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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>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mn>15</mn><mo>×</mo><mn>30</mn><mo>×</mo><mn>60</mn><mo>»</mo><mo>=</mo><mn>27000</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">J</mi><mo>»</mo></math> ✓</span></p>
<p> </p>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo>=</mo><mn>0</mn><mo>.</mo><mn>32</mn><mo>×</mo><mi>c</mi><mo>×</mo><mfenced><mrow><mn>290</mn><mo>-</mo><mn>250</mn></mrow></mfenced></math> <em><strong>OR </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2100</mn></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">J</mi><mo> </mo><msup><mi>kg</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo> </mo><msup><mi mathvariant="normal">K</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> <em><strong>OR</strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">J</mi><mo> </mo><msup><mi>kg</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo> </mo><msup><mo> </mo><mn>0</mn></msup><msup><mi mathvariant="normal">C</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> ✓</p>
<p><span class="fontstyle0"><em><br>Allow any appropriate unit that is</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>g</mi><mi>y</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>×</mo><mi>t</mi><mi>e</mi><mi>r</mi><mi>m</mi><mi>p</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>u</mi><mi>r</mi><mi>e</mi></mrow></mfrac></math></span></p>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">«intermolecular» bonds are formed during freezing </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0"><br>bond-forming process releases energy<br></span><span class="fontstyle3"><em><strong>OR</strong></em><br></span><span class="fontstyle4">«</span><span class="fontstyle0">intermolecular</span><span class="fontstyle4">» </span><span class="fontstyle0">PE decreases </span><span class="fontstyle4">«</span><span class="fontstyle0">and the difference is transferred as heat</span><span class="fontstyle4">» </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle2"><br></span><span class="fontstyle4">«</span><span class="fontstyle0">average random</span><span class="fontstyle4">» </span><span class="fontstyle0">KE of the molecules does not decrease/change </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle2"><br></span><span class="fontstyle0">temperature is related to «average» KE of the molecules «hence unchanged» </span><span class="fontstyle2">✓</span></p>
<p> </p>
<p><em><span class="fontstyle5">To award MP3 or MP4 molecules/particles/atoms must be mentioned.</span></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">mass of frozen oil <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mfrac><mrow><mn>27</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></mrow><mrow><mn>130</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></mrow></mfrac><mo>»</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>21</mn><mo> </mo><mo>«</mo><mi>kg</mi><mo>»</mo></math> </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">unfrozen mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>32</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>21</mn><mo>»</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>11</mn><mo> </mo><mo>«</mo><mi>kg</mi><mo>»</mo></math> </span><span class="fontstyle2">✓</span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<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,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"></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>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>E</em><sub>k</sub> = « <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>(</mo><mn>1</mn><mo>.</mo><mn>38</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>23</mn></mrow></msup><mo>)</mo><mo>(</mo><mn>373</mn><mo>)</mo></math>» = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>21</mn></mrow></msup></math> «J» <strong>✓</strong></p>
<p><em>v = </em>«<em><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mn>3</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>38</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>23</mn></mrow></msup><mo>×</mo><mn>6</mn><mo>.</mo><mn>02</mn><mo>×</mo><msup><mn>10</mn><mn>23</mn></msup><mo>×</mo><mn>373</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>018</mn></mrow></mfrac></msqrt></math></em>»<em> = </em>720 «m s<sup>−1</sup>» <strong>✓</strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>particles can be considered points «without dimensions» <strong>✓</strong></p>
<p>no intermolecular forces/no forces between particles «except during collisions»<strong>✓</strong></p>
<p>the volume of a particle is negligible compared to volume of gas <strong>✓</strong></p>
<p>collisions between particles are elastic <strong>✓</strong></p>
<p>time between particle collisions are greater than time of collision <strong>✓</strong></p>
<p>no intermolecular PE/no PE between particles <strong>✓</strong></p>
<p> </p>
<p><em>Accept reference to atoms/molecules for “particle”</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<em>mL = P</em> t» so «<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfrac><mrow><mn>1600</mn><mo>×</mo><mn>200</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>14</mn></mrow></mfrac></math>» = 2.3 x 10<sup>6</sup> «J kg<sup>-1</sup>» <strong>✓</strong></p>
<p>J kg<sup>−1 </sup><strong>✓</strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«all» of the energy added is used to increase the «intermolecular» potential energy of the particles/break «intermolecular» bonds/<strong>OWTTE</strong> <strong>✓</strong></p>
<p><em>Accept reference to atoms/molecules for “particle”</em> </p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of mcΔT <strong>✓</strong></p>
<p>0.86 × 4200 × (100 – <em>T</em>) = 0.3 × 1800 × (<em>T</em> +10) <strong>✓</strong></p>
<p><em>T</em><sub>eq</sub> = 85.69«°C» ≅ 86«°C» <strong>✓</strong></p>
<p><em>Accept T<sub>eq</sub> in Kelvin (359 K).</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mfrac><msup><mi>v</mi><mn>2</mn></msup><mi>R</mi></mfrac><mo> </mo><mi>so</mi><mo> </mo><mfrac><msup><mn>220</mn><mn>2</mn></msup><mn>1600</mn></mfrac><mo> </mo><mi>so</mi><mo> </mo><mi>R</mi><mo>=</mo><mn>30</mn><mo>.</mo><mn>25</mn></math> «Ω» <strong>✓</strong></p>
<p><em>Must see either the substituted values <strong>OR</strong> a value for R to at least three s.f.</em></p>
<p> </p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of parallel resistors addition so <em>R</em><sub>eq</sub> = 15 «Ω» <strong>✓</strong></p>
<p><em>P</em> = 3200 «W» <strong>✓</strong></p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<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,iVBORw0KGgoAAAANSUhEUgAAAd0AAADICAYAAACtUTvyAAARR0lEQVR4nO3df1TUdb7H8VezHa8Rl9Mtb1muNhMzUvgDL2XpylEq14317oJgdd3FxPJXaWoZWsrkDyxXzDAV0xUTks3TJgS2Xm+phV5LS5eN0PXigLB2Ney4Hs/cOej13Ib7B0MCAgkMnyF5Pv4qGL68BWae8/3Od76f62pqamoEAAA6nCXQAwAA0FUQXQAADCG6AAAYQnQBADCE6AIAYAjRBQDAkOsDPQC6FrvVFugRAJVVVgR6BHRRRBfG8YCHQOKJHwKJw8sAABhCdAEAMIToAgBgCNEFAMAQogsAgCFEFwAAQ4guAACGEF0AAAwhugAAGEJ0AQAwhOgCAGAI0QUAwBCiCwCAIUQXAABDiC4AAIYQXQAADCG6AAAYQnQBADCE6AIAYAjRBQDAEKILAIAhRBcAAEOILgAAhhBdAAAMIboAABhCdAEAMIToAgBgCNEFAMAQogsAgCFEFwAAQ4guAACGEF0AAAwhugAAGEJ0AQAwhOgCAGAI0QUAwBCiCwCAIUQXAABDiC4AAIYQXaDdLsqVlSh7+EIVur2Gvqdbrj0ZWrSlVN6AzQCgtYgu8GPkLtLbz65T8Xd1H+guR1KOyv66WNEh3K2Bzop7JwAAhhBdwG9O68sP39CUcJvsVpvs4ZO1ao9Lnvo38VapaEuKRlt9t4lJUXZho9vokqqK8rVq0tDa2zS+nbtQziETtbW6WiWLHlHf8IUqdFc3Orx8VoUpI2SPXa/CQ+/IGdOv+Zk8Ln2cPlkDrTbZrUM1Jf0dZafEcqga6ABEF/CX6s+0q9im5C/KVVZZqv3rrNr11IvKLDpf+3nvSRVMH6OkvT/V4oOlKqss15er7tanzzyhufknfa/NeuUp2qCnEnfoJ1Pf1/HKitptzbtBf0zybSskWqkHN2tcUJAGLPoPHW/pkHLxGq0oCNIT75U0P1PyE5p9dITeO1KussoPNeef/lMrc74y8AMDuh6iC/hL0Fglz/21HMEWSd3Uc/hYPRZRob1fnZFXXrn3bZJzZ6jmzEvSfT27SbIoOOw3em3dKO2fv0n73F5J53Q4b5u+jv+tJgzu6buDNt5WO2aKHKbIoP9qONPeIUpd8pjCgi2SQhSWlKrViX38/dMBIOn6QA8AXNv+V+Vl38ijW1S0u1DVQdG687Zu9T5vUXAvm0KrN2tP0bOKju6h6KV79ZXcchV+oE/OfyfpnA5vWKmtx6QBY9o5TvDtsjukgvozOSYqvGf9mYLVy967nd8IQFPY0wVMqn5bkwaGXn6t1mpT358vVsn3N/DKU5qjKeERiknK1OHzXkn/rIdXvSVnhHwBB/BjxZ4uYFLEQu18P0mO5p7uekuVO3eZDo5I176MON1Rdzt3oZyuammAqUEBdAT2dAEjblbkyGgFuYr116pL9T7uladojUZbE5Xtuih5vlGZSwp94B71rHfv9HrO6+8dNlOFTnnqv1Ls0amyr/3+3QAQXcAQi0KGP6XUEQflfPktHa66JMkrj2u7li/YLM2apQRHdymkvx6O76GSd7dpny/O3qoDynh5uT6qrre54Ntld/xD7X9Xe+Rp0zt76mYq1Iq07XJ5vJLccuWv0Yqck+375wJoEtEFTLH0UeyKt7U66r+1cEiY7NZQDYrdoVumZmrTrMEKliT10PAZr2nRvV9o0pAw2a02DUo5qJ8mvqaV9c8ottj0i+cSdGnRI+obPk255RfbMVOm5tyyQwn9Q2W3/kIrKv5FU2YN8cM/GEBj19XU1NQEegh0HXarTWWVFYEeAy26KFfWJCWUTdL+pdEKCfQ4fsbfIAKJPV2gy/LKXbhQA8OfVnap2/exS6o6lKUVaRf0ZPygay64QKARXaDLsihk+NPKerWvPh0T4XsLU5hGbbig0TkZmhl5U6AHBK45HF6GUV3v0F7todqY90e2/FahTskt154t+sPpkXp5fNg18wy96/0NojO5Vu5HAPztiuUDAbQX0QUAwBCiC7TLJVUV1Vs6zxorZ1ah7z2vzfNWHVJOSqzva/ppdEqWCl11JzP5TnCyjtOq/PpL/MXKueWQqtyNluJbfUBVDb7dD810Fcv+Nbl8IMv8Ae1FdIE2u6TT+fM0KvET3bpkT+0yfEdelX3/S0pI3q7TzTTKezpfMx6aqX23vqj9JypUVnlAr9s/18zYhSo4Xf9qVQe1dsNfZJv3Ye2yfFn3q8j5mKKGpOloVKq+rCzXlx9Ol9Y/ryXb65YGbMVMLS3715rlAwFcNe5FQFu5P9Ob8z9S6NwXNL1uGb7gfprw+jLF7k3Xm/vONvFFZ7VvXbo+ckxV8oyhvks9+pbTiy+Sc91ncn9/2z4aN+9ZxTpCdHlZviAN+P77WRTsGKxhDrf2Hz7h20NtxUwtLvsHoCOw4IGP3WoL9Aj4UfHKXfSJCqp7KNZ6S8Nnr8G3y+44q5W7jyg5utGVndxHtCfvpILirbqt4Repl723qtM+UdHcKEV26Ez9m/7yBsv+hV3T79Hl/m4OZ4o3RHR9+MNA25zU1qTB2trEZ4JaWBGoOmeiInOa+qLQev/TW/ZewcZm6iq4ryOQiC7QLsPk3JWpCY7uzXz+os5c8bEgDViUp9yk5t776q13iLkjZmrqsDcAE3hNF2gTi0IiH1RsULk+P/ptw9dAPYe0KiZSY7JKr3xt1LeKUPnnxxqdcXxeRekJssdmydXmF1TbOBMAY4gu0FYhP9PTrw7R/vmpyjhUVRszT6kKfrdUazVRzrGOJu5gPTT8mecUtXe5Fq2te6uPW678dDnfkGYsjGvfVavaNFMz/LJ8IID6iC7QZt10R9xi5a4bpm9fflh9rTbZ+ydpxy0T9cfNUxUZ3PTdy3LHr5VWsEzDvv2dou6yyW6NUMKfbtKUPH9c77htMzU9qJ+WDwTwPa69DACAIezpAgBgCNEFAMAQogsAgCFEFwAAQwJwcQzfot5poco8uFDRIZcaLvKtUmWPidfKARnavzT6Ki9F13ibPJeA/3DJwJZxhSd0rEaP78EuZY8Zp/wxW5WbFCa5spTw883qn5Wr1OgeAZjPK49rjzJzzmn0wsd/8C1/AYhudzmSclSW1Nm3CVzW3rDYrTa/xakzbYsnJOh4jR7fO937xc/pcPZSrS2ZqNFXcWt2CQEAMKQd0a1bCPs1FexaoynhttqFsGNSlFN0Wm7XrsuLb4dP1pq6q+PoolxZibJf9aLYXnlKczQlvKnFuus02qa7UM7wfhrz1h4d3pKi0dba2QZOWqOPXe27qi1q7d69O9AjADCouLhY586da/sG6h6X0/O0K32yBlptslv7aXTKOyqqOivXnssdGThpvQ5X1a0t3dpmuFWa9bQGNuhO07dzFWbJGdOvtlPWWDmzCuX6/tJrvsY1/r7uQjnDbRqYUii3zqowJUGTck5KxYsVc9cIOQtbvrZ5+/d0izfr93t7K/mLcpWd+FSZ95doUfwwRS0vV9TSvSqrLNaOuddr44Tl+qDBAt1XwytP6Tt6fkyGNDdTr8+sW3/0alSrZMlqFfzjeL1bWaGyE59qda/dmjIzW0Vcz67d3s/L07jHH5fL5Qr0KAAMqKyo0Nj4+HY+4a5WyRvZ2md7QZ9VVuj4wdUa/OdX9NiQX2nF0fu05EiFyo78SXOUrScX/7tOt/qh2q3SrHl6NE2a8/5KPVu3pnQzt0t45lPdumSPjldW6PjBF3Xr/pcU82hGKxrRQ9FLc5WZ2EeKWKidJ/b+4OvK7Y9u/YWwLT0V+eAgBWmY5sxL0n09u0kKkWPYAwqtLtLh463Zy/yuYXCT+qm1i5wFJT6n5Liw2q+rm+3Y5yr5prXxR2MZ69bpqcmTNXXyZP0hJ0cXLlwI9EgAOlBsXJw2bNyoTRs3avozz+jUqVNt2k79x2VLzwhF39tDipiq5Bm+nargUP0sKlTVe/+i463aQaof3OWaENbCabjuIuWkfamoV52a7guzpedQPfv6Mo3723qlbnN12EvHnfc13apdWjN7mT52TFXyE60P7pUsCu5lU6i+Vtkpjx8GxMiRI7UtL0/Hjh3T6JgYFRcXB3okAB3I4XBo67vvatSoURoxLEoF+fmd5An3JZ3ZvUbPL9qn0LmzNb6l4Mord9EnKqgO1QP9bm0YweDbZXdI5WXfqKMq0f6zlx029WrNRdSvUvXuD/TVv/1KD23foPTtD2ltXB8jzxA4G7PtEmLjlFuQr4iIiIDNwO/PvI76mZt6KxJ/M203Z/ZzemHePE17etpVfkWQQu23+2EnqrEqfZxzQo8m3q8daev1wajlir2jWzO3vaQzleWqbmFr1SWVOuPt7/cppU68iH1QYoa2Lh2iM3dPUsz8dH1wf0s/RP/hPYetc+HCBeXl5mpTZqZmzZ4d0ODW8ffvkAfllnXEfcbkz5z7fOsdOHBAC156STG//KUmJE0I9DiS+mhc1ialDv+77i6JlzN1hAZnxOmOJvfUuuk2a6iCVN7s1oIGWHWbRWrbAfSWdd7Dy5Kk7nKMnaUZd34k57rPxHnHnUtxcbGeTErSsWPHtC0vT7FxcYEeCUAHOnfunFIWLNDqVauU/sYbSp47VzfccEOgx7rM4lDCwmnqvTNdb+5r7ixii0IiH1RsULk+P/ptw9duPd+ozCXf3niwetl7+39Ev2/R34Lv1aRXpql3zhq9VXQ+0NPAZ0Vamp6bNUszZ8/W0lde0c033xzokQB0oN27d2tsfLzuuecevZWV1SmOal3JouDI8Uqd1UNbl29t/izkkEglzh2k/fNTlVH3tiLPUWU//5K23jlNzrEOWdRdocNGakD1R3on71jta7yeUhWkpWtrg2PT9eN8UR7P//3AhJ2eRcGDYjUl5rTWLtjC2306ib59+2rHzp0aOnRooEcBYMCNN96oDRs36reJiZ1r7/YKN2nQ4+M16m/r5dz452ZOiApRWNJy5a4bpm9fflh9rTbZ+89XWdQy7XxvuiJ95ylZHPFK2/QbKe1fNchqk/3RLfqf2JlaEBFUb1vdFfrIRCVeWqGYu+7V+G3NH7aWWMQe1xh/XiLRn9vsTJdu9Oe2OuLn3ZHbBQLtR7CnCwDAtaHTnr0MdCb+OJvWn2fkdtZtAWgZ0QV+AIc5AfgLh5cBADCE6AIAYAjRBQDAEKILAIAhRBcAAEOILgAAhhBdAAAMIboAABhCdAEAMIQrUvlwKTxzuMITAon7ulnc3xsiuj78YZjBAx46A+7vCBQOLwMAYAjRBQDAEKILAIAhRBcAAEOILgAAhhBdAAAMIboAABhCdAEAMIToAgBgCNEFAMAQogsAgCFEFwAAQ4guAACGEF0AAAwhugAAGEJ0AQAwhOgCAGAI0QUAwBCiCwCAIUQXAABDiC4AAIYQXQAADCG6AAAYQnQBADCE6AIAYAjRBQDAEKILAIAhRBcAAEOILgAAhhBdAAAMIboAABhCdAEAMIToAgBgCNEFAMAQogsAgCFEFwAAQ4guAACGEF0AAAwhugAAGEJ0AQAwhOgCAGAI0QUAwBCiCwCAIUQXAABDiC4AAIYQXQAADCG6AAAYQnQBADCE6AIAYAjRBQDAEKILAIAhRBcAAEOILgAAhhBdAAAMIboAABhCdAEAMIToAgBgCNEFAMAQogsAgCFEFwAAQ66rqampCfQQ6DrsVlugRwBUVlkR6BHQRRFdXFPsVhsPqNcAfo+4VnF4GQAAQ4guAACGEF0AAAwhugAAGEJ0AQAwhOgCAGAI0QUAwBCiCwCAIUQXAABDiC4AAIYQXQAADCG6AAAYQnQBADCE6AIAYAjRBQDAEKILAIAhRBcAAEOILgAAhhBdAAAMIboAABhCdAEAMIToAgBgCNEFAMAQogsAgCHX1dTU1AR6CAAAugL2dAEAMIToAgBgCNEFAMAQogsAgCFEFwAAQ4guAACG/D+rUuUzuD454AAAAABJRU5ErkJggg=="></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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rkbkXqgQKlwa9rQVzBd7wMXtITH4Ccw1k+Lkq0mHK+yK6Nq1bfxAw7vPSQq9ELfbq6ipgYuPqFYfeQ0jswdAqmkrqwnPsH7236G39gnMNijpSgRj/nQUAzyru12X8RnyxaK16Bi30HjiSGvxiHaNxeGWeKzUP5R8ELoa1HQe4stFXUGh46Bn/NrQERUjYbvUfnkX1h5tD+WyGeraxGODxEVshAZReKvmPUYkieMQ2z2cPls1mLJxa7p/yNOFMff9tlWzWfRV+EfvRWZiXpRU4/EzDzkRD+E/7HfVXEdZ41vICRsOc6P3STObk+L7Z4Pzx3Tnc6y6+Msmm6L9Tvs23QAGOiP7q5lb2ENXP3/jNHlSaU1vMPXi/fUCgw8swtGoxHGTQmYEPI6cpQa5bz7oqd8sJaIENCtNx7S1u1A2qq9K9oqt6FpC7cOrZSF2qu+jY4IGDkU2pL3MWnaImwyfvarA7HGOxybLUfw74HnsVnaN8YNMEwIRVyOQ5dUTaw/Iu/QD077TnC5H30fuhcwn8SZ8m3Uor1ra+W2eOx2buig3CYiupWGDypax7PegQgd2w8o+RJfHb8MXDiCveIPo/ah3ugmnZGJc0MfEQaOWPZi7pD29vvXSR3OoqtTtB/LZqQCI2YiPqynOLuVmig7y16GWR+ZlfH3+jmLpttgLcFPlioOqG1d0d4hH1jz0xEX3B/DwmZjy6mr0tEZ41b8A4HK+nId3NDO8ZPg1M6d1xKe+tnYnLwU0zvuwdSoZzDMV+c0H6SOrGeREfd/4TvsGczYclK00Rr3j5uL+EB3pcItlL0GzvtOtOPaXqTFkgIUXv51YYqISNLwQaWVG1zblj1MC7Rzu0e5LXTwx8gRnihJeRXTDBtgzCgb8rlddTiLrob1fB4OlWjh/UgPe9CRlZ1ll8BsPle+jfVxFk23QaPFPTpxMLxQiEuOx8LLRbh4TbktDU0seRNJ3wUj8Yu9WB09Fnr9KAzu9FtcUGpUq1I7auEK7yF6hM/9WO55TE+eg9Gn/4WoZ5fjM6l3sk6sKPpsJSYlnceIxP04vHoaRuv10A/WiX1ayyde3WsgThaKLooAo3WHW/nnnojo9t3ZvyQaHfQL1yM58QV03PEmosKGwtd5Pkgd1fosuhrWSwWwoJU4UWxbeecoZ9kl5wtxWSmiO0RzHwaO7uc0vGBF8fGDyC7vaLmCwvNFTkMTos6ZkzArS+X2mXC0/GAvDuKmT7CpxAuP9dWp9Oo1KbSMw0sTh4s35Ankna/qsyKex1ET9ilLlVlxubAAJfDGIz07VLzPi8+JIF7LoR/N7+DVSxri+QqHHT+rxafwVbY0JNQVneReUiKiX+fO/yVx8cYQfQTmbj8GS+4eJMcPx2nDFPnKg7rP9fgVZ9EKTTt36HBNnCheFn/OHShn2dqObhW9KHSHtMYDgU9gBD7EWws2y/M1rPl78PbMZchVagDtoOv5AJDz/7AlR7oC5TryTR9gwVsfigM0cO1iUUXgLKnczkJRByNiMHnw7Qw/NgDpCp2JAZUnohcfw/YtmYDvw+j9+7bo0LMf/HAYq5an4Zj8PL5A0rrt8nO9mQYuuj/AFwewYcshuYdQntS+4B2kyDunEEXlwzYFOHAqH4UnTiiXdJdpj8GTY8RrkIoZcR/KjykPJ70dD0OuL6Jn6eHNnEJE9UBdf0qk0BI+ERMD3VFyKA/nK/1hLFOIo1nVDeTU4Sy6GpqOXuglDfF8ccThD3PZ2boW3t6/l+et0J2l8QzBws1LEXR+njxfwytgEW4E6cXBt4wb/P/2FhJDS2HQPwidrisCZubC++/zES3NJXJ8f2n/iIdK31PamYGzQUuxeWEIPNXy6dDoEDJrJRKDzmDGMF/7VWa+o7Gh48swJk2EvzT/y/sZrEp9HQP3zcBw6XkMfQ83Bgx32B+ORFDxD8eSxKcAw+PwFe15BcTjqPckJEYPrOil6fAIXogJwjVRp/fItTha3ntlZ38N1mF6x43yY+q8AjDp7FAkGlfgZX83pRYR0a8kfYV+vTmXZovo0snWJyHb9ovNYkuL6GXr0ucdW/YvynpRei5tsq1Ll0BbQvYl240zabYXuv/BFjQzzfbtpRti/Q3bpaPJtgipLCHTdsl2xfbtmmdE/f62iDXfiOVrtnOZK8T6TuVtVH7Mn2zZCXqxTi/W/STaE/Wz19lmBv1BlHWydZ+5x/ZzpW04Yzv+7RnbaYdtku5zJi3K1r38McVWndtte0NqI2ixLVvazkqPWaaq50uNSn5detki0ixKwa3wNSMiUrs7es6o8RyBWesXlJ8V63Q6+A7fiI4z1yHp5f5wkSbHhr2D1Jhe2BcXJM78umLovy5hwOi+SgvOanMW3UKcKD6DmMCfRJ0AjEw67DSBt+wKixfRccNo5WxTOsteUH72WhsFBQW4cuWKskT16yIyYgdB12Miko5VDIUYl7yHndqhGBnQ0V5GRER3Pf5TwgayYsUKtGvXDuPGjVNKqD5Z803Y/MEyzDDsUOZhaOEbOgOvhY/GEOmLxWpF+kLBOv6jPiIialQMKg1E6lF5/HE9/v3vD9CpUyellIiIiOqC8/IbiLu7O6Kjp2HZsmVKCREREdUVg0oDCgoKwvHjx7F//36lhIiIiOqCQz8N7Ouvv0ZU1EvYvn0H2rRpo5QSERFRbbBHpYH16dMHAwcOQmpqqlJCREREtcUelUYgTaz18+uNzz//khNriYiI6oA9Ko1AmlibmLiUE2uJiIjqiEGlkXBiLRERUd0xqDQSaSJtbGwsFi1axG+sJSIiqiUGlUYkTazt1q0bduzYoZQQERFRTTiZtpGVTazNyTkoz10hIiKi6qk6qEj/zp7qn8VyWrlF9Ovxc1r/+BklqqD6oPLhh/9RlpqOa9euYd68uQgNDZOHghrTU089wT+CVK+a6uf0TuFnlKgyzlG5A1q1aiWHlJSUZDm0EBERUdUYVO4QqSdF+vK3zMwvlRIiIiJyxqByB40d+zSWLl2CoqIipYSIiIgcMajcQa6uroiIiMSGDR8oJUREROSIQeUOe/TRITh06JD8rbVERERUGYPKHSZNrH3hhYmcWEtERFQFBhUVePDBBzmxloiIqAoMKirx+OOjObGWiIjICYOKStx7772cWEtEROSEQUVFyibWnj79vVJCRETUvDGoqEjZxNp3331XKSEiImreGFRUpmxi7X//+5lSQkRE1HwxqKiQNLF248aNnFhLRETNHoOKCkkTa0eNGoWPP/5YKSEiImqeGFRUSppY+8UXn3NiLRERNWsMKirFibVEREQMKqrGibVERNTcMaio3IgRIzixloiImi0GFZXr3LkLnnzySf7DQiIiapYYVO4Cf/rTYPlKICIiouaGQYWIiBrZ9zBG9obOLwGmUqWIqBoMKkRE1Mi6QL/6ICw50+DfQikiqgaDChEREakWgwoREdWjUuQbp0CnC4dhUyIie3QWt8VPcCxSTPmwynWchn7yjYjU9Ua4IQWJkQH2+rpRiE3JQr79DjJrfhZSYkcp6zujR2Qi0s28IrKpY1AhIqIGsBuG2FwMMubCkpeJ5ICDiNVPwmJTobLeWQE+MSzBwUFrkGs5iczkh5EdOw7hi7NQLK0uzsLi8HGYd/4xpGaelNtc4bkL40PegPHsdbkFapoYVIiIqAF4YsT8mQjzcRVHGk8MeTUO0b65WJWag+r6QLQjZiI+rCdc0BIeQ6ZgXrQvcld9jANFl2H+aBEMuf0wfXo4+nu0tLcZ8wpCkYoZy/ZX2ybd/RhUiIioAXjjkZ4dKg4yLvej70P3omSrCcervNJHC+9HesCj/A6u6Na3F7QlX+Kr49/h8N5DgPtD6H1/a2W94PoA+g90r6FNagoYVIiIqAHcA7d2jpf0tIZre61yuyqt0MGtrcNBSYO2rm6iVLhRgsIL14CCBOi7KnNe5J8/ImpngVybmi4GFSIiagRXUXSxRLldG1ZcLiqE/J3cv9XCrYOILH5zkJ53GhaL0w8vc27SGFSIiKgB5CDrqMPE2aJvsGtTHrSP+aNblaGiAPuyTjjMNSmAadcnKNE+jL7d7kPPQb1Ek7uw78RVZb1gPYakEB/oQpJgdrg6iJoWBhUiImoAeUh5KxFG6fJh61lkLHwHKRiD+ZMHwFWp4awk5R0sMB5DMa4jP2Ml3kq5jhHzIzHYtS0eCHwCI7SfYsGCJGTlX5euVUbW0rexIMcX0bP08ObRrMniS0tERA3AE4EP/YyVw3yh8wrApLPDsWbzbOg9Wyrrb6YN9EXpyhD46roiYNIpBK1Zj4V6nXyg0njqsXxPGmZ23IoxAV1Fm/0wZpsHZhpX4GV/N3sD1CT9xiYot1VHmixF9U8a0yWqL/yc1r+7+zMqfeHbVAREmRFtTEW0v4tSXgPpC98CpuBA9Gbx4w9ONyFHqg4qRER0t2FQofrFHhUiIpVRW4/KlStX0KZNG2UJOHPmDObMmYOtWz9GevoeeHt7K2skDCpUv9ijQkREN1mwYAF+/vlnrFuXLC/n5ByEu7u7fFsKLqdPn0bnzp0rBRiihsCgQkTUDBmNRpw7dw7ff/899u3bi9Wr36vUM7J//37ce++9DCN0xzGoEBE1QV9//TVOnTpVHkbGjx9fKYhIQcXFRYv77vPC7373u/LeEiK1YVAhIroLSfNELl++jMOHD6O4uBhdu3bFgAEDlLXAihUr0K5dOxFGXNCzZ0+GEbprMagQEalUQUEBfvzxR3z3XZ7c8+HYIyIFEamnxNfXVw4jgwcPZhChJolBhYjoDioLI1LvSJ8+fZRS+2TWbdu2YuDAQejSpQv+8pe/OF1dQ9Q8MKgQETUw6SoZKZB06tRJKQF2796F558fL98eNy4MAQEB0Ov18jIRVWBQISJqQNIQzfz5czFv3lsikIxTSu09KdLVNLyihqhmDCpERESkWg30TwmlbyacAp0uCAZTsf1bB3Wd4WcwiTVO64iIiIiq0UBBpQU89Ethseyo3dcnExEREVWhgYIKERER0a9Xi6DyPYyRvaELjsX7hgj00HWW/1lgj8iVyDIfRnp5mQ+CY40wF1vFfeo2vGPNT0dcsI94jDnIyL+ulFJNpK+3lq4kICIiaspq36OS+xE2/vQM9uRZkGt8FfftnIMxw8bjg99GiLKTyEwOBVKm45WPzJCiSq0VH0by6zOQhFAkJ72KIR4tlRVUkwsXLiA4OEgOLERERE1V7YOK9im8FjMUHhoNXPyCMNZPK8qCMS78EVHWEh6DRiDIvQQ5e4/ggnKXWyo6iKSp4xF3OoQhpY6k71uQ/onYokWLMHPmTPlSRyIioqam9kGllRtc2yrVNW3h1qEVMNAf3V1r30Rlh2EIexJxO1si9LWJDCm3QfqWyo0bN8pfFPX443r5n4wRERE1JbX4HhVpjspjiDoQDuOBafBv4VCGeGSu1sNDKio1wdAvRPwsFWUjAeNUBESZEW1MRbTnbkQGTMGB6M3ipzcuyuvEQVXrA99Op5HbYjKMH02Bv0vVoUeaE0O1k5NzkP/vg4iImg4pqNTMYkuL6GXr0ucdW/YvSlFZWUSa7ZxSYvsl25bQp5NS9ovtXNpkW5cugbaE7Es2sWCL6NLJ1ichW6wpWzfQNnPPedul7MW2oC5/sI1ac9R2Q2mKau/bb7+1PfHEE7YZM2bYfvzxR6WUiIioabjdcZt6oEV717Zw8dNj4oj/g5wFy7H5LK/4qS3pih/pq7kjIyMwdepUzJs3jz0pRETU5NzBoKLQ6BASNxMjkIoZ8dtwtk6XDDVfs2fPRlFREbZv34EBAwYopURERE3LnQ8qgsZzCCZM6I+SbWvxYU6hUko1kXpQpk+fzn9oRkRETRr/KSERERGplip6VIiIiIiqwqBCREREqsWgQkRERKrFoEJERESqxaBCREREqsWgQkRERKrFoEJERESqxaBCREREqsWgQkRERKrFoEJERESqxaBCREREqqXq//Wj03VWbhERNR8Wy2nlFhHxnxISERGRarFHpRni2RrVJ35O6x8/o0QVVB9UPvzwP8oS1YennnqCfwSpXvFzWr/4GSWqjJNpiYiISLUYVIiIiEi1GFSIiIhItRhUiIiISLUYVIiIiEi1GFSIiIhItRhUiIiISLUYVIiIiEi1GFSIiIhItRhUiIiISLUYVIiIiEi1GFSIiIhItRhUiIiISLUYVIiIiEi1GFSIiIhItRhUiIiISLUYVIiIiEi1GFSIiIhItRhUiIiISLUYVIiIiEi1GFSIiIhItRhUiIiISLUYVOgudx35pvWIDfaBTtdZ/ukRmQCjKR9WpcbNSpFvnFJev+InCAZTsVJHsObDlBKL4LL1PSKQmFVTu0REVN8YVOjuVrQfS56NR/ZDC5Cea4ElLxMrPPcgSv8Kks1XlUrOCnE0Kwfwm4P0vNOwWMp+diDa36W8jmnxJDz7aXcsVtpNfuICFo6ZhMWmQqUOERE1NAYVuotZUWT6BJtK+mFseDC8XcTbWeOJwaFj4IdD2Hv4B6WeE+uPyDv0A7S9vNCxmk+A1WzELMMPGD3uf+GjtDsk5hWEarOw9tOTKFXqERFRw2JQobvYZRz/6kuUaB+AV8eWSpl4U9/fG0PdC7Av6wSKlLJKis/BbG6Fgf0fgKtSVNlVnNi3CznaP2O4v7tSJrgOwdwjp5ET7Y8WSlHFMNIoxL7/T0T2cBwmOoZj6YkVZcFxMJqr3CIiIqoGgwrdxa6i6GIJ0MoNrm0d3soaLe7RaVFyvlBEmZuVHjdha0lrlG6JQY+y+SfBsUgpn9dSiks/XRTttkThN6scgoZjHWdfIWXjNYzbcxKW3DRE37cXC8cMg/6DlnhBlOVlrkU4PkTUK5tg5iQXIqJaY1Chu9gVFJ6voodC0xZuHVopC86u4tTBbBSIWy0GxSFLnptiQe7i7vj02bL5Jz/BcvgcULASM96HHDQslpPIfK0N1uurm6PihdDXJmKIR0vApRdGju0nl40e91f0F2Uaj4ehD/ICcg7g8AUOHBER1RaDCjUzreEdvl4Ej0ysDu8J+9RZDVx8hmDkwBMwzDJW9Hhox2B+/PNy0ABawmPwExjrl4tVqTlVDClp0d61tXK7Bdq53SN++6F/dzd7ERER3RYGFbqLtYFbxypmmVgvo/DCNWWhjiwFuGRV2m11H3QdKua+lPXUlGw14Tg7RYiIGgWDCt3FWsO1vRa4Voiiyw4TP6wl+MlSAm1HN7RViurGBZ2871NuV0Hnjnb85BARNYrf2ATltupIExip/knfGdI0WFGUMQsPh53A9PT3EO5tH3qxmpOgHzYfiN8MY7iPUxq/iIxYPcI2/RnJX87CEFdlrfUYkvQhWNDrX/hy7mCginYr1xmiXDEkXfUzFQFRZkQbU5XvYSkrAxIzF0HvIV0jVAyTYQz0Bm+HsqaBn9P613Q+o0T1QAoqRHetn/fYZnbvZOsekWw7eumGzXbpqC1t5khbl+5RtrQz15RKjm7YLmUvtgV16W+LWPON7ZJcds12bs9sW5DjfW58Z0t7ob+t+wtptjOiWfFAtm/T3qhcR/aL7VzaZFuXLoG2hGx7axVlk21p535Ryi7ZshMCncqIiOhW2IFNdzfXAXhp/QKMPj0Hw3110PkOQ1R2b8xdPwMhnvb5JaWmBPjpeiPS+L1Y0sDFfyKSjDPRc+94+MqXJ3fF0HWu+Pvm2dAr94FGB/3C9Vjq8zGGeUl1fBGypX3lOkRE1OBUPfRDjaOgoADu7g5fbEZUDb5XiKixsUelGbty5QrWrVuHxx/XKyVE1ZNCip9fbxiNRqWEiKjhMag0U19//TWCg4Nw5swZbN++Qyklqp7Uk5KTcxCZmZl48sknYTablTVERA2HQz/NjHRW/O677yI7Oxtz586Ft7e3soao9nbv3oXZs2fjb3+bgDFjxqBNmzbKGiKi+sWg0szwUlKqb489NgorVqxQloiI6heDSjMjddfHxsaiW7duiImJ4cRIui3SkOGcOXPk26+//jo6deok3yYiqm+co9LMSEM9a9euha+vrzyJVurCJ6otaQK2NJn2mWeexpgxo+WeFIYUImpI7FFpxhzPitl1T7cihZTnnnuOvXFE1KgYVEgeDuKkWroVKahIk7HZg0JEjYlBhYiIiFSLc1SIiIhItRhUiIiISLUYVIiIiEi1GFSIiIhItRhUiIiISLUYVIiIiEilgP8PKscAbPcBwG0AAAAASUVORK5CYII="></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>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>energy required for milk entering in 1 s = mass x specific heat x 73 ✓</p>
<p>16 kW <em><strong>OR</strong> </em>16000 W ✓</p>
<p> </p>
<p><em><strong>MP1</strong> is for substitution into mcΔT regardless of power of ten.</em></p>
<p><em>Allow any correct unit of power (such as </em>J s<sup>-1</sup><em> OR </em>kJ s<sup>-1</sup><em>) if paired with an answer to the correct power of 10 for <strong>MP2</strong>.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Underestimate / more energy or power required ✓</p>
<p>because energy transferred as heat / thermal energy is lost «to surroundings or electrical components» ✓</p>
<p> </p>
<p><em>Do not allow general term “energy” or “power” for <strong>MP2</strong>.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the temperature has increased so the internal energy / « average » KE «of the molecules» has increased <em><strong>OR</strong></em> temperature is proportional to average KE «of the molecules». ✓</p>
<p>«therefore» the «average» speed of the molecules or particles is higher <em><strong>OR</strong> </em>more frequent collisions « between molecules » <em><strong>OR</strong> </em>spacing between molecules has increased <em><strong>OR</strong> </em>average force of collisions is higher <em><strong>OR</strong> </em>intermolecular forces are less <em><strong>OR</strong> </em>intermolecular bonds break and reform at a higher rate <em><strong>OR</strong> </em>molecules are vibrating faster. ✓</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>conduction/conducting/conductor «through metal» ✓</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>e</mi><mi>σ</mi><mi>A</mi><msup><mi>T</mi><mn>4</mn></msup></math> where <em>T</em> = 357 K ✓</p>
<p>use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mn>2</mn><mi>π</mi><mo> </mo><mi>r</mi><mo> </mo><mi>l</mi></math> « = 0.236 m<sup>2</sup>» ✓</p>
<p><em>P</em> = 87 «W» ✓</p>
<p> </p>
<p><em>Allow 85 – 89 W for <strong>MP3</strong>.</em></p>
<p><em>Allow ECF for <strong>MP3</strong>.</em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>convection «is likely to be a significant loss» ✓</p>
<p><br>«due to reduction in density of air near pipe surface» hot air rises «and is replaced by cooler air from elsewhere»</p>
<p><em><strong>OR</strong></em></p>
<p>«due to» conduction «of heat or thermal energy» from pipe to air ✓</p>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Most candidates recognized that this was a specific heat question and set up a proper calculation, but many struggled to match their answer to an appropriate unit. A common mistake was to leave the answer in some form of an energy unit and others did not match the power of ten of the unit to their answer (e.g. 16 W).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates recognized that this was an underestimate of the total energy but failed to provide an adequate reason. Many gave generic responses (such as "some power will be lost"/not 100% efficient) without discussing the specific form of energy lost (e.g. heat energy).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was generally well answered. Most HL candidates linked the increase in temperature to the increase in the kinetic energy of the molecules and were able to come up with a consequence of this change (such as the molecules moving faster). SL candidates tended to focus more on consequences, often neglecting to mention the change in KE.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates recognized that heat transfer by conduction was the correct response. This was a "state" question, so candidates were not required to go beyond this.</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Candidates at both levels were able to recognize that this was a blackbody radiation question. One common mistake candidates made was not calculating the area of a cylinder properly. It is important to remind candidates that they are expected to know how to calculate areas and volumes for basic geometric shapes. Other common errors included the use of T in Celsius and neglecting to raise T ^4. Examiners awarded a large number of ECF marks for candidates who clearly showed work but made these fundamental errors.</p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>A few candidates recognized that convection was the third source of heat loss, although few managed to describe the mechanism of convection properly for MP2. Some candidates did not read the question carefully and instead wrote about methods to increase the rate of heat loss (such as removing more insulation or decreasing the temperature of the environment).</p>
<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>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>mention of atoms/molecules/particles</p>
<p>sum/total of kinetic energy and «mutual/intermolecular» potential energy</p>
<p><em>Do not allow “kinetic energy and potential energy” bald.<br>Do not allow “sum of average ke and pe” unless clearly referring to total ensemble.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>i<br>«intermolecular» potential energy/PE of an ideal gas is zero/negligible</p>
<p><br>ii<br><strong>THIS IS FOR USE WITH AN ENGLISH SCRIPT ONLY</strong><br>use of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T = \frac{{PV}}{{nR}}">
<mi>T</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>P</mi>
<mi>V</mi>
</mrow>
<mrow>
<mi>n</mi>
<mi>R</mi>
</mrow>
</mfrac>
</math></span> <em><strong>or</strong></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T = \frac{{1.4 \times 21}}{{0.46 \times 8.31}}">
<mi>T</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>1.4</mn>
<mo>×</mo>
<mn>21</mn>
</mrow>
<mrow>
<mn>0.46</mn>
<mo>×</mo>
<mn>8.31</mn>
</mrow>
</mfrac>
</math></span></p>
<p><em>Award mark for correct re-arrangement as shown here not for quotation of Data Booklet version.</em><br><em>Award <strong>[2]</strong> for a bald correct answer in K.</em><br><em>Award <strong>[2 max]</strong> if correct 7.7 K seen followed by –265°C and mark BOD. However, if only –265°C seen, award <strong>[1 max]</strong>.</em><br><br>7.7 K<br><em>Do not penalise use of “°K”</em></p>
<p>ii<br><strong>THIS IS FOR USE WITH A SPANISH SCRIPT ONLY</strong><br><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T = \frac{{PV}}{{nR}}">
<mi>T</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>P</mi>
<mi>V</mi>
</mrow>
<mrow>
<mi>n</mi>
<mi>R</mi>
</mrow>
</mfrac>
</math></span></p>
<p><br><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T = \frac{{1.4 \times 2.1 \times {{10}^{ - 6}}}}{{0.46 \times 8.31}}">
<mi>T</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>1.4</mn>
<mo>×</mo>
<mn>2.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>0.46</mn>
<mo>×</mo>
<mn>8.31</mn>
</mrow>
</mfrac>
</math></span></p>
<p>T = 7.7 ×10<sup>-6</sup> K<br><em>Award mark for correct re-arrangement as shown here not for quotation of Data Booklet version.</em><br><em>Uses correct unit conversion for volume</em><br><em>Award <strong>[2]</strong> for a bald correct answer in K. Finds solution. Allow an ECF from MP2 if unit not converted, ie candidate uses 21 m3 and obtains 7.7 K</em><br><em>Do not penalise use of “°K”</em></p>
<p> </p>
<p>iii<br>models used to predict/hypothesize</p>
<p>explain</p>
<p>simulate</p>
<p>simplify/approximate <br><em>Allow similar responses which have equivalent meanings. Response needs to identify <strong>one</strong> reason.</em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<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 src="data:image/png;base64,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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>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«<em>v</em> = <em>c</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{sin }}i}}{{{\text{sin }}r}}">
<mfrac>
<mrow>
<mrow>
<mtext>sin </mtext>
</mrow>
<mi>i</mi>
</mrow>
<mrow>
<mrow>
<mtext>sin </mtext>
</mrow>
<mi>r</mi>
</mrow>
</mfrac>
</math></span> =» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{3 \times {{10}^8} \times {\text{sin}}\left( {33} \right)}}{{{\text{sin}}\left( {46} \right)}}">
<mfrac>
<mrow>
<mn>3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>8</mn>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<mtext>sin</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>33</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>sin</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>46</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>2.3 x 10<sup>8</sup> «m s<sup>–1</sup>»</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>light strikes AB at an angle of 57°</p>
<p>critical angle is «sin<sup>–1</sup><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{{2.3}}{3}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>2.3</mn>
</mrow>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> =» 50.1°</p>
<p><em>49.2° from unrounded value</em></p>
<p>angle of incidence is greater than critical angle so total internal reflection</p>
<p><strong><em>OR</em></strong></p>
<p>light strikes AB at an angle of 57°</p>
<p>calculation showing sin of “refracted angle” = 1.1</p>
<p>statement that since 1.1>1 the angle does not exist and the light does not emerge</p>
<p><strong><em>[Max 3 marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>total internal reflection shown</p>
<p>ray emerges at opposite face to incidence</p>
<p><em>Judge angle of incidence=angle of reflection by eye or accept correctly labelled angles</em></p>
<p><em>With sensible refraction in correct direction</em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>mass = «<em>volume</em> x <em>density</em>» (0.75)<sup>3</sup> x 920 «= 388 kg»</p>
<p>energy required to raise temperature = 388 x 2100 x 20 «= 1.63 x 10<sup>7</sup> J»</p>
<p>energy required to melt = 388 x 330 x 10<sup>3</sup> «= 1.28 x 10<sup>8</sup> J»</p>
<p>1.4 x 10<sup>8</sup> «J» <em><strong>OR</strong> </em>1.4 x 10<sup>5</sup> «kJ»</p>
<p><em>Accept any consistent units </em></p>
<p><em>Award <strong>[3 max]</strong> for answer which uses density as 1000 kg<sup>–3</sup> (1.5× 10<sup>8</sup> «J»)</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>in solid state, nearest neighbour molecules cannot exchange places/have fixed positions/are closer to each other/have regular pattern/have stronger forces of attraction</p>
<p>in liquid, bonds between molecules can be broken and re-form</p>
<p><em>OWTTE</em></p>
<p><em>Accept converse argument for liquids</em></p>
<p><strong><em>[Max 1 Mark]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<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>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>222 <em><strong>AND</strong> </em>4</p>
<p> </p>
<p><em>Both needed.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>alpha particles highly ionizing<br><em><strong>OR</strong></em><br>alpha particles have a low penetration power<br><em><strong>OR</strong></em><br>thin glass increases probability of alpha crossing glass<br><em><strong>OR</strong></em><br>decreases probability of alpha striking atom/nucleus/molecule</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>conversion of temperature to 291 K</p>
<p><em>p</em> = 4.5 x 10<sup>–9</sup> x 8.31 x «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2.91}}{{1.3 \times {{10}^{ - 5}}}}">
<mfrac>
<mrow>
<mn>2.91</mn>
</mrow>
<mrow>
<mn>1.3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>5</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span>»</p>
<p><em><strong>OR</strong></em></p>
<p><em>p</em> = 2.7 x 10<sup>15</sup> x 1.38 x 10<sup>–23</sup> x «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2.91}}{{1.3 \times {{10}^{ - 5}}}}">
<mfrac>
<mrow>
<mn>2.91</mn>
</mrow>
<mrow>
<mn>1.3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>5</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span>»</p>
<p>0.83 or 0.84 «Pa»</p>
<p> </p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>electron/atom drops from high energy state/level to low state</p>
<p>energy levels are discrete</p>
<p>wavelength/frequency of photon is related to energy change <em><strong>or</strong> </em>quotes <em>E</em> = <em>hf <strong>or</strong> E</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{hc}}{\lambda }">
<mfrac>
<mrow>
<mi>h</mi>
<mi>c</mi>
</mrow>
<mi>λ</mi>
</mfrac>
</math></span></p>
<p>and is therefore also discrete</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>peer review guarantees the validity of the work<br><em><strong>OR</strong></em><br>means that readers have confidence in the validity of work</p>
<p> </p>
<p><em>OWTTE</em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<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>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{3.0 \times 8.31 \times 290}}{{0.15}}">
<mfrac>
<mrow>
<mn>3.0</mn>
<mo>×</mo>
<mn>8.31</mn>
<mo>×</mo>
<mn>290</mn>
</mrow>
<mrow>
<mn>0.15</mn>
</mrow>
</mfrac>
</math></span><strong>»</strong></p>
<p>48 <strong>«</strong>kPa<strong>»</strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>mass = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{860}}{{3100 \times 23}}">
<mfrac>
<mrow>
<mn>860</mn>
</mrow>
<mrow>
<mn>3100</mn>
<mo>×</mo>
<mn>23</mn>
</mrow>
</mfrac>
</math></span><strong>»</strong> 0.012 <strong>«</strong>kg<strong>»</strong></p>
<p> </p>
<p><em>Award </em><strong><em>[1] </em></strong><em>for a bald correct answer.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{2}">
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</math></span> 1.38 × 10<sup>–23</sup> × 313 = 6.5 × 10<sup>–21</sup> <strong>«</strong>J<strong>»</strong></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>larger temperature implies larger (average) speed/larger (average) KE of molecules/particles/atoms</p>
<p>increased force/momentum transferred to walls (per collision) / more frequent collisions with walls</p>
<p>increased force leads to increased pressure because P = F/A (as area remains constant)</p>
<p> </p>
<p><em>Ignore any mention of PV = nRT.</em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<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 src="data:image/png;base64,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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>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}{v^2} = 0.24\,{\text{gh}}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mn>0.24</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>gh</mtext>
</mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = 11.9">
<mi>v</mi>
<mo>=</mo>
<mn>11.9</mn>
</math></span> «m s<sup>–1</sup>»</p>
<p> </p>
<p><em>Award GPE lost = 65 × 9.81 × 30 = «19130 J»</em></p>
<p><em>Must see the 11.9 value for MP2, not simply 12.</em></p>
<p><em>Allow g = 9.8 ms<sup>–2</sup>.</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>internal energy is the total KE «and PE» of the molecules/particles/atoms in an object</p>
<p>temperature is a measure of the average KE of the molecules/particles/atoms</p>
<p> </p>
<p><em>Award <strong>[1 max]</strong> if there is no mention of molecules/particles/atoms.</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>arrow vertically downwards from dot labelled weight/W/mg/gravitational force/F<sub>g</sub>/F<sub>gravitational</sub> <strong><em>AND</em></strong> arrow vertically upwards from dot labelled reaction force/R/normal contact force/N/F<sub>N</sub></p>
<p>W > R</p>
<p> </p>
<p><em>Do not allow gravity.</em><br><em>Do not award MP1 if additional ‘centripetal’ force arrow is added.</em><br><em>Arrows must connect to dot.</em><br><em>Ignore any horizontal arrow labelled friction.</em><br><em>Judge by eye for MP2. Arrows do not have to be correctly labelled or connect to dot for MP2.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em><br>recognition that centripetal force is required / <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{m{v^2}}}{r}">
<mfrac>
<mrow>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>r</mi>
</mfrac>
</math></span> seen</p>
<p>= 468 «N»</p>
<p>W/640 N (weight) is larger than the centripetal force required, so the skier does not lose contact with the ground</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>recognition that centripetal acceleration is required / <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{v^2}}}{r}">
<mfrac>
<mrow>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>r</mi>
</mfrac>
</math></span> seen</p>
<p>a = 7.2 «ms<sup>–2</sup>»</p>
<p><em>g</em> is larger than the centripetal acceleration required, so the skier does not lose contact with the ground</p>
<p> </p>
<p><em><strong>ALTERNATIVE 3</strong></em></p>
<p>recognition that to lose contact with the ground centripetal force ≥ weight</p>
<p>calculation that v ≥ 14 «ms<sup>–1</sup>»</p>
<p>comment that 12 «ms<sup>–1</sup>» is less than 14 «ms<sup>–1</sup>» so the skier does not lose contact with the ground</p>
<p> </p>
<p><em><strong>ALTERNATIVE 4</strong></em></p>
<p>recognition that centripetal force is required / <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{m{v^2}}}{r}">
<mfrac>
<mrow>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>r</mi>
</mfrac>
</math></span> seen</p>
<p>calculation that reaction force = 172 «N»</p>
<p>reaction force > 0 so the skier does not lose contact with the ground</p>
<p> </p>
<p> </p>
<p><em>Do not award a mark for the bald statement that the skier does not lose contact with the ground.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em><br>0 = 8.2<sup>2 </sup>+ 2 × <em>a</em> × 24 therefore <em>a</em> = «−»1.40 «m s<sup>−2</sup>»</p>
<p>friction force = <em>ma </em>= 65 × 1.4 = 91 «N»</p>
<p>coefficient of friction = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{91}}{{65 \times 9.81}}">
<mfrac>
<mrow>
<mn>91</mn>
</mrow>
<mrow>
<mn>65</mn>
<mo>×</mo>
<mn>9.81</mn>
</mrow>
</mfrac>
</math></span> = 0.14</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em><br><em>KE</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span><em>mv</em><sup>2</sup> = 0.5 x 65 x 8.2<sup>2</sup> = 2185 «J»</p>
<p>friction force = KE/distance = 2185/24 = 91 «N»</p>
<p>coefficient of friction = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{91}}{{65 \times 9.81}}">
<mfrac>
<mrow>
<mn>91</mn>
</mrow>
<mrow>
<mn>65</mn>
<mo>×</mo>
<mn>9.81</mn>
</mrow>
</mfrac>
</math></span> = 0.14</p>
<p> </p>
<p><em>Allow ECF from MP1.</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«76 × 9.6»= 730<br>Ns <em><strong>OR</strong></em> kg ms<sup>–1</sup></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>safety net extends stopping time</p>
<p><em>F</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\Delta p}}{{\Delta t}}">
<mfrac>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>p</mi>
</mrow>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>t</mi>
</mrow>
</mfrac>
</math></span> therefore <em>F</em> is smaller «with safety net»</p>
<p><em><strong>OR</strong></em></p>
<p>force is proportional to rate of change of momentum therefore <em>F</em> is smaller «with safety net»</p>
<p> </p>
<p><em>Accept reverse argument.</em></p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<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>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>a gas in which there are no intermolecular forces</p>
<p><strong><em>OR</em></strong></p>
<p>a gas that obeys the ideal gas law/all gas laws at all pressures, volumes and temperatures</p>
<p><strong><em>OR</em></strong></p>
<p>molecules have zero PE/only KE</p>
<p> </p>
<p><em>Accept atoms/particles.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>N</em> = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{pV}}{{kT}} = \frac{{5.3 \times {{10}^5} \times 2.1 \times {{10}^{ - 4}}}}{{1.38 \times {{10}^{ - 23}} \times 310}}">
<mfrac>
<mrow>
<mi>p</mi>
<mi>V</mi>
</mrow>
<mrow>
<mi>k</mi>
<mi>T</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>5.3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>5</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>2.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>4</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>1.38</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>23</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>310</mn>
</mrow>
</mfrac>
</math></span><strong>»</strong> 2.6 × 10<sup>22</sup></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>«</strong>For one atom <em>U</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{2}">
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</math></span><em>kT</em><strong>»</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{2}">
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</math></span> × 1.38 × 10<sup>–23</sup> × 310 / 6.4 × 10<sup>–21</sup> <strong>«</strong>J<strong>»</strong></p>
<p><em>U = </em><strong>«</strong>2.6 × 10<sup>22</sup> × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{2}">
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</math></span> × 1.38 × 10<sup>–23</sup> × 310<strong>»</strong> 170 <strong>«</strong>J<strong>»</strong></p>
<p> </p>
<p> <em>Allow ECF from (a)(ii)</em></p>
<p><em>Award </em><strong><em>[2] </em></strong><em>for a bald correct answer</em></p>
<p><em>Allow use of U</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{2}">
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</math></span><em>pV</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>p</em><sub>2</sub> = <strong>«</strong>5.3 × 10<sup>5</sup> × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2.1 \times {{10}^{ - 4}}}}{{6.8 \times {{10}^{ - 4}}}}">
<mfrac>
<mrow>
<mn>2.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>4</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>6.8</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>4</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span><strong>»</strong> 1.6 × 10<sup>5</sup> <strong>«</strong>Pa<strong>»</strong></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>«</strong>volume has increased and<strong>» </strong>average velocity/KE remains unchanged</p>
<p><strong>«</strong>so<strong>» </strong>molecules collide with the walls less frequently/longer time between collisions with the walls</p>
<p><strong>«</strong>hence<strong>» </strong>rate of change of momentum at wall has decreased</p>
<p><strong>«</strong>and so pressure has decreased<strong>»</strong></p>
<p> </p>
<p><em>The idea of average must be included</em></p>
<p><em>Decrease in number of collisions is not sufficient for MP2. Time must be included.</em></p>
<p><em>Accept atoms/particles.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<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>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>Internal energy is the sum of all the PEs and KEs of the molecules (of the oxygen) ✔</p>
<p>PE of molecules in gaseous state is zero ✔</p>
<p>(At boiling point) average KE of molecules in gas and liquid is the same ✔</p>
<p>gases have a higher internal energy ✔</p>
<p> </p>
<p><em>Molecules/particles/atoms must be included once, if not, award <strong>[1 max]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1:</strong></em></p>
<p>flow rate of oxygen = 8 «g s<sup>−1</sup>» ✔</p>
<p>«2.1 ×10<sup>5</sup> × 8 × 10<sup>−3</sup>» = 1.7 «kW» ✔</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2:</strong></em></p>
<p><em>Q</em> = «0.25 × 32 ×10<sup>−3</sup> × 2.1 × 10<sup>5</sup> =» 1680 «J» ✔</p>
<p>power = «1680 W =» 1.7 «kW» ✔</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>V</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{nRT}}{p} = ">
<mfrac>
<mrow>
<mi>n</mi>
<mi>R</mi>
<mi>T</mi>
</mrow>
<mi>p</mi>
</mfrac>
<mo>=</mo>
</math></span>» 4.9 × 10<sup>−3</sup> «m<sup>3</sup>»</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>ideal gas has point objects ✔</p>
<p>no intermolecular forces ✔</p>
<p>non liquefaction ✔</p>
<p>ideal gas assumes monatomic particles ✔</p>
<p>the collisions between particles are elastic ✔</p>
<p> </p>
<p><em>Allow the opposite statements if they are clearly made about oxygen eg oxygen/this can be liquified</em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<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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"></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>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«He behaves as ideal gas if» <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>∝</mo><mi>T</mi></math> «at constant V» <strong>✓</strong></p>
<p>uses two points to show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>∝</mo><mi>T</mi></math> <strong>✓</strong></p>
<p><em><strong><br>MP1</strong> can also be described as <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>p</mi><mi>T</mi></mfrac><mo>=</mo><mi>k</mi><mo> </mo><mtext mathvariant="bold-italic">OR </mtext><mfrac><mi>p</mi><mi>T</mi></mfrac><mtext>=</mtext><mfrac><mrow><mi>n</mi><mi>R</mi></mrow><mi>V</mi></mfrac></math></em></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>100</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow><mrow><mn>250</mn><mo>×</mo><mn>8</mn><mo>.</mo><mn>31</mn></mrow></mfrac><mo>=</mo><mo>«</mo><mn>0</mn><mo>.</mo><mn>048</mn><mo> </mo><mtext>mol</mtext><mo>»</mo></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mn>0</mn><mo>.</mo><mn>048</mn><mo>×</mo><mn>4</mn><mo>=</mo><mo>»</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>19</mn><mo> </mo><mo>«</mo><mtext>g</mtext><mo>»</mo></math> ✓</p>
<p><em><br>Allow any correct data point to be used. </em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizes that pressure will double <strong>✓</strong></p>
<p>graph will be steeper <em><strong>OR</strong></em> gradient will be larger <strong>✓</strong></p>
<p>graph will still go through the origin <strong>✓</strong></p>
<p><em><strong><br>MP1</strong> can be expressed as e.g.“<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>∝</mo><mi>n</mi></math>” <strong>OR</strong> “<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>n</mi><mi>R</mi></mrow><mi>V</mi></mfrac></math>will double”.</em></p>
<p><em>Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>v</mi><mo>=</mo><mn>2</mn><mi>n</mi><mi>R</mi><mi>T</mi></math> for <strong>MP1</strong>.</em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<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 src="data:image/png;base64,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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>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the total «random» kinetic energy of the molecules/atoms/particles ✓</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mo>«</mo><mfrac><mrow><mi>n</mi><mi>R</mi><mi>T</mi></mrow><mi>V</mi></mfrac><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>24</mn><mo>×</mo><mn>8</mn><mo>.</mo><mn>31</mn><mo>×</mo><mn>300</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>20</mn></mrow></mfrac><mo>=</mo><mo>»</mo><mn>3</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo> </mo></math>«Pa» ✓</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img 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"></p>
<p>straight line joining (300, 3) and (500, 5) ✓</p>
<p>drawn only in the range from 300 to 500 K ✓</p>
<p> </p>
<p><em>Allow <strong>ECF</strong> from <strong>(b)(i)</strong> for incorrect initial pressure. </em><br><em>Allow tolerance of ± one grid square for the endpoints.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>temperature is the same for both gases ✓</p>
<p>«average» kinetic energy is the same «because <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi>k</mi></msub><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mi>k</mi><mi>T</mi></math> <em><strong>OR </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi>k</mi></msub></math> depends on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> only» ✓</p>
<p><br><em>Award <strong>[1 max]</strong> for a bald statement that kinetic energy is the same.</em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<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>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m = \frac{{4.0 \times {{10}^{ - 3}}}}{{6.02 \times {{10}^{23}}}}">
<mi>m</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>4.0</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>6.02</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>23</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span>«kg»</span><em><span style="background-color:#ffffff;"><br></span></em></p>
<p><em><span style="background-color:#ffffff;"><strong>OR</strong><br></span></em></p>
<p><span style="background-color:#ffffff;">6.64 <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">×</span> 10<span style="font-size:14px;"><sup><span style="text-align:left;color:#000000;text-indent:0px;letter-spacing:normal;font-family:Verdana , Arial , Helvetica , sans-serif;font-variant:normal;font-weight:400;text-decoration:none;display:inline !important;white-space:normal;float:none;background-color:#ffffff;">−27 </span></sup></span></span><span style="background-color:#ffffff;">«kg»</span><em><span style="background-color:#ffffff;"> ✔</span></em></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}m{v^2} = \frac{3}{2}kT/v = \sqrt {\frac{{3kT}}{m}} /\sqrt {\frac{{3 \times 1.38 \times {{10}^{ - 23}} \times 320}}{{6.6 \times {{10}^{ - 27}}}}} ">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
<mi>k</mi>
<mi>T</mi>
<mrow>
<mo>/</mo>
</mrow>
<mi>v</mi>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mn>3</mn>
<mi>k</mi>
<mi>T</mi>
</mrow>
<mi>m</mi>
</mfrac>
</msqrt>
<mrow>
<mo>/</mo>
</mrow>
<msqrt>
<mfrac>
<mrow>
<mn>3</mn>
<mo>×</mo>
<mn>1.38</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>23</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>320</mn>
</mrow>
<mrow>
<mn>6.6</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>27</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</msqrt>
</math></span> <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></p>
<p><span style="background-color:#ffffff;"><em>v</em> = 1.4 <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">×</span> 10<sup>3</sup> «<span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">ms</span><sup><span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">−</span><span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">1</span></sup>» ✔</span> </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N = \frac{{pV}}{{kT}}/\frac{{5.1 \times {{10}^5} \times 3.2 \times {{10}^{ - 6}}}}{{1.38 \times {{10}^{ - 23}} \times 320}}">
<mi>N</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>p</mi>
<mi>V</mi>
</mrow>
<mrow>
<mi>k</mi>
<mi>T</mi>
</mrow>
</mfrac>
<mrow>
<mo>/</mo>
</mrow>
<mfrac>
<mrow>
<mn>5.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>5</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>3.2</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>1.38</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>23</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>320</mn>
</mrow>
</mfrac>
</math></span></span></p>
<p><em><strong>OR</strong></em></p>
<p><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N = \frac{{pV{N_A}}}{{RT}}/\frac{{5.1 \times {{10}^5} \times 3.2 \times {{10}^{ - 6}} \times 6.02 \times {{10}^{23}}}}{{8.31 \times 320}}">
<mi>N</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>p</mi>
<mi>V</mi>
<mrow>
<msub>
<mi>N</mi>
<mi>A</mi>
</msub>
</mrow>
</mrow>
<mrow>
<mi>R</mi>
<mi>T</mi>
</mrow>
</mfrac>
<mrow>
<mo>/</mo>
</mrow>
<mfrac>
<mrow>
<mn>5.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>5</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>3.2</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>6.02</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>23</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>8.31</mn>
<mo>×</mo>
<mn>320</mn>
</mrow>
</mfrac>
</math></span> <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></p>
<p><span style="background-color:#ffffff;"><em>N</em> = 3.7 <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">× </span>10<sup>20</sup> ✔</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4 \times {{10}^{20}} \times 4.9 \times {{10}^{ - 31}}}}{{3.2 \times {{10}^{ - 6}}}} =» 6 \times {10^{ - 5}}">
<mfrac>
<mrow>
<mn>4</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>20</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>4.9</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>31</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>3.2</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mrow>
<mo>»</mo>
</mrow>
<mn>6</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>5</mn>
</mrow>
</msup>
</mrow>
</math></span> ✔</span></p>
<div class="question_part_label">di.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;">«For an ideal gas» the size of the particles is small compared to the distance between them/size of the container/gas<br></span></p>
<p><span style="background-color:#ffffff;"><em><strong>OR</strong></em><br></span></p>
<p><span style="background-color:#ffffff;">«For an ideal gas» the volume of the particles is negligible/the volume of the particles is small compared to the volume of the container/gas<br></span></p>
<p><span style="background-color:#ffffff;"><em><strong>OR</strong></em><br></span></p>
<p><span style="background-color:#ffffff;">«For an ideal gas» particles are assumed to be point objects ✔<br></span></p>
<p><span style="background-color:#ffffff;">calculation/ratio/result in (d)(i) shows that volume of helium atoms is negligible compared to/much smaller than volume of helium gas/container «hence assumption is justified» ✔</span></p>
<div class="question_part_label">dii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>The mark was awarded for a clear substitution or an answer to at least 3sf. Many gained the mark for a clear substitution with a conversion from g to kg somewhere in their response. Fewer gave the answer to the correct number of sf.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>At HL this was very well answered but at SL many just worked out E=3/2kT and left it as a value for KE.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Again at HL this was very well answered with the most common approach being to calculate the number of moles and then multiply by N<sub>A</sub> to calculate the number of atoms. At SL many candidates calculated n but stopped there. Also at SL there was some evidence of candidates working backwards and magically producing a value for ‘n’ that gave a result very close to that required after multiplying by N<sub>A</sub>.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was well answered with the most common mistake being to use the volume of a single atom rather than the total volume of the atoms.</p>
<div class="question_part_label">di.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In general this was poorly answered at SL. Many other non-related gas properties given such as no / negligible intermolecular forces, low pressure, high temperature. Some candidates interpreted the ratio as meaning it is a low density gas. At HL candidates seemed more able to focus on the key part feature of the question, which was the nature of the volumes involved. Examiners were looking for an assumption of the kinetic theory related to the volume of the atoms/gas and then a link to the ratio calculated in ci). The command terms were slightly different at SL and HL, giving slightly more guidance at SL.</p>
<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>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>weight of cylinder = <em>Ahg ρ </em> ✔</p>
<p>pressure = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{F}{A}">
<mfrac>
<mi>F</mi>
<mi>A</mi>
</mfrac>
</math></span> = <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{Ahg\rho }}{A}">
<mfrac>
<mrow>
<mi>A</mi>
<mi>h</mi>
<mi>g</mi>
<mi>ρ</mi>
</mrow>
<mi>A</mi>
</mfrac>
</math></span></span> ✔</p>
<p><em>Allow use of A = </em><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi {r^2}">
<mi>π</mi>
<mrow>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span></span><em> in MP1</em>. </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of PV = nRT and V = Area × (0.190) seen ✔</p>
<p>substitution of P = <em>p</em><sub>o</sub> + <em>p</em><sub>m</sub> «re-arrangement to give answer»✔</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognition that <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{nRT}}}}{{\text{A}}}">
<mfrac>
<mrow>
<mrow>
<mtext>nRT</mtext>
</mrow>
</mrow>
<mrow>
<mtext>A</mtext>
</mrow>
</mfrac>
</math></span></span> is constant <em><strong>OR</strong></em> 190<em>p<span style="font-size:11.6667px;"><sub>o</sub></span> </em>+ 190<em>p<sub>m</sub> = </em>208<em>p</em><sub>o</sub> − 208<em>p</em><sub>m</sub></p>
<p><em><strong>OR</strong></em> <em>p</em><sub>o</sub> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{398}{18}">
<mfrac>
<mn>398</mn>
<mn>18</mn>
</mfrac>
</math></span> <em>p</em><sub>m</sub> ✔</p>
<p>pressure due to mercury <em>p</em><sub>m</sub> = 0.035 × 1.36 × 10<sup>4</sup> × 9.81(= 4.67 × 10<sup>3</sup> Pa) ✔</p>
<p>1.03 × 10<sup>5</sup> ✔</p>
<p>Pa <em><strong>OR</strong></em> Nm<sup>-2</sup> <em><strong>OR</strong></em> kgm<sup>-1</sup>s<sup>-2</sup> ✔</p>
<p><em>Do not award for a bald correct answer. Working must be shown to award MP3.</em></p>
<p><em>Award MP4 for any correct unit of pressure (eg “mm of mercury / Hg”)</em>.</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>same number of particles to collide with a larger surface area <em><strong>OR</strong></em> greater volume with constant rms speed decreases collision frequency ✔</p>
<p><em>Look for a correct statement that connects pressure to molecular movement/collisions</em>.</p>
<div class="question_part_label">b.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This question was fairly well answered with a not insignificant number of candidates making clearly wrong substitutions (such as F=mgh) to make the equation work out. As a “show that” question the derivation should be neatly laid out with the fundamental equations written out and the substitutions/cancelations clearly shown.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was generally well answered. Most candidates took the time to show the set up and substitutions they used to derive the given expression. A small number of candidates attempted to “show that” by making unit substitutions - this is not acceptable for a question like this.</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was left blank by many candidates. Of those who attempted a solution, few appreciated the difference made to the derived equation from 4bi when the tube was rotated. It should be noted that this was also the “unit question” on this exam, and a candidate could have been awarded a mark for clearly writing <span style="text-decoration:underline;">any</span> correct unit of pressure without doing any calculations. Candidates should be reminded to keep an eye out for this opportunity and to at least write a unit even if the question seems unapproachable.</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was generally poorly answered with the candidates split between answers that generally demonstrated some good understanding of physics (such as connecting the increase in volume AND constant rms speed of particles with the rate of collisions with the mercury) and answers that did not (such as gases want to rise so the gas it will hit the mercury less).</p>
<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>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>Correct conversion of T «T = 310 K» seen ✓</p>
<p>« use of = <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mfrac><mrow><mi>p</mi><mi>V</mi></mrow><mrow><mi>k</mi><mi>T</mi></mrow></mfrac></math> to get » 2.3 × 10<sup>23</sup> ✓</p>
<p> </p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong> i.e., T in Celsius (Result is 2.7 x 10<sup>24</sup>)</em></p>
<p><em>Allow use of n, R and N<sub>A</sub></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>density decreases ✓</p>
<p>volume is increased <em><strong>AND</strong> </em>mass/number of particles remains constant ✓</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>internal energy is constant ✓</p>
<p><br>internal energy depends on kinetic energy/temperature «only»</p>
<p><em><strong>OR</strong></em></p>
<p>since temperature/kinetic energy is constant ✓</p>
<p> </p>
<p><em>Do not award <strong>MP2</strong> for stating that “temperature is constant” unless linked to the correct conclusion, as that is mentioned in the stem.</em></p>
<p><em>Award <strong>MP2</strong> for stating that kinetic energy remains constant.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>a) This was well answered with the majority converting to K. Quite a few found the number of moles but did not then convert to molecules.</p>
<p>bi) Well answered. It was pleasing to see how many recognised the need to state that the mass/number of molecules stayed the same as well as stating that the volume increased. At SL this recognition was less common so only 1 mark was often awarded.</p>
<p>bii) This was less successfully answered. A surprising number of candidates said that the internal energy of an ideal gas increases during an isothermal expansion. Many recognised that constant temp meant constant KE but then went on to state that the PE must increase and so the internal energy would increase.<br><br></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<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>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mfrac><mrow><mi>p</mi><mi>V</mi></mrow><mrow><mi>k</mi><mi>T</mi></mrow></mfrac></math> <em><strong>OR</strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup><mo>×</mo><mn>0</mn><mo>.</mo><mn>36</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>38</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>23</mn></mrow></msup><mo>×</mo><mn>295</mn></mrow></mfrac></math> ✔</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mn>8</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mn>24</mn></msup></math> ✔</p>
<p><em>NOTE: Allow <strong>[1 max]</strong> for substitution with T in Celsius.</em><br><em>Allow <strong>[1 max]</strong> for a final answer of n = 14.7 or 15</em><br><em>Award <strong>[2]</strong> for bald correct answer.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>p</mi><mi>T</mi></mfrac></math> = constant <em><strong>OR </strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mrow><mi>n</mi><mi>R</mi><mi>T</mi></mrow><mi>V</mi></mfrac></math> <em><strong>OR </strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>N</mi><mi>k</mi><mi>T</mi></mrow><mi>V</mi></mfrac></math> ✔<br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mn>9</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>4</mn></msup></math>« Pa »✔</span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Allow ECF from (a) <br>Award <strong>[2]</strong> for bald correct answer</span></em></p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mi>A</mi><mo>×</mo><mo>∆</mo><mi>p</mi></math> <span style="background-color: #ffffff;">✔</span></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>72</mn><mo>×</mo><mfenced><mrow><mn>1</mn><mo>.</mo><mn>0</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>94</mn></mrow></mfenced><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup><mo> </mo></math><em><strong>OR </strong></em>4.3 × 10<sup>3</sup> « N »✔</p>
<p><em>NOTE: <span style="background-color: #ffffff;">Allow ECF from (b)(i)<br>Allow ECF from MP1</span></em></p>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">force is «very» large ✔</span></p>
<p><span style="background-color: #ffffff;">there must be a mechanism that makes this force smaller<br><em><strong>OR</strong></em><br>assumption used to calculate the force/pressure is unrealistic ✔</span></p>
<div class="question_part_label">b(iii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(iii).</div>
</div>
<br><hr><br>