAhHi0nHw/h8OXOp+rX6HZTOtdz2iPqhpEmsiK/nQkj1VL/RuTmT4kyqlkooNrXFa7eKmNe/t/058elnUN7zW+3PiU/3p+Xfa7fi07FEbBNSEapu7JOQ8hVhaxB6B7m3PePbtn81oDCUvf1ntZ+9f6PLHSEVrfAG/gmpbYtY2qVWEfLaZy9i3uv3tj9FvxRQ6Gvv+a32p8SX5t4I8eViarmPkGqpZidfhBQhVUs9q0h67bMXWbn+HKCgq9hLGnvts+tX0qXVfkKqlZId/RBShFQt/bxF1Go/e5HF9ZUABV2t6/faZ9evlnstbIRUCxU7+yCkCKlaCnqLqNV+9iIb/TuoS9evlnstbIRUCxU7+yCkCKlaClpF0mufGVKYQUX/DsrSd2b9annXykZItVKyox9ASgYC1qO9MAhHi0nHw/h8OTOrflv9DkrnWm57RP1QziRWxNdzIaQaq//48YfL8+ef3fP66tWXy6NHHywACl4vX35xdMy7d98tT558dGuHH7RZs3AmxZlULU9QbGqL124VMa9/b/tcfPoZlNe/t30uPt1fXv/e9lZ8OtaIbUKqoapPn358gEwKqbdvvznsxxrLzc3NAVj6OAAMkIINy7NnnxzaAF7WQkj5irA1CL2D3Nue8bXtXw0ojC1v/3jbz96/Vn3y2gkpr4LLslxfXx8Ag5kPgKHhA/cAzsOHV0dn0vtSiMmBaJPOuMSm14RU2yKmtcW2twh5289exLzX722v9UsBxf6181vrl46NLd4TUg1Uxq05wASzoLWQAsgEXGiLdjKLkpDgF7MzayGkCKlajniLvNXeKmJW+2i7xJcDFHSLPr/lX+Ir9aHVPtpuxVeKu9V+QqqBkvo2Xg5SuZkSbu/JjEsDS4cDQAFU1mJBymofbe+d5Nb1MT5Lobp9Bv1KgKpf2TbWGfTbRon8WQipvC5n7S3NpOAMIAJM5AVIyQIYyaxK9mFd2q+PwbYFqehPWpZ/axBa7aPtjO+yZ6Kfv3ixXF29v7x+/VU6dA7vo/PL8j97/mVFbbiTkGooZglSuJ0HKOHZlSz4kgReWEowKu0XH7ImpC67yM5exKwiHWnHDOrBg/eKgMIYijz/Gv+z96/Uoag1IdVQ2RKkMEuSW3tyOrkF+ObN1wdbaSaVu90nszG9lkTHmi9qwBz484IZFAD1208/5Zg4sS6gTukckrrVY01INVQ9BynZl35LD18tB2Swv/bFCZlt1cLkTIozqVp+RM8UUMxqS/T5c/71M6gR49N6zR6fvpaIbUKqoaoCpHTWhFlSCik9k5JtrPWSa6ftsm1BSo7rtbYGYa+45LyMT5Q4bz2afhpQuKLR4ktVZnypIsfvCaljPVzvSpACoHDbDrf2ZMEMSd/K4495RZn769wnZX2U124VCa9/b3vGt36mnAIKeUL91uunx5VsW/rJcVFrQqqhsiVI4RQAFWZG8hwJP+bVCwAGcIkd0OJ/i/STQt4ib7W3BqHVPtrO+NYV2RygkEHUb51+uh7pbUs/fWzENiEVoerGPq3bfdFF1PJvJbnVPtrO+GKLWHT/wX8JUBiK7N/Y/o0ud4RUtMIb+CekYgfhFkW2liYssvX+tf4eFPWr62flt6VfLXdb2AipFip29kFIxQ5CaxBH260iEX1+y3/P+DCDsv4eVM/4UBpG1q9FfNHlj5CKVngD/4CUDASsR3uhSIwWk46H8flyppd+a/8eVK/4dI7VtkeMT+CFuBFfz4WQ6ql+o3NzJsWZVC2VUGhqi9duFTGv/1x7/QwqZ9fX2yM+ff5Lj09fa8Q2IRWh6sY+CSlfEWYRm0s/DSgMtUuHgHV90XZrfESXO0IqWuEN/BNScxXZNCWsImMVCat9tH3L+FJAQUvr+raML+3bPcSXu+aW+wiplmp28kVIEVK11LOKuNe+FQRygMJ1W/FvFV+pDy49vtJ1t9pPSLVSsqMfQoqQqqWfVSS99i0gUAIUrtuKf4v4PPrPHl/t2lvYCKkWKnb2QUgRUrUUtIq41x5dZK3fQVnxR8dnnd+yzx5fLfda2AipFip29kFIEVK1FLSKpNceWWQxg7J+B2XFHxkfdLfOb9lnj6+Wey1shFQLFTv7AKRkIGA92guDcLSYdDyMz5czUfqt/R2U7svcdlR8uXOds2/E+FDS5FoQX8+FkOqpfqNzcybFmVQtlVBsaovXbhWxc/zrZ1DntNfXGxGf9r/3+LQWEduEVISqG/skpHxFmEVsLP00oDCU9g4B7/V721vjI7rcEVLRCm/gn5Aaq8imXR5dJLz+ve2tInaK/xRQ0PKU9qn2eN8yvpz/vceX06TlPkKqpZqdfBFShFQt9bxF1GrfCgI5QOG6rPNb9lbxlTS2zm/ZZ4+vpEur/YRUKyU7+iGkCKla+llF0mtvUWRLgMJ1jRBfpL4t9OsZX+3cLWyEVAsVO/sgpAipWgp6i7zV3ltkvb+Dio7P8u+1e/Xznt9qb8VXy70WNkKqhYqdfRBShFQtBa0i5LVbRazmHzMo7++gav6hiyc+tLf8e+2zx1fLvRY2QqqFip19AFIyULAe7YVBOFpMOh7G58uZc/Vr9Tso3Ze57XPjy/mK2DdifChpcq2Ir+dCSPVUv9G5OZPiTKqWSig2tcVrt4pYzr9+BpWz63i99nPia3l+K/7Z49NaRWwTUhGqbuyTkPIV4dmLhFUEo+2n6qcBhaEyWnzp8GV8nEmlOcH3JypASBFStZQZqcimgELcI8WX05HxEVK5vOC+ExQgpAipWrqMUmRzgELco8RX0pDxEVKl3OD+lQoQUoRULVVGKLIlQCHuEeIbXb+R46vF1sLGZ1ItVOzsg5AipGop2BsC0b+Dsq7v1GdmqZaWf6999vhSvVq/J6RaK9rBHyFFSNXSzltErfa1IosZVPTvoDzxQTerfbS9pt8M8dVyr4WNkGqhYmcfgJQMJKxHe2EQjhaTjofx+XKmpN9Wv4PSfZnbLsWXO7bHvhHjQ0kTLRBfz4WQaqz+48cfLs+ff3bP6/X19fLkyUcLgIIXtm9ubm6Pe/fuuyM7/Lx69eWtvbbBmRRnUrX8QLGpLV57rojpZ1Be/972ufi0Hl7/3vazx6e1jNgmpBqq+vTpxwcApZACjB49+mB5+fKLw9kALEAIoJIFdg2uZ88+OfgCvKyFkPIV4dmLhLdIetun+mlAIXe9/r3t0/jS8eT1720/e3ypnq3fE1INFJVZEmY+AEYKKbwHhPQix6Lt27ffHNphrZeHD69uwab3p9uEFCGV5oR+7y2iVntdZFNAIQ6rfbRdx6d1ke3o81v+Z49PdIxaE1INlMWsCLMkzJhykAKgMDMqLWiLdvr2H46FX8zOrIWQIqRqOWIVSa9dimwOUIjL69/bXuIraeT1720/e3wlXVvtJ6QaKCkzoBKkZEYkt/AAFcBHoISZFo5JFxwDUFmLBSmrfbTdGoTR57f8Mz5Lobod+pUAVW+5jZX969O5t36ElK//jlrnICX7ACH9RQg8f5JnUoBRCVK5/UcnXZbDLCzdp997P+l521tJ7vXvbc/4fDPRz1+8WK6u3l9ev/5Kp93ttrd/vO3Zv77+tfS77eigDUKqobACJP1MSvalt+30cyhCyjeIWMT66YcZ1IMH7xUBheHl7R9ve6vIev17288eX8MSmnVFSGVlOW+nACkHKflmn3iWY7H/1Nt9uL2XviTRseaLGmyRA5hBAVC//fRT5tyFjTvUKZ1DUrd6rAmphqoLeDSk4B637FJI4Vt9AA1uAda+OCG3BGthWs+kvJ/0vO2R7LXF69/bnvGdPhPTz6Co3+n66fEwu376WiK2CamGqpYghdt5KWzkdh9+ByXb8gUMCSkHN7HptQUpfWyPbWsQ9ohJn5PxaTXsbQ0oHE39bM1qR1C/mjrLQkjV9TnJWoIUZk0Azps3X9/6A7T0cyr+mPdWmnsb3pmS1d4qElb7aPtI8aWAQmeNFN+95GF87meCVv/mNG+5j5BqqGYJUjhF+t8epb+bAsAALnnWBGjpbwPWwrRmUtFF1PJvJbnVPtrO+NbdrsoBCnlJ/dbpVxrDs+tXuq5W+wmpVkp29ENI7btIREMc/kuAQtrPXmS30K9WHmbXr3ZtLWyEVAsVO/sgpAipWgp6i7D196BmL7JefbztZ9evlnstbIRUCxU7+yCkCKlaCnqKKGZQ1t+Dmr3IevSB7t72s+tXy70WNkKqhYqdfQBSMlCwHu2FQThaTDoexpfPmbV/D4r65fXTOVbbHlE/lDSJGfH1XAipnuo3OjdnUpxJ1VIJxaa25Oz6GVTOrv1ZRcxqH21nfKf3/yn9q4+N2CakIlTd2CchFTsIo4uo5X/rIqsBhVQeLb50eDE+X/579Uv7o/V7Qqq1oh38EVK+Qbo1BNIU8RYJq/0p9hRQiNVqT/32nX9pPrd+T0i1VrSDP0Jq30XCgshaew5QSGerPSG17/yLLnmEVLTCG/gnpPZdJCyIrLGXAEVI2ZBeo2+tDMwO+dq1tbARUi1U7OyDkCKkailoFVHrd1BW+9mLrHV90fbZ9avlXgsbIdVCxc4+CClCqpaCtSKLGZT1O6hae5x39iJrXV+0fXb9arnXwkZItVCxsw9ASgYS1qO9MAhHi0nHs9f41v4OSmuV296rfjktztk3on4oaXItiK/nQkj1VL/RuTmT4kyqlkooNumin0Hl7Pp4y24VMat9tJ3x3e//lv2rfUVsE1IRqm7sk5CKHYTRRdTy37rIakAhVa3zW/bW8aXDxzq/ZWd8seMj7a/W7wmp1op28EdIxQ5CqwhG21sW2RRQSFdv/C3jyw0fxufL72j9cn3Wch8h1VLNTr4IKd8g3kuRzQEKKRtdxLz+ve330r+l8hOtX+m8rfYTUq2U7OiHkCKkaumHIlUCFNpFFzGvf297Qip2fNRyr4WNkGqhYmcfhFTsIPQWSW97b5H1/g7Kit8bn+Xfa2d8seMjuvwRUtEKb+CfkIodhN4i6W3vKbKYQXl/B2XF74kPw8Py77UzvtjxEV3iCKlohTfwD0jJQMZ6tBeKxGgx6XguNb5Wv4PSWuW2L1W/3LVG7BtRP/nwgOtFfD0XQqqn+o3OzZlU7CdFDNTaEm23ikTu/PoZVM6ur8drPye+lue34md8vvy19NN9GbFNSEWourFPQip2EFpFMNpuFYn0/BpQSMXUnqan135qfK3Pb8XP+GLHR9qfrd8TUq0V7eCPkIodhFYRjLafUmRTQCEdR4ovNzwYX/12WrQ+ln8r/3J92nIfIdVSzU6+CClCCqmXAxT2W0XIa7eKmNe/tz3jix0f0WWPkIpWeAP/hFTsIPQWSW/7NUW2BChCiv9Le3T+RZc4Qipa4Q38E1L7hlT076CsIrcGorVhYPn32hlf7Pio9W0LGyHVQsXOPgip2EHoLZLe9rUiixlU9O+grPhr8WFoWO2j7YwvdnxElz9CKlrhDfwDUjLQsR7thSIxWkw6nlnj2+p3UFqr3Pas+uWupce+EfWTDxfQA/H1XAipxuo/fvzh8vz5Z1Wvz559sjx8eHV0zLt33y1Pnny0ADh4wc+rV18eHVN6w5lU7CdFDNTaEm3PFQn9DCr6/Jb/XHxaL6t9tJ3x+fLX0k/3dcQ2IdVQ1adPPz4ApgapN2++PhyTQurRow8OkLq5uTlEBJABPoCXtRBSsYMwuoha/tMioQGF3LDaR9vT+NJ8jT6/5Z/xxY6PtL9bvyekGih6fX19AAxmPgBGCVIAEGAEQGlIvX37zaEd1nrBMS9ffqF3ZbcJqdhBaBXBaLsusimgkBDR57f86/hyCWq1j7YzvtjxkevzlvsIqQZq4tYcYAII1SCF2RGOxYxLQwpt0U5mURKSHCvvS2tCKnYQRhdRy78U2RygkBNW+2i7xFfKz+jzW/4ZX+z4KPV7q/2EVEqaEKUAABfnSURBVAMlZQZUg5Tc5sPtuxRSmHlpaElIOA6gshYLUlb7aLtVJKLPb/mfIb4SoKxr28I+g35b6HDuOahfXTlCqq7PSdYSpLAft/nk1l0KqfS9nLS0X+yytiBlfdKMtluDMPr8lv/R4/v8xYvl6ur95fXrr6TLj9bW9UXbR9eP8XEmdTRg9vymBCm5zSfapPBJ35eOk/3pmpCKHYTRRb7mHzOoBw/eKwIKuVBrv4WdELjc/EP+WP2b1qPW7zmTaqhoDlL6Np+cKoXSqbf7AKX0JYmENV+XoQFmUADUbz/9lH3KvN40B1CrdB2R2tVjTUg1VD0HKQApBYp+D4jVvjiB305ZC/zVFn7Srn/SFcCXNOyhn34GNWJ8WivGV88vK39m10/nQsQ2IdVQ1Rykcu7TmVT0V9BzMWy5zxqEW8aSO9do8WlAId7R4ks1ZHypIqe9p351vQipuj4nWc+FFE7CH/OWpbY+iXrtVpHw+j+lfQooqDJSfLleYnycSeXyotU+QqqVksti/k5KTpXOpLAft/30f4sEaPG/RfpJsVOKvGis11b7UYpsDlC4jlHi05rqbcZHSOl8aL1NSLVWtIM/PpOav0iUAIV0IgTm799aWZi9f2vX1sJGSLVQsbMPQmruImb9PajZi5g1k422U7/Y8RFd/gipaIU38E9IxQ7CyCKKGZT196BYZOftXwx/K39m79/oEkdIRSu8gX9ASgYC1qO9MAhHi0nH0yu+tX8Pqld8WqPaNuPzjbkR9RO4ot8RX8+FkOqpfqNzcyY13ydt/QwKhaC2WEXCah9tZ3z1/rP0n12/Wu62sBFSLVTs7IOQmqtIaEAhdS69iFnXF22fHQLR+lj+Lf2iyx8hFa3wBv4JqXkglQKKkLIhbRVRy24VWat9tH32+KJLHCEVrfAG/gmpOSCVAxQhRUgRUvUiSUjV9ZnCSkiND6kSoAgpQoqQqpdZQqquzxRWQmpsSFm/g7JuJ81exKzri7ZTv9jxEV0kCalohTfwT0jFDkJPEcUMyvodlOWfRXbc/sXwtvrPss/ev9EljpCKVngD/4CUDASsR3thEI4Wk44nKr61v4PSseS2o+LLneucfYzPN+ZG1E/gi3xAfD0XQqqn+o3OzZnUeJ+09TMoDPTaYtmtImG1j7Yzvn33by23W9gIqRYqdvZBSI1VJDSgkBpeSBACY/VvOtz33r+pHq3fE1KtFe3gj5Aap4ilgEI67L2Iea/f256Qjx0f0SWPkIpWeAP/hFTsIFxbJHOAIqT8kF6rf2moEVKx46Oke6v9hFQrJTv6IaRiB+GaIlkCFNJiTfta+rDI9u/fWv/svX9r2rSwEVItVOzsg5DqW8S8v4Oyihwh1bd/rf7x2mfv3+jyR0hFK7yBf0KqXxHDDMr7OyiryM1exKzri7ZTv9jxEV3iCKlohTfwD0jJQMd6tBeKxGgx6XjOja/V76B0LLntc+PL+YrYx/h8Y25E/VC2JFcQX8+FkOqpfqNzcyYV+0kRgzVd9DOonF0f77VbRcLr39ue8d3Pj1P6f3b99LVGbBNSEapu7JOQ2rZIaEChq71F3mo/exGzri/aTv1ix0d0uSOkohXewD8hFTsIdRFNAUVILeZ/m6P1yw2HaDshFTs+cn3ach8h1VLNTr4IqdhBKEU0Byh0udhL3e+1s8hu079R/Wf1/+z9W9Kt1X5CqpWSHf0QUvFFrAQodLtVhLz22YuY9/q97alf7PiILn2EVLTCG/gnpGIHYfTvoKwizCIb27+W/tH22fs3usQRUtEKb+CfkIorYphBRf8OyiqCsxcx6/qi7dQvbnxsUN4WQmoLlYPPAUjJQMd6tBeKxGgx6XhK8W31OygdS267FF/u2B77GJ9vzI2oH0qW5BLi67kQUo3Vf/z4w+X588/uecU+wERez559cnTMu3ffLU+efHRrh59Xr748Oqb0hjOp9p8U9TMoDNbaEm23ikT0+S3/jM+XH7PrVxsbLWyEVAsV/9/H06cfHyCTQgr7Hz36YAGIsGCN94CSLPL+5ubmsAsQA3ykjRyXWxNSbYuEBhT0top0tH32Ihatj+Wf+rUdH7kaFLmPkGqg7vX19QE4mPkAGBpSsGHfy5dfHJ0J77Ef9rdvvzlsY62Xhw+v7rXTdtkmpNoNwhRQ0NgqgtF2Ftl2/StjRq+j+8/yP3v/ai0jtgmpBqri1hygg1lQCqmS+zdvvj4ci7UAS2ZR0gZ+MQuzFkKqTRHLAQraW0Um2j57EYvWx/JP/dqMD6sORdkJqQbKygzoFEgJmDCTwswLs6Z0AaAAKmuxIGW1j7ZbRSL6/JZ/xFcClNV2C/sM+m2hw7nnoH7nKvdTu976EVK+/jtqfQqk8AxKZklYlyCV23900mU5zMjSffq99Ukz2m4lefT5Lf+fv3ixXF29v7x+/ZWW7Xbbah9tH10/xhc7U4nOL8u/1b+3AyVog5BqKOxaSOFLEYCU3N4jpHyD3BpkNTtmUA8evFcEFNKj1n4Lu1UkGF89f6hfXR8rfyz9GpbQrCtCKivLeTvXQAq3+TA70t/aO/V2H27vpS9JJKz5WqcBZlAA1G8//ZSaMW+YAyoHUAF1HTmvIrZpRUi10fHgxYIUYAS44MsSepHnUzKzEhueR+mvqcv+dG09k7I+KUXbBaBp3PI++vw5//oZ1IjxiTZYM77YmUAuP7T+0fbZ+1drFbFNSDVUtQQp7Ads0hmUnDr6K+hynl5raxBuHZcGFM49WnypHowvVeS099TvNL3So3vrR0ilPeJ4X4IUZkSY7ci3AHOn4I95c6r8tK/lJ9kUUDiDNQhbnj93lZZ/xseZVC5vZJ+VP167lX8SR9SakGqobA5S8nuo9BmSvMetPiw4Tv+3SIAW/1uknzrHO8ikfQ5QOIM1CKX9T9Hc/zfazvgIqftZd7end/7dRRKzRUjF6LqpVz6TsotYCVDoKELA1q+W0NRv3/rVcqOFjZBqoWJnH4RUvUhYfw+KRbaun/VJnfrtW7/o8kdIRSu8gX9CqlwkMIOy/h4Ui2xZP6QvIeXT59L1iy5xhFS0whv4B6RkIGA92gsQ6BHT2r8H1Su+tZowPl9OU7/T9ZMPJ8hR6NdzIaR6qt/o3JxJ3f+kq59BYaDVFmsQWu2j7Yyv3n+W/tQvVr/a2GphI6RaqNjZByF1PAg1oNA1LGLH+qTpaulj2QkBn76z65fmU+v3hFRrRTv4I6TuikQKKHQHi+ydPrn0tPSx7LMXWev6ou2z65fLqZb7CKmWanbyRUj9VIRzgEKXWEVm9iJhXV+0nfr5PgTMrl902SOkohXewD8h9dfq34OyivTsRcK6vmg79SOkIsscIRWp7ka+9w4p63dQVpFmkd13kbXyI9o+e/5FlzlCKlrhDfzvGVK4xWf9DsoqMrMXCev6ou3Ub9+Qjy5xhFS0whv4B6SkEGE92gtFLCKmtb+Dss4dFZ913rV2xufLaep3un4oW5Kf0K/nQkj1VL/Rufc4k9JfksBgqi2W3RqEVvtoO+Nj/3ry25ufVv7VYmthI6RaqNjZx94gpQEF6aMHode/t71VJLz+ve0Z374hGl3+CKlohTfwvydIpYAipPyQJqR8kNm7ftEljpCKVngD/3uBVA5QhBQhZUGCMz0fhC39okscIRWt8Ab+9wCpEqAIKUKKkPJByKtfdIkjpKIV3sD/pUPK+zso7yC02kfbrU+y0ee3/DM+HyRm1y+6xBFS0Qpv4P+SIYUZlPd3UCyyviJK/ajfBmWseApCqijNPAZASgoJ1qO98EnxnJha/Q7KOve58Vl+W9kZny+nqd/p+qH6Sf5Cv54LIdVT/UbnvsSZlH4GhcFSW7x2axB6/XvbMz5f/1O/WP1qY7OFjZBqoWJnH5cGKQ0oSOst8lZ7FrHYImbpH21n/8b2b3T5I6SiFd7A/yVBKgUUIbWYf747ushb/gmBWAhY+kfbrf6NLnGEVLTCG/i/FEjlAEVIEVLeImwVWa9/b/vZ44sucYRUtMIb+L8ESJUARUgRUnuHgPf6ve0tiEaXOEIqWuEN/M8OqejfQVmD1BqEVvtoO+Pb9+206Pyy/Fv5F13iCKlohTfwPzOkMIOK/h2UdxBa7aPtVpGIPr/ln/HtG6LRJY6QilZ4A/+AlBQSrEd7oYjlYtrqd1C5c+t9pfj0MT23GZ8vp6nf6fqhbEnOQ7+eCyHVWP3Hjz9cnj//7J7Xly+/WAATeT179slyc3Nze9y7d98tT558dGuHn1evvry11zZmnEnpZ1AYDLUl2m4NwujzW/4Zny8/qF+sfrWx28JGSLVQ8f99PH368QEyKaQEUAIdAOnRow8WHC8L3gNSAi5ADPDBsdYyG6Q0oHBtVpGOtrOIxRax6P6z/LN/Y/tX16cffvjbgvHdciGkGqh5fX19AAwgBGCkkAJ88NILwPXw4dVh19u33xzaYa0X2HGctcwEqRRQuDaryETbWcRii1h0/1n+2b+x/avr0x/+8B+HWva73/3r8uOPP2rT2duE1NnS3TXErTnABLOgHKQAmxRcb958fTgWMyWZacksSjzDr55tyf50PQukcoDCtVhFJtrOIhZbxKL7z/LP/o3t37Qe/elPf1yurt4/vP7yl/9JzSe/J6ROlux+A5kB5SAl+9IZEeAEuABWAJjMqrR3AAqgshYLUlb7aDuKRAlQ0ede498qYmt8RB7D+HzqUr/t9cNtv1/+8p8PNe7Xv/6Va1ZFSPn676i1AEnPmgRGJUhhP2BUglRu/9FJl+WQCOk+/d76pBlt//zFi8Onqtevv9Jh3W5Hn9/ybxUxq320nfHFzgSi+8/yP3v/3g7kzAZmUjKrwgzrnIWQOke1QhtC6r4w+ET14MF7SwlQaGEN4mj77EUiWh/LP/XbN0Tvj/rjPXg29Zvf/MvhwzRmV6cuhNSpilWOz0FK9pVmUufc7sPtPb6oAXOAOTBbDvz85/948q0/QqoCnVNNAiR9uw8+al+cwPMsAAzJhvZ6wfOo9FuB2i7baDvywvjO7x1qd752aEn9+ur37bffLr/4xT8d+gHf/DvnG3+ElK8Pj1qXINX7K+hHQXZ4w0JxvujU7nzt0JL69dEPMMLX0KE/IOX57RQh5evDo9YlSMnvp3r9mPcoyA5vWCjOF53ana8dWlK/7fXDlyVwWw9fmDj3yxI6akJKq+HcLkEKbnELEANGXvhGn769h2dTmHGJHf8DhUDNCosD0VKobh9Zv5Fjg6qMr55blvXS9AOUcE34ggS+NNViIaRaqEgfVIAKUAEqsOAZVIsf8GopCSmtBrepABWgAlRgKAUIqaG6g8FQASpABaiAVoCQ0moMso3/sBbPrHBvFy98hT33Oyv9DAtfV0+fYclX28VP+udBzr3cNfHJl0Xk3LLW1xEVH65L/hd5nBfa4JmfXvA/gfTSb018vfXTWkE/5KNeeuunY8nF11M/jA/Jd73WGvbUb018evzoa0DcskSOXzkH1oSUVmOQ7fTPdsiA0wU+PUaSSpJIEghtsWA/2uiBcu7lpufOxYfz1/5Lp8j4cI2IEYMRi3xpRbTBvvQattRvTXw99dN5IdqledNTvzXx9dSv9FcNdNw99VsTX+5nMzr+yPGrz4NtQipVpPN7Kfjyn9ZKOFLY8L6UZHrGlUsya+DKuWrrNfGhfe782m/O3iI++ZQIX3rRP6juqd+a+HrqpzUTnaCdhpTsx1ovW+SfPp/EkcaHY3L5pdvm7C3yD+ew/EjcvfSz4sM16L7Uusl2pH5yDlkTUqLE4Gv5RIuvrSPJMAXXX2FH+Pq2B5IMbfSCW15op2cU2u7Z1vHBj5XkW8enzzeifjq+UfRDPmGGidg0pEbRrxRfb/2gFYp4aemtnxUf6gPqRApRfT1pvsIWVV8IKa38wNtIetwiwAIgIEnSBcmHgSu/18Jg0IskX/p8Rh9z7raOT2YL2Cf3sxG7nHfr+BAH9NK3/0bSL41vBP2QY5Jv0EpDaoT8q8XXWz+5lQfdJP/1WOytnxWf3C3R4xfbMn62Hr+E1LlVecN2AhdJdBSMUpHF/vR4CbW0X+znrlO/kuQYjLIgwQVU6fFyTGm/2E9dyydWFAodyyj6leLrrV96OyqFVG/9rPh66qcBqfMVRV5ysKd+a+KT57PyoRLXgW3kAQBVGqel/VqHc7YJqXNU27gNZkdIcll6JrnEoNdpfNqmtxE3ji0lc2m/9nHOtgBSNBxNvzS+0jVupR/6CIVKltEgZcUncafrrfRLz4v3+EAiRX60/Evjy8WPfYgfoC2N09L+kr+1+wmptUp1Og6FFYMSn2BkQaIgYdJFBuGW0/FcfGlc8l7i3jI+ObfMWgAEiUNssu6hn5xbxyf70rXEHakfziG3+eT8KaQkDrHLegv91sQn8aRriTtSv/Sc8h4zEXnOI3GITdZb6CfnStc6vtQm71GHMN631o+Qkh4YbI1EQEKgYKCw6kUKGo7RiyQR9smnHm1fk4j6+Np2Lb5SOz04o+NLY9DXPoJ+tfhSm7zfQj/0izxHya3R7z31WxOf6JWut9AvPae8l/zDbKOnfhJPutbxpTZ5j/oCkGLZcvwSUtIDA62RyIBTOoOSENN78rIfiYMBgAWAw0svsOEY72LFVzoP4pEkj4pPtMGg04vEhCIrx2Ctly30k3PX4pNYdWzY3kK/9Jx4D12k3/BerqGHfmvi66lfSRvEJDPU0jFb5l/adzq+3NiUPMBxWHLHlHTP9dkp+wipU9Ta4FjMmpCsSOh0pqRPDzsSRY6Rh50ACBZ5eIw1FgGLLjYHw4n/rIlPjpGElvPjumRWGBUfzqVnlHiPc0IvHU8v/dbE11s/xKiXFFKw9dRPx4btNL7e+qX5hzGKfTIWe+tnxSdjU4MMYwftZJFj5Jpa1Rfxr9eElFZjgG3cksjdZpF9AiF8EgekZD+KhiSMXEbqC4ASqMkxp65Tn3J+WUt8WOv4sC02OWfqq0V88I1rhC+JKQUUjuml39r4euon/SPrFAK99ZO4ZJ2Lr6d+ufxLx+Zo+ZfGh/cYNzKGcmMzavxKv8qakBIluKYCVIAKUIHhFCCkhusSBkQFqAAVoAKiACElSnBNBagAFaACwylASA3XJQyIClABKkAFRAFCSpTgmgpQASpABYZTgJAarksYEBWgAlSACogChJQowTUVoAJUgAoMpwAhNVyXMCAqQAWoABUQBQgpUYJrKkAFqAAVGE4BQmq4LmFAVIAKUAEqIAoQUqIE11SAClABKjCcAoTUcF3CgKgAFaACVEAUIKRECa6pABWgAlRgOAUIqeG6hAFRASpABaiAKEBIiRJcUwEqQAWowHAKEFLDdQkDogJUgApQAVGAkBIluKYCVIAKUIHhFCCkhusSBkQFqAAVoAKiACElSnBNBagAFaACwylASA3XJQyIClABKkAFRAFCSpTgmgpQASqwUwUePrxafvazv6++rq+vs+qgbc725s3XB3/v3n13r92zZ58cbM+ff3bPlu4gpFJF+J4KUAEqsGMF3r795gCQV6++NFXAMU+efJQ9rgQpgAlAXAMoOCaksvJyJxWgAlRgnwq8fPnFASK52VGqCGZEOD635CAlvtcCCn4JqZy63EcFqAAV2KkCT59+vDx69MGqq8dxmHnllhRS5wAKfgmpnLrcRwWoABXYqQIAT+kWnpYEMy08jyotGlK4LYhbfJh5nboQUqcqxuOpABWgAheqAMADmJRu4enLxjE16AikZAYFv2uec+lzYJuQShXheypABajAThWQL00AMNaC2VYNOgIpwAm3EB8//vAw81rzrEufm5DSanCbClABKrBjBWTWswYkpa+ei3wCKQAKi9weBKxOWQipU9TisVSAClCBC1YAs6M1X5rAjMs6TiClfyclEKzdJkzlJaRSRfieClABKrBTBQAemfnUJMBXyK2vkecgBZ8A4SnPpwipWk/QRgWoABXYiQKnfGkCMCt99VzkKkHq5ubmMAuzbheKH0JKlOCaClABKrBjBQQqFnzk2ZIllfjTt/ukjXxBY83zKUJKVOOaClABKkAFhlOAkBquSxgQFaACVIAKiAKElCjBNRWgAlSACgynACE1XJcwICpABagAFRAFCClRgmsqQAWoABUYTgFCarguYUBUgApQASogChBSogTXVIAKUAEqMJwC/wcCM/5BZaEelAAAAABJRU5ErkJggg=="></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce whether helium behaves as an ideal gas over the temperature range 250 K to 500 K.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Helium has a molar mass of 4.0 g. Calculate the mass of gas in the container.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A second container, of the same volume as the original container, contains twice as many helium atoms. The graph of the variation of <em>P</em> with <em>T</em> is determined for the gas in the second container.</p>
<p>Predict how the graph for the second container will differ from the graph for the first container.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A quantity of 0.24 mol of an ideal gas of constant volume 0.20 m<sup>3</sup> is kept at a temperature of 300 K.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by the internal energy of an ideal gas.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the pressure of the gas.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The temperature of the gas is increased to 500 K. Sketch, on the axes, a graph to show the variation with temperature <em>T</em> of the pressure <em>P</em> of the gas during this change.</p>
<p><img 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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A container is filled with 1 mole of helium (molar mass 4 g mol<sup>−1</sup>) and 1 mole of neon (molar mass 20 g mol<sup>−1</sup>). Compare the average kinetic energy of helium atoms to that of neon atoms.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A container of volume 3.2 × 10-6 m<sup>3</sup> is filled with helium gas at a pressure of 5.1 × 10<sup>5</sup> Pa and temperature 320 K. Assume that this sample of helium gas behaves as an ideal gas.</span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">A helium atom has a volume of 4.9 × 10<sup>-31</sup> m<sup>3</sup>.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">The molar mass of helium is 4.0 g mol<sup>-1</sup>. Show that the mass of a helium atom is 6.6 × 10<sup>-27</sup> kg.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Estimate the average speed of the helium atoms in the container.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Show that the number of helium atoms in the container is about 4 × 10<sup>20</sup>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Calculate the ratio <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{total volume of helium atoms}}}}{{{\text{volume of helium gas}}}}">
<mfrac>
<mrow>
<mrow>
<mtext>total volume of helium atoms</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>volume of helium gas</mtext>
</mrow>
</mrow>
</mfrac>
</math></span>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">di.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Explain, using your answer to (d)(i) and with reference to the kinetic model, why this sample of helium can be assumed to be an ideal gas.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">dii.</div>
</div>
<br><hr><br><div class="specification">
<p>A tube of constant circular cross-section, sealed at one end, contains an ideal gas trapped by a cylinder of mercury of length 0.035 m. The whole arrangement is in the Earth’s atmosphere. The density of mercury is 1.36 × 10<sup>4</sup> kg m<sup>–3</sup>.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">When the mercury is above the gas column the length of the gas column is 0.190 m.</p>
</div>
<div class="specification">
<p>The tube is slowly rotated until the gas column is above the mercury.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">The length of the gas column is now 0.208 m. The temperature of the trapped gas does not change during the process.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="text-align:left;">A solid cylinder of height <em>h</em> and density <em>ρ</em> rests on a flat surface.</p>
<p style="text-align:center;"><img src="data:image/png;base64,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"></p>
<p style="text-align:left;">Show that the pressure <em>p</em><sub>c</sub> exerted by the cylinder on the surface is given by <em>p</em><sub>c</sub> = <em>ρgh</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that (<em>p</em><sub>o</sub> + <em>p</em><sub>m</sub>) ×<sub> </sub>0.190 = <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{nRT}}{A}">
<mfrac>
<mrow>
<mi>n</mi>
<mi>R</mi>
<mi>T</mi>
</mrow>
<mi>A</mi>
</mfrac>
</math></span></span> where</p>
<p><em>p</em><sub>o</sub> = atmospheric pressure</p>
<p><em>p</em><sub>m</sub> = pressure due to the mercury column</p>
<p><em>T</em> = temperature of the trapped gas</p>
<p><em>n</em> = number of moles of the trapped gas</p>
<p><em>A</em> = cross-sectional area of the tube. </p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the atmospheric pressure. Give a suitable unit for your answer.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the gas particles in the tube hit the mercury surface less often after the tube has been rotated.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>A fixed mass of an ideal gas is contained in a cylinder closed with a frictionless piston. The volume of the gas is 2.5 × 10<sup>−3 </sup>m<sup>3</sup> when the temperature of the gas is 37 °C and the pressure of the gas is 4.0 × 10<sup>5 </sup>Pa.</p>
</div>
<div class="specification">
<p>Energy is now supplied to the gas and the piston moves to allow the gas to expand. The temperature is held constant.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the number of gas particles in the cylinder.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Discuss, for this process, the changes that occur in the density of the gas.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Discuss, for this process, the changes that occur in the internal energy of the gas.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">The air in a kitchen has pressure 1.0 × 10<sup>5</sup> Pa and temperature 22°C. A refrigerator of internal volume 0.36 m<sup>3</sup> is installed in the kitchen.</span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">The refrigerator door is closed. The air in the refrigerator is cooled to 5.0°C and the number of air molecules in the refrigerator stays the same.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">With the door open the air in the refrigerator is initially at the same temperature and pressure as the air in the kitchen. Calculate the number of molecules of air in the refrigerator.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Determine the pressure of the air inside the refrigerator.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">The door of the refrigerator has an area of 0.72 m<sup>2</sup>. Show that the minimum force needed to open the refrigerator door is about 4 kN.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Comment on the magnitude of the force in (b)(ii).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(iii).</div>
</div>
<br><hr><br>