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</div><h2>SL Paper 3</h2><div class="specification">
<p>An ideal nuclear power plant can be modelled as a heat engine that operates between a hot temperature of 612°C and a cold temperature of 349°C.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the Carnot efficiency of the nuclear power plant.</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>Explain, with a reason, why a real nuclear power plant operating between the stated temperatures cannot reach the efficiency calculated in (a).</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>The nuclear power plant works at 71.0% of the Carnot efficiency. The power produced is 1.33 GW. Calculate how much waste thermal energy is released per hour.</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>Discuss the production of waste heat by the power plant with reference to the first law and the second law of thermodynamics.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>correct conversion to K «622 K cold, 885 K hot»</p>
<p>\({\eta _{{\rm{Carnot}}}} = 1 - \frac{{{T_{{\rm{cold}}}}}}{{{T_{{\rm{hot}}}}}} = 1 - \frac{{622}}{{885}} = 0.297\) <em><strong>or</strong></em> 29.7%</p>
<p><em>Award <strong>[1 max]</strong> if temperatures are not converted to K, giving result 0.430.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the Carnot efficiency is the maximum possible</p>
<p>the Carnot cycle is theoretical/reversible/impossible/infinitely slow</p>
<p>energy losses to surroundings «friction, electrical losses, heat losses, sound energy»</p>
<p><em>OWTTE</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.71 × 0.297 = 0.211</p>
<p><em>Allow solution utilizing wasted power «78.9%».</em></p>
<p>1.33/0.211 × 0.789 = 4.97 «GW»</p>
<p>4.97 GW × 3600 = 1.79 × 10<sup>13</sup> «J» </p>
<p>Award <strong>[2 max]</strong> if 71% used as the overall efficiency giving an answer of 1.96 × 10<sup>12</sup> J.</p>
<p><em>Award <strong>[3]</strong> for bald correct answer.<br></em></p>
<p><em>Watch for ECF from (a).</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Law 1: net thermal energy flow is <em>Q</em><sub>IN</sub>–<em>Q</em><sub>OUT</sub></p>
<p><em>Q</em><sub>OUT</sub><em> refers to “waste heat”</em> </p>
<p>Law 1: <em>Q</em><sub>IN</sub>–<em>Q</em><sub>OUT</sub> = ∆<em>Q</em>=∆<em>W</em> as ∆<em>U</em> is zero</p>
<p>Law 2: does not forbid <em>Q</em><sub>OUT</sub>=0</p>
<p>Law 2: no power plant can cover 100% of <em>Q</em><sub>IN</sub> into work</p>
<p>Law 2: total entropy must increase so some <em>Q</em> must enter surroundings </p>
<p><em>OWTTE</em></p>
<div class="question_part_label">d.</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>
<br><hr><br><div class="specification">
<p>A wheel of mass 0.25 kg consists of a cylinder mounted on a central shaft. The shaft has a radius of 1.2 cm and the cylinder has a radius of 4.0 cm. The shaft rests on two rails with the cylinder able to spin freely between the rails.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-12_om_16.44.54.png" alt="M18/4/PHYSI/SP3/ENG/TZ2/06"></p>
</div>
<div class="specification">
<p>The stationary wheel is released from rest and rolls down a slope with the shaft rolling on the rails without slipping from point A to point B.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-12_om_16.47.09.png" alt="M18/4/PHYSI/SP3/ENG/TZ2/06.a"></p>
</div>
<div class="specification">
<p>The wheel leaves the rails at point B and travels along the flat track to point C. For a short time the wheel slips and a frictional force <em>F </em>exists on the edge of the wheel as shown.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-12_om_16.49.45.png" alt="M18/4/PHYSI/SP3/ENG/TZ2/06.b"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The moment of inertia of the wheel is 1.3 × 10<sup>–4</sup> kg m<sup>2</sup>. Outline what is meant by the moment of inertia.</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>In moving from point A to point B, the centre of mass of the wheel falls through a vertical distance of 0.36 m. Show that the translational speed of the wheel is about 1 m s<sup>–1</sup> after its displacement.</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>Determine the angular velocity of the wheel at B.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the effect of <em>F </em>on the linear speed of the wheel.</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>Describe the effect of <em>F </em>on the angular speed of the wheel.</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>an object’s resistance to change in rotational motion</p>
<p><strong><em>OR</em></strong></p>
<p>equivalent of mass in rotational equations</p>
<p> </p>
<p><em>OWTTE</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>ΔKE + Δrotational KE = ΔGPE</p>
<p><strong><em>OR</em></strong></p>
<p>\(\frac{1}{2}\)<em>mv</em><sup>2</sup> + \(\frac{1}{2}\)<em>I</em>\(\frac{{{v^2}}}{{{r^2}}}\) = <em>mgh</em></p>
<p> </p>
<p>\(\frac{1}{2}\) × 0.250 × <em>v</em><sup>2</sup> + \(\frac{1}{2}\) × 1.3 × 10<sup>–4</sup> × \(\frac{{{v^2}}}{{1.44 \times {{10}^{ - 4}}}}\) = 0.250 × 9.81 × 0.36</p>
<p><em>v</em> = 1.2 <strong>«</strong><span class="Apple-converted-space">m s<sup>–1</sup></span><strong>»</strong></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>ω</em> <strong>«</strong><span class="Apple-converted-space">= \(\frac{{1.2}}{{0.012}}\)</span><strong>»</strong> = 100 <strong>«</strong><span class="Apple-converted-space">rad s<sup>–1</sup></span><strong>»</strong></p>
<p><strong><em>[1 mark]</em><br></strong></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>force in direction of motion</p>
<p>so linear speed increases</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>force gives rise to anticlockwise/opposing torque on</p>
<p>wheel ✓ so angular speed decreases ✓</p>
<p> </p>
<p><em>OWTTE</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>A constant force of 50.0 N is applied tangentially to the outer edge of a merry-go-round. The following diagram shows the view from above.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-11_om_06.31.00.png" alt="M18/4/PHYSI/SP3/ENG/TZ1/06"></p>
<p>The merry-go-round has a moment of inertia of 450 kg m<sup>2</sup> about a vertical axis. The merry-go-round has a diameter of 4.00 m.</p>
</div>
<div class="specification">
<p>The merry-go-round starts from rest and the force is applied for one complete revolution.</p>
</div>
<div class="specification">
<p>A child of mass 30.0 kg is now placed onto the edge of the merry-go-round. No external torque acts on the system.</p>
</div>
<div class="specification">
<p>The child now moves towards the centre.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the angular acceleration of the merry-go-round is 0.2 rad s<sup>–2</sup>.</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, for the merry-go-round after one revolution, the angular speed.<span class="Apple-converted-space"> </span></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, for the merry-go-round after one revolution, the angular momentum.</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>Calculate the new angular speed of the rotating system.</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>Explain why the angular speed will increase.</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>Calculate the work done by the child in moving from the edge to the centre.</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>Γ<strong> «</strong>= <em>Fr</em> = 50 × 2<strong>»</strong> = 100 <strong>«</strong>Nm<strong>»</strong></p>
<p>α <strong>«</strong> \( = \frac{\Gamma }{I} = \frac{{100}}{{450}}\) <strong>»</strong> =0.22 <strong>«</strong>rads<sup>–2</sup><strong>»</strong></p>
<p> </p>
<p><em>Final value to at least 2 sig figs, </em><strong><em>OR </em></strong><em>clear working with substitution required for mark.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>«</strong>\(\omega _t^2 - \omega _0^2 = 2\alpha \Delta \theta \)<strong>»</strong></p>
<p><strong>«</strong>\(\omega _t^2 - 0 = 2 \times 0.22 \times 2\pi \)<strong>»</strong></p>
<p>\({\omega _t} = 1.7\) <strong>«</strong>rads<sup>–1</sup><strong>»</strong></p>
<p> </p>
<p><em>Accept BCA, values in the range: 1.57 to 1.70.</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><strong>«</strong><em>L</em> = <em>Iω = </em>450 × 1.66<strong>»</strong></p>
<p>= 750 <strong>«</strong>kgm<sup>2</sup> rads<sup>–1</sup><strong>»</strong></p>
<p> </p>
<p><em>Accept BCA, values in the range: 710 to 780.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>«</strong><em>I</em> = 450 + <em>mr</em><sup>2</sup><strong>»</strong></p>
<p><em>I</em><strong> «</strong>= 450 + 30 × 2<sup>2</sup><strong>»</strong> = 570 <strong>«</strong>kgm<sup>2</sup><strong>»</strong></p>
<p><strong>«</strong><em>L</em> = 570 × <em>ω</em> = 747<strong>»</strong></p>
<p><em>ω</em> = 1.3 <strong>«</strong>rads<sup>–1</sup><strong>»</strong></p>
<p> </p>
<p><em>Watch for ECF from (a) and (b).</em></p>
<p><em>Accept BCA, values in the range: 1.25 to 1.35.</em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>moment of inertia will decrease</p>
<p>angular momentum will be constant <strong>«</strong>as the system is isolated<strong>»</strong></p>
<p><strong>«</strong>so the angular speed will increase<strong>»</strong></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>ω<sub>t</sub></em> = 1.66 from bi <strong><em>AND</em></strong> <em>W</em> = ΔE<sub><em>k</em></sub></p>
<p><em>W</em> = \(\frac{1}{2}\) × 450 × 1.66<sup>2</sup> – \(\frac{1}{2}\) × 570 × 1.31<sup>2</sup> = 131 <strong>«</strong>J<strong>»</strong></p>
<p> </p>
<p><em>ECF from 8bi</em></p>
<p><em>Accept BCA, value depends on the answers in previous questions.</em></p>
<p><em><strong>[2 marks]</strong></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.</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>A cylinder is fitted with a piston. A fixed mass of an ideal gas fills the space above the piston.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-12_om_16.52.30.png" alt="M18/4/PHYSI/SP3/ENG/TZ2/07._01"></p>
<p>The gas expands isobarically. The following data are available.</p>
<p style="text-align: center;">\[\begin{array}{*{20}{l}} {{\text{Amount of gas}}}&{ = 243{\text{ mol}}} \\ {{\text{Initial volume of gas}}}&{ = 47.1{\text{ }}{{\text{m}}^3}} \\ {{\text{Initial temperature of gas}}}&{ = -12.0{\text{ °C}}} \\ {{\text{Final temperature of gas}}}&{ = + 19.0{\text{ °C}}} \\ {{\text{Initial pressure of gas}}}&{ = 11.2{\text{ kPa}}} \end{array}\]</p>
</div>
<div class="specification">
<p>The gas returns to its original state by an adiabatic compression followed by cooling at constant volume.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the final volume of the gas is about 53 m<sup>3</sup>.</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 J, the work done by the gas during this expansion.</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>Determine the thermal energy which enters the gas during this expansion.</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>Sketch, on the <em>pV </em>diagram, the complete cycle of changes for the gas, labelling the changes clearly. The expansion shown in (a) and (b) is drawn for you.</p>
<p><img src="data:image/png;base64,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"></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>Outline the change in entropy of the gas during the cooling at constant volume.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>There are various equivalent versions of the second law of thermodynamics. Outline the benefit gained by having alternative forms of a law.</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><strong><em>ALTERNATIVE 1</em></strong></p>
<p><strong>«</strong>Using \(\frac{{{V_1}}}{{{T_1}}} = \frac{{{V_2}}}{{{T_2}}}\)<strong>»</strong></p>
<p><em>V</em><sub>2</sub> = \(\frac{{47.1 \times (273 + 19)}}{{(273 - 12)}}\)</p>
<p><em>V</em><sub>2</sub> = 52.7 <strong>«</strong><span class="Apple-converted-space">m<sup>3</sup></span><strong>»</strong></p>
<p> </p>
<p><strong><em>ALTERNATIVE 2</em></strong></p>
<p><strong>«</strong>Using <em>PV</em> = <em>nRT</em><strong>»</strong></p>
<p><em>V</em> = \(\frac{{243 \times 8.31 \times (273 + 19)}}{{11.2 \times {{10}^3}}}\)</p>
<p><em>V</em> = 52.6 <strong>«</strong><span class="Apple-converted-space">m<sup>3</sup></span><strong>»</strong></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>W</em> <strong>«</strong><span class="Apple-converted-space">= <em>P</em>Δ<em>V</em></span><strong>»</strong> = 11.2 × 10<sup>3</sup> × (52.7 – 47.1)</p>
<p><em>W</em> = 62.7 × 10<sup>3</sup> <strong>«</strong><span class="Apple-converted-space">J</span><strong>»</strong></p>
<p> </p>
<p><em>Accept 66.1 × 10<sup>3</sup> J if 53 used</em></p>
<p><em>Accept 61.6 × 10<sup>3</sup> J if 52.6 used</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Δ<em>U</em> <strong>«</strong><span class="Apple-converted-space">= \(\frac{3}{2}\)<em>nR</em>Δ<em>T</em></span><strong>»</strong> = 1.5 × 243 × 8.31 × (19 – (–12)) = 9.39 × 10<sup>4</sup></p>
<p><em>Q</em> <strong>«</strong><span class="Apple-converted-space">= Δ<em>U</em> + <em>W</em><strong>»</strong> = 9.39 × 10<sup>4</sup> + 6.27 × 10<sup>4</sup></span></p>
<p><em>Q</em> = 1.57 × 10<sup>5</sup> <strong>«</strong><span class="Apple-converted-space">J</span><strong>»</strong></p>
<p> </p>
<p><em>Accept 1.60 × 10<sup>5</sup> if 66.1 × 10<sup>3</sup> J used</em></p>
<p><em>Accept 1.55 × 10<sup>5</sup> if 61.6 × 10<sup>3</sup> J used</em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>concave curve from RHS of present line to point above LHS of present line</p>
<p>vertical line from previous curve to the beginning</p>
<p> </p>
<p><img src="images/Schermafbeelding_2018-08-13_om_08.30.16.png" alt="M18/4/PHYSI/SP3/ENG/TZ2/07.d.i/M"></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>energy is removed from the gas and so entropy decreases</p>
<p><strong><em>OR</em></strong></p>
<p>temperature decreases <strong>«</strong>at constant volume (less disorder)<strong>» </strong>so entropy decreases</p>
<p> </p>
<p><em>OWTTE</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>different paradigms/ways of thinking/modelling/views</p>
<p>allows testing in different ways</p>
<p>laws can be applied different situations</p>
<p> </p>
<p><em>OWTTE</em></p>
<p><strong><em>[1 mark]</em></strong></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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</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>The <em>P–V</em> diagram of the Carnot cycle for a monatomic ideal gas is shown.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The system consists of 0.150 mol of a gas initially at A. The pressure at A is 512 k Pa and the volume is 1.20 × 10<sup>–3</sup> m<sup>3</sup>.</p>
</div>
<div class="specification">
<p>At C the volume is <em>V</em><sub>C</sub> and the temperature is <em>T</em><sub>C</sub>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by an adiabatic process.</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>Identify the two isothermal processes.</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>Determine the temperature of the gas at A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The volume at B is 2.30 × 10<sup>–3</sup>\(\,\)m<sup>3</sup>. Determine the pressure at B.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \({P_B}V_B^{\frac{5}{3}} = nR{T_C}V_C^{\frac{2}{3}}\)</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 volume at C is 2.90 × 10<sup>–3</sup>\(\,\)m<sup>3</sup>. Calculate the temperature at C.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State a reason why a Carnot cycle is of little use for a practical heat engine.</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>«a process in which there is» no thermal energy transferred between the system and the surroundings</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>A to B <em><strong>AND</strong> </em>C to D</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(T = \frac{{PV}}{{nR}}\)</p>
<p>\(T\left( { = \frac{{512 \times {{10}^3} \times 1.20 \times {{10}^{ - 3}}}}{{0.150 \times 8.31}}} \right) \approx 493\) «K»</p>
<p> </p>
<p><em>The first mark is for rearranging.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({P_B} = \frac{{{P_a}{V_A}}}{{{V_B}}}\)</p>
<p>\({P_B} = 267{\text{ KPa}}\)</p>
<p> </p>
<p><em>The first mark is for rearranging.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«B to C adiabatic so» \({P_{\text{B}}}V_{\text{B}}^{\frac{5}{3}} = {P_{\text{C}}}V_{\text{C}}^{\frac{5}{3}}\) <em><strong>AND</strong></em> <em>P</em><sub>C</sub><em>V</em><sub>C</sub> = <em>nRT</em><sub>C</sub> «combining to get result»</p>
<p> </p>
<p><em>It is essential to see these 2 relations to award the mark.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({T_{\text{C}}} = \left( {\frac{{{P_{\text{B}}}V_{\text{B}}^{\frac{5}{3}}}}{{nR}}} \right)V_{\text{C}}^{\frac{{ - 2}}{3}}\)</p>
<p>\({T_{\text{C}}} = \) «\(\left( {\frac{{267 \times {{10}^3} \times {{\left( {2.30 \times {{10}^{ - 3}}} \right)}^{\frac{5}{3}}}}}{{0.150 \times 8.31}}} \right){\left( {2.90 \times {{10}^{ - 3}}} \right)^{\frac{{ - 2}}{3}}}\)» = 422 «K»</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the isothermal processes would have to be conducted very slowly / OWTTE</p>
<p><em><strong>[1 mark]</strong></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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</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>
<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 flywheel consists of a solid cylinder, with a small radial axle protruding from its centre.</p>
<p style="text-align: center;"><img 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vLNN9+sdrnwvGKOv2TQVbI0rl69qmK6Eu+VcIOMA0g+sQzgtSnWG7CbP6Kq6AmkTSpD1qyV+PMrY9Bbz4oIeK81C9AIW1NvMZFaDIge+4uJABZvVPjJVGTxgM38JfbUU0/hnnvuUelygnzmzJlxt1dgNB81LmMUTdoWb4uhiLYpMJQtidrWYmh3y9vOxx9/jPz8fBrf0BAGdRdjwkHhiu/Ce/bswb333hvfEELovZ4/K/mywefMhtBgG295+OGHceHCBRrgNnI0ejs9YaOk4rycxAprampMG8sMl3ok9aqyshKnT59W/T179qyqWrxYp9OJlJQUyGejxlSfimzGQTh/zCRUIn3Vd/PwV47nw0Og3esS5ONBAgEIHDlyRA3I3H///QFKWvOyeKuyzsFDDz2E5ORkFbNt3769mnp79913o127drh27Rp27NihJiScP39eDWCJQfZ36EbsmWeeUXX6K2fG85cuXYLL5UKvXr3MKJ6tZOLAnK3UGbnOiIES70hmQtnp0AcbpU8yACUGN9Dov3jL8qUkWQOSuuVr4EqMumzKKXvCWfEQ+WXa8ezZs60ovrVktkW2MzsRcQJPP/10FNecjXh31BrICxYsUBMmWpucEEgSmawgExxmzpzpsa7yunXrorIecCD5Qr0uaxmbcTJJqP0x8330hK31nRkzaWXZPk2TiVLWPyRMMG/ePNxxxx3KWw3k+QbqsXjGslebTOd+8803MXDgQMMx40B1x/K66FwmZRiNf8dSViu3zewIK2svSrLLK/fTTz8dpdYi24wMMEpIpX///upVu60GWKSVOqZOnYpx48bhkUceUQN6ke1FdGqXMIvEhnlElgCNcGT52qL2ixcvKq/R6p0Rj1VyX5944gllNJv7ozaKfBRFh49ht9oIsh8mhbBfmExyePfdd2O0lXxzb8L2oW/fvjhx4kTY6mNFvgnQCPvmwrNuBL7++mu1PqzbKUt+3LRpE37xi194GmAArgtncLT2NNYv34Lvf7MCNdpxFOb2cFu/tvXuyiCW/Mhruxh4meywdOnS1m+ywNWkpCTbePVmxk0jbGbtmES2gwcP4rbbbjOJNKGJISEVyfCQ9Q88Dxfqq0/hOLrgoenPI7f39b1/Pcv5/kvPA+7Ro0dzAcmK2LJlS9i3C2puIEofxBPW86Sj1GRcNkMjHJdqD77Tt956a/A3megOfVPSloNMjZtC1mbn4jd3Na0ZG4TcMrFB0tDc14KQGLF4wrJbhtUP+fLiEVkCNMKR5WuL2mUFLVn5y6qHeKvSB5+bkqpNIa/4Xji8lQ5L+EHCDv4OfXFzKxsxWaZScqF5RJYAjXBk+dqi9s8++8zD07Nap0pKSlQc2GcmhOzWe7zD9S1yDHZOjFOgqcgSH961K9Q9eA0KwmKWJ0AjbHkVsgOBCIix9LfwUOOgXArSuiUFqkZdlxl2kuZmZEsi8ZQld9jKh+Q8S395RI4AjXDk2NqiZknrsvIh8ovX6nsHiKZBuWzvjSR991hCELIesNFDjxNLOMSqR1ZWFnOFI6w8GuEIA7Z69efOnbP0RA2RXyYd+D4aB+UwoCe6GPxPEK+65eCe79rlrBgx2aWCBwn4I8ClLP2R4flmApJba9WjdQPYGUMXlaMmQOfEA5ZDH2wLUNzjsj7hwbcn7lGUf8QpAYPf/3FKh922PAFZF7igoACyDoIc8lv/Mfp3ZmYm3POAg4GSl5cXTHGWjUMCNMJxqPR46rLM+lqxYkXz4kOyCJH+Ixz0z/riRN5/iycti9jo8d14Yse+RocAjXB0OLOVGBHo2bNnm2Z9SVpbMDFgX920+mxDX33iufARoBEOH0tb1iSTNKw84cAM8lt9tqEtH2wTdYpG2ETKMKMo8hpu1VlTkp72r3/9S8kfi1xXPb3v9ttvN6NqDcn07bffGirHQqEToBEOnR3vNCkBfbEe8YLLy8vVGg4nT56MurSyYagcPmfqRV2a0BqUNTeY2REaO6N3MUXNKKk4LydenZmNiXi6YnBlPV85ZMqwviuEpJiJNx9Killb1P7xxx+35XbeGycE6AnHiaLb0k3ZVUMmPZjxkGnECxcuVDsfixGWzcNlGUnZPUMfUJPNO2UBn2jGtuVLYc6cOWZEZlimWIRwDAtno4L0hG2kzEh1xWyTNcQ4iFHV12V47rnn1Kw0f566nJd1hOXVWtZ8iMaxatUqrFu3DlbOE5atjfzPNowGxfhog55wfOi5Tb3s3r27Kba5cfd6a2pqlEEVrzc7OztgqESWsRRPOBqrmomcItfYsWPbxD3WN8u2VjwiT4CecOQZW74Fp9OJ+vr6mPRDvN7t27c3LxsZyOv1J6R4w+IFjx8/Hr/61a8iNvlCFuuRRX5Wr14d8IvBn6xmOS/bWvlbfc4sMtpBDnrCdtBihPugr38Q4WY8qpfBNNmZolOnTqirqwvK6/WoyO0PGeWfP3++ihdHYmUzGbycN2+eWrt4wIABbi1b82NFRYXlt7WyAnkaYStoKcYydu7cWcVgIy2GeL0S55V1eNeuXYvRo0erWK9sJx+uNCkJXUjmhAzchdMQS12DBw9G//79Vf2RZhWN+mXbJk40iTzpBE2fNB/5ttiChQmIYfzkk0+aMw7C2RU9hUwG28RAjhkzJmLhAl1uaVMW5tm8ebMyyPr5UH5LnHnu3Llq8E+Mu/shiwVZ8V9MvHrJs7ai7O78rfCZnrAVtGQCGWVd3HBOeBDP0dvr3bdvn3qVj8ZiOZIzLGl3O3bsUEZfjHKwhwz0SchEcpM3bNjQZmMebPuRLG/1daQjySbcddMTDjdRm9Yni5nL4Jx4qqEe4l0dOXJEhRqOHTsWNa83kLxigGW5SznEk5XBKH/hDzG8Bw8e9BgolBCHv8OqnnA49O2PCc97EqAR9uTBv/wQEOMjhmrNmjV+Svg/LV6vpGyJ5ysetcR6oz17zb9016/oBnb//v0qp1j2VxN55ZBQiWx4KhNXJO4roQwjg29WNcLi4T/++OOG+nidID+FQoBGOBRqcXqPGBR9KnAgBN5erwyujRo1KiIx5UCyhHpdBgplwoIcMjipz8ALpj4rGmE9HixrKfubABMMA5ZtnQDzhFvnw6tuBGT2lMSFW/NixZuUgSrd633yySdbLe9Wvek+itENxfCariNBCiQLD4nHTwMcJLgQi9MIhwguHm8bPnw4ZPDM2wiL5ySv8DJAJTPZxOuNVCZFPHKPdp/LysogMwx5RIcAwxHR4WyLVuT1XCZP6K+putc7bdo0LFiwAA8++CBjiF6atmI4QtIRZWAuGlkqXrji8k96wnGp9tA6La/mEl6QxWnEI5bDfcnI0GrlXWYiIOteyDR1GuDoaYVGOHqsLd2S/HPK+rgyk+2BBx5Q04iNZAdYutNxKLyEIrwnnMQhhqh22VyTNVwVKMpJRU5RBVwAXFVFyEl4FEVVP0YJigt1JbPhbG7zR1QVPYoE52yU1IlERo6me3KKUGX0FiPVtigT+XYk/CCvpTKDTdbp7dOnD06dOoXdu3dDVlbjYS8CEtuX0JJksfCIHgFzGeHo9dtgSzei98SPoNUsxNDk+EHlb8lI8ZB69eql4r+SN8vDXgRkIo1kwMRjRkgsNclwRCzpm6ht8XqNLpQuA3DiGfO11UQKDIMoMhmHi7iHAWSQVXi5dy7UV5WgKD8HMqqrfobko6ikCo2ryeqv6/+BJcXFWJLXr6lcDvLXHUJtXRV2L8mDU93bD3lLD6DW7ZXcVXsYxc3Xpf4c5BeVoKrerVAwHagrQb7TiSH5y5tlceaXoE5CGUbactXicPES5Dkb++rMexs7jpx3k8BHOMLrnoQEab8IJVXSqvGjdflcqD+8FEMS+mFS8VcqNKNqrj+EJUOccE4qxnk/yFy1h7CuWX+BZZMpu/r2QEYXStdjwaGst2CcEEtGk4Bkuoj+vdMPoylDvLblaYTry7FqyizsS/s/+F7ToGk/oeaVm7F+2Fx85BGX3YKZK8qRMudAY5m9v8ahJ++Bs88CnPj3t1CtNeD7ky8CBc9i7pYmI1J/CG8/PgVb203G4QapW0NDzYtot34ypqwqbzLyoaihFqXrj6HjywegNXyN0skZSDbU1hUcfvsZZKy4jNGl30HTGlA1JwVH/rYbtX7FaLzn4a034feHf1J90Bo+wyvtNmLYlEIcNvplElC+RCSlP4UlBT1QNLUAW85fA3AFh1e9gZmVuVj5xih09dSckth1vhjPpE9CSZdXUaMYV+BPaQcwPms2ilUdjR2T2J/74jkZGRlBLxkpHpMM0vGwBwHZ+km2gOIRAwKylKV+NFQWatkYqxVW/qCf8vrdoH2392XNgXRt1t6L1699t1eb5XBo2YUntQb9bMNJrTDboTlm7dW+05ruc7ys7f2uuYSmaT9olYVjNWQXapVyWt3Tq7megPKodtHURnPDjTIGakvd69UPXc5mBk3y6XX5vEfTPOX06pMuVvNvgyyk/PefagVZDs0xcZN28tO3tSz01SZuPtPE2Ludi9reWenXWTa313i+UQ+NJ7/55htt3bp12rlz55pLBfvh6tWr2sCBA7XKyspgb42r8oB8V5v7EB2KLkWnPKJPwCMmnOjsiwey5mJu4Xb0zbkR9d3+HUN7J4fhqyERyUMXoqZGwh1/R/GeyxIwwJVP12DS4l1A9ogwtKFXYaQtF+rK92B9bQrmd0vSbwSQiKRuqeiHU27n3D4mD8WimnKgvgolxX/HFbl05VOsmLQYpRiLcW5F/X80Il/T3UkZeHbJTPwtYyx+WeRAVsEWLMvtAR9OMFD3BXauPwzHhJ7o4lEgCd3SUlA7dw/K52SpAUYZeGnLamgiXSw2z/TPlFfaQkD3gjlNuS0UQ7/X498VSYPw4rZSbLjnW2x+czKGpd3iJ26bgjQP42VAgPoTKMrrj/Zpj2PFp98og9chZzHKC8cCx0+h2uirvIGmELCtH3HhzKlWwg7+GqlDRdEkONunYdiKTxuNcIeR+FP5amTjNCqrDe7DFlA+PeCbiKS7cjFtYl8Ad+OhIb3h/pXhS8raxcNwix7PV79vQtqkTb6KtvmcTG2VwTzJpuBhTQISCxYdcppy7PTn4QkrMZJ6Y2iu/DyDRTIIteUvWD51GLIq96JiUeOyfsGL+yOqPnoDk3YPxubqt5Hb9YamKi6hJP80gNTgq/R7h5G2bkCXnqlw+PN4/dTtqvornp90CCM3n8GaZo9UBit34TgAY7uKGZFPF+Aazm8pwNSinyMrqwIzX/wvDNn2PNKTPL879dKAA9mFJdgxsY9vb/l6wbB8Es9p6dKlKlNClqrkYT0C9IJjrzN//82NkiU6kJ77JPImpKP26Blc0B20oOWuR3XlaaDf3ejr0A2wRCT+H65c+ino2lq/wUhbiUjOGI4JDm/v1YX66lPKoLZsQ7/2S9zX9zY3I/c/+P5KMJkRRuRrbN11fjtenVqMtIJ3sXXDYkysLMCL/gYxk+9EzgQnjh/4l0dGihrQWzIKCRGaPKKPpkdjK/mWOuGZthCQ7BbxhOkFt4Vi2+/1MMKNM9RykF9c0ZySJjHcnYeAiVOGIdWjdDCNd0RGTjYcuzZiben5xpQrVy0OLXsVU4tOBFORgbIG20rOxPSV92L9+HwUVaikNtRXbcGCN9f6CVPohrsM69fubzJ011B7aA1mT33Hzz2+xDUon+srbHn1NRSlzcSSZzOQ3HUU3liZi8qZb2DVYRWN9qq8M7Kmz8bIHa9h9jI9NbAOVcWL8eJMoGBhLnqHrD+vprz+lK3kZY81ybrgYQ0CoqsXXnhBvcUwFhxbnXn8Wyb2Ho+15VNw69axaK/iie3QPmsrbp32Z8wf42dAyJD8iUjOmoZtawfgn8O6oZ3U3e0l/P32PGzZPAsOQ3UYLWS0rRvQNXchStf1xb6hEvtuh/ZTyjFw2nT43awmORN/2LYIg/6ZB2c7yS1Ox0t/74y8LZswy3AnjMinhyF6oGDJU03hhxvQdcxMrJz4lQpL+PhoAsYAAA3GSURBVEqHS+w6BstKl2HwhTea5LsFWVs7Ylr5GsxI72AUYNDlZCsgmdosoQke1iCwadMmtWuInvNtDantKSWXsrSnXqPeK/GsZMv31atXczlLN/pmXMpSQhDjx4/nms9ueorlRw9POJaCsG1rE5BX2vnz52Py5MkMS5hYlfJlKfvHia64RoQ5FEUjbA492EIK2XWYYQlzq7KwsFDtJN3aDtHm7oH9pGuZoma/PrJHUSQggz0SlpCp0PxHjyJ4A01JNoRMV5etp3iYhwBjwubRhW0kkZhjWloazp07F/c7NJglJlxdXa1WvWPM3nz/ZgxHmE8nlpdIsiU2b96sNvxk2lrs1Sk6mDdvntIHsyFirw9vCegJexPh32EjsHLlShw7dgxr1qwJW51Wq8gMnrAMxMkh+dw8zEeAnrD5dGIbiSZNmqT6IsaYR2wICPtvv/1WecKxkYCtBiJATzgQIV5vEwF5FX7ssccwfPhw9TrcpsoseHMsPWHZH/Ctt95iPrDJnxt6wiZXkNXFk/xh8cZkVF5+eESHgGRCiAEWQ8x84OgwD7UVGuFQyfE+wwS6deumjIEYY26JZBhbyAWFsaQKigEW9jzMTYDhCHPrx1bS6WlSsqD81KlTbdU3f52JdjiCBtifJsx7npM1zKsb20mme8T6Ls3xYoijpUgJ98jbBj3gaBEPTzsMR4SHI2sxSEA3xJK6JgaDecQGwQUoJixpgANAMullhiNMqhi7iyXGd/r06aqby5cvV3vW2bHPkQ5HxAtHOz4bep/oCesk+DuqBCRrQiZx9O/fX601IVOdeQRHQGLskv53xx13wM5fZMFRsV5pesLW05ntJJatkXJyctRUZz1ebJdORsoTtjMzu+jeaD9ohI2SYrmIEhCvTgbqZN2Jl156yTa5reE2whJ+kB1MZGPVDRs2KF4RVQwrjzgBhiMijpgNGCEgA3YffvghunfvjhEjRoAbh7akdvToURW6kSv79u2jAW6JyJJn6AlbUm32FlqMjezQkZWVZXmvOBye8OXLl7Fq1Srl/XIpSvs9+/SE7adTy/dIllsUT69v377o1KmTynuNx1Q26bPk/MqbQXJysmLCpSgt/3i36ACNcAskPGEGApI9ITPrZGH4gwcPqtfweJryLH2VzAfpu8R+JV4uTHjYjwDDEfbTqS17JCGK119/XfVt5syZuO+++yzRz2DDEWJ8CwoKLNdPSyjDpELSCJtUMRTLNwF3IyWe8siRI03tIRoxwhJ22L9/P959913VaSt9yfjWEs8GQ4BGOBhaLGsaAuIZf/DBB8prXLFihdrl2YwrhrVmhCUtT1LNZM0HGYQcPXq0ZTx80zwINhCERtgGSoznLkjmwPbt29W6CU6nU8WRxaCZZQ1dbyMs8paXl2PTpk1q6yfx5seMGcMlJ+P4IaYRjmPl263r4h2XlZUpz1IMssy+u/fee2OaTytGuLKyUg2wScjhvffew4IFC9RAo1Xi2nZ7TszWHxphs2mE8oSFgBjkL774QqV4bd26FRJnFYOckpKiJoREylOW+K5kdJw4cUIZXhlkkzCDbO+UmZkJppiFRb22qoRG2FbqZGd8EZAQwMmTJ/Hll18q4yiGceDAgSoOKzP0xGu+7bbbcOutt6rbb775Zr/hAYnjXr16VZW7ePEivv76a9TU1ODs2bMoLS3FZ599pgy+5Dj36tVLGV5N03yJxXMkoAjQCPNBiEsCYpgvXbqkjLIAqKiowJUrVxQL3Zj6AqMbb/2aeNdyiNHt3Llzi1i0d0xYv4+/SUAnQCOsk+BvEogAARrhCEC1WZWcMWczhbI7JEAC1iJAI2wtfVFaEiABmxGgEbaZQtkdEiABaxGgEbaWvigtCZCAzQjQCNtMoewOCZCAtQjQCFtLX5SWBEjAZgRohG2mUHaHBEjAWgRohK2lL0pLAiRgMwI0wjZTKLtDAiRgLQI0wtbSF6UlARKwGQEaYZsplN0hARKwFgEaYWvpi9KSAAnYjACNsM0Uyu7YgYAL9VU7sWT2B6hytdafH1FV9CgSnLNRUtdqwdYq4bUYE+AqajFWAJu3N4HQVlG7hJL8ERh29DlU7piI3nSVbP2QUL22Vi87RwIkYHYCNMJm1xDlsyGBOlSVFCF/iBPiKSckODEkvwglVXUAmrzgxYeBXZOQ1i4D+SX/F3Uls+FMyEH+mreQ55R75Pw5z3BEXQnynU7krNmNQ+vyMUTVnQBn3lLsVnXrKJvCHXn9Gtt35mHJX9coeZz5JRApeESPAI1w9FizJRIA4EL94UJMGX8AaX+qgGx9pDV8hlfabcSwaX9Flaszhi76BHtnpQPZhahsKMeioZ2byO3C+jIHXq5qQEPNRkwe1MkH0VrsmrwEm9s/hW2q7mps6PoJsqcU4nB9Y9zYdX4Lns96EccHf4jvpUzVTHTcthyLS2t91MdTkSZAIxxpwqyfBDwIXEPNsX+itN99yOyd3HglsSuGLtwJbWeg+G86JuQ9hD5JiUh09EKvJN//vo5Z+ZiT2wdJUnuiAxnD0+Eo/SeO1VxTnnbp8oXYMXIeFj7Zt7FMUl9MXLEMsxwegvKPKBHwrcUoNc5mSCD+CNwAZ/9/Q9aud1G4ZT9KiktR1eShRoZFIpK6paIfTqOyuh6o+wI719eg332/gsP9vz/JibR+tMKR0UHrtbqrofWSvEoCJBAGAolISn8e2yqX4J4r2/HmI0OQ1r4dEobko6ikCvVhaIFVWIsAjbC19EVpbUEgEUm9s5A7cRH+W9PQUFOOzQ9dwNxhj+PNkku26CE7YZwAjbBxVixJAhEhkOhIR+7kPExw1ODomUuI6LSL5DuRM8GJ45U1nl53fQ0qj3NgLiIKDlApjXAAQLxMAuEl0DTLbchsFDenjdWhas8eHEIupuSkIBFJ6JaW0tTsj6iv/58witAZWdNnY+T6RVhQXNFoiOsrULxgERbTBoeRs/GqaISNs2JJEggDgRvR+8llKJ/WEVuzbmnKE74FWVs7Ytq2ORjT9QYANyJ15DN4+dpcpLVLwSMfnUJDGFrWq0jsOgbLSmfg1q1j0V5yiXv/EaeHPoOCbA7M6Yyi+ZvTlqNJm23FHYHQpi3HAJOrAkUjJ6Eyf6tbXnIM5IjDJukJx6HS2eV4JiAz8jLgzFuHCj01zlWLQ8v+iLnXfotHB3WMZzgx6TuNcEyws1ESiBWBzsj6w5+xsl8JhkpqnIQj2mXjnYbR2PbB75HuZwJIrKSNh3YZjogHLbOPMSNgmXBEzAixYXrCfAZIgARIIIYEaIRjCJ9NkwAJkACNMJ8BEiABEoghARrhGMJn0yRAAiRAI8xngARIgARiSIBGOIbw2TQJkAAJ0AjzGSABEiCBGBKgEY4hfDZNAiRAAjTCfAZIgARIIIYEaIRjCJ9NkwAJkACNMJ8BEiABEoghARrhGMJn0yRAAiRAI8xngARIgARiSIBGOIbw2TQJkAAJ0AjzGSABEiCBGBKgEY4hfDZNAiRAAjTCfAZIgARIIIYEaIRjCJ9NkwAJkACNMJ8BEiABEoghARrhGMJn0yRAAiRAI8xngARIgARiSIBGOIbw2TQJkAAJ0AjzGSABEiCBGBKgEY4hfDZNAiRAAjTCfAZIgARIIIYEaIRjCJ9NkwAJkACNMJ8BEiABEoghARrhGMJn0yRAAiTwMyIgARJoJJCQkBARFJGqV9O0iMjLSqNLgEY4urzZmskJWMWwRcqwm1w9thSP4QhbqpWdIgESsAoBGmGraIpykgAJ2JIAjbAt1cpOkQAJWIUAjbBVNEU5SYAEbEmARtiWamWnSIAErEKARtgqmqKc1iDgqkBRTipyio7h/KF3kOdMQEJCP+QtPYBa1zXUHl6P/CFOJCQ4MSS/GFX1Lmv0i1JGjACNcMTQsuK4JFBfg8rjV1G/8X189N0DeKemAd+XT8TZGW9gycuvYMVXA/HKf9egoXolUtYvROGhy3GJiZ2+ToB5wtdZ8BMJtJGAC3Xle7C+9m7M2PYKXkjvoOpztb8FN6AGV+5ZjTW5PaA8n/Yd0Bk1OHrmElzo3Hiuja3zdmsSoCdsTb1RalMSuIYLZ06hNjsXv7mr0QADP+JU2SfY5XgYvxt+e5Ox1Y11JsZl9qQBNqUuoycUjXD0WLMluxNwnUHZxjI4BvREl+b/rHpUV54G+qWiW5J+sslYO1LRs8sNdqfC/gUgoD8VAYrxMgmQQEACKh7sxIScO5GsF3ZdwpmjV5A97tdI1f/bdGM9YTgykvWT+g38HW8E+ATEm8bZ3wgR0EMMKUjrltTchuvUP7BxVwcM6OkW91XGGuiX5sT1ks238EOcEaARjjOFs7uRIqDHg0cgM/XGpkZcqK8+heOObORkdGxu2HXhDI7WMh7cDCTOP9AIx/kDwO6HiYAeYvCIB19G+c5dqPWIB+sDdYwHh4m85atJ0Kyydp/lUbMDZicgy0Na5d/BSrKaXe+xlo+ecKw1wPZJgATimgCNcFyrn50nARKINQEa4VhrgO2TAAnENQEa4bhWPztPAiQQawI0wrHWANsnARKIawJcwCeu1c/OexPgBpreRPh3pAnQCEeaMOu3DAGrpKdZBigFNUSA4QhDmFiIBEiABCJDgEY4MlxZKwmQAAkYIkAjbAgTC5EACZBAZAjQCEeGK2slARIgAUMEaIQNYWIhEiABEogMARrhyHBlrSRAAiRgiMD/B+kPwtX2BfuIAAAAAElFTkSuQmCC"></p>
<p>The following data are available for the flywheel.</p>
<table style="width: 396.667px;">
<tbody>
<tr>
<td style="width: 207px; padding-left: 90px;">Flywheel mass <em>M</em></td>
<td style="width: 208.667px;">= 1.22 kg</td>
</tr>
<tr>
<td style="width: 207px; padding-left: 90px;">Small axle radius <em>r</em></td>
<td style="width: 208.667px;">= 60.0 mm</td>
</tr>
<tr>
<td style="width: 207px; padding-left: 90px;">Flywheel radius <em>R</em></td>
<td style="width: 208.667px;">= 240 mm</td>
</tr>
<tr>
<td style="width: 207px; padding-left: 90px;">Moment of inertia</td>
<td style="width: 208.667px;">= 0.5 MR<sup>2</sup></td>
</tr>
</tbody>
</table>
<p><br>An object of mass <em>m</em> is connected to the axle by a light string and allowed to fall vertically from rest, exerting a torque on the flywheel.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The velocity of the falling object is 1.89 m s<sup>–1</sup> at 3.98 s. Calculate the average angular acceleration of the flywheel.</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 the torque acting on the flywheel is about 0.3 Nm.</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>(i) Calculate the tension in the string.</p>
<p>(ii) Determine the mass <em>m</em> of the falling object.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>\({\omega _{{\text{final}}}} = \frac{v}{r} = 31.5\) «rad s<sup>–1</sup>»</p>
<p>«\(\omega = {\omega _o} + \alpha t\) so» \(\alpha = \frac{\omega }{t} = \frac{{31.5}}{{3.98}} = 7.91\) «rad s<sup>–2</sup>»</p>
<p><em><strong>ALTERNATIVE 2</strong></em><br>\(a = \frac{{1.89}}{{3.98}} = 0.4749\) «m s<sup>–2</sup>»</p>
<p>\(\alpha = \frac{a}{r} = \frac{{0.4749}}{{0.060}} = 7.91\) «rad s<sup>–2</sup>»</p>
<p><em>Award <strong>[1 max]</strong> for r = 0.24 mm used giving \(\alpha \) = 1.98 «rad s<sup>–2</sup>».</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\Gamma = \frac{1}{2}{\rm{M}}{{\rm{R}}^{\rm{2}}}\alpha = \frac{1}{2} \times 1.22 \times {0.240^2} \times 7.91\)</p>
<p>= 0.278 «Nm»</p>
<p><em>At least two significant figures required for MP2, as question is a “Show”.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>i</p>
<p>\({F_T} = \frac{\Gamma }{r}\)</p>
<p>\({F_T} = 4.63\) «N»</p>
<p><em>Allow 5 «N» if Γ= 0.3 Νm is used.</em></p>
<p> </p>
<p>ii</p>
<p>\({F_T} = mg - ma\) so \(m = \frac{{4.63}}{{9.81 - 0.475}}\)<br><em>m </em>= 0.496 «kg»</p>
<p><em>Allow ECF</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 solid cylinder of mass <em>M</em> and radius <em>R</em> rolls without slipping down a uniform slope. The slope makes an angle <em>θ</em> to the horizontal.<br><img src="data:image/png;base64,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" alt><br>The diagram shows the three forces acting on the cylinder. <em>N</em> is the normal reaction force and <em>F</em> is the frictional force between the cylinder and the slope.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State why <em>F</em> is the only force providing a torque about the axis of the cylinder.</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>(i) The moment of inertia of a cylinder about its axis is \(I = \frac{1}{2}M{R^2}\). Show that, by applying Newton’s laws of motion, the linear acceleration of the cylinder is \(a = \frac{2}{3}g\sin \theta \).</p>
<p>(ii) Calculate, for <em>θ</em>= 30°, the time it takes for the solid cylinder to travel 1.5 m along the slope. The cylinder starts from rest.</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A block of ice is placed on the slope beside the solid cylinder and both are released at the same time. The block of ice is the same mass as the solid cylinder and slides without friction.</p>
<p>At any given point on the slope, the speed of the block of ice is greater than the speed of the solid cylinder. Outline why, using the answer to (b)(i).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The solid cylinder is replaced by a hollow cylinder of the same mass and radius. Suggest how this change will affect, if at all, the acceleration in (b)(i).</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>because <em>Mg</em> and <em>N</em> act through the axis</p>
<p><em><strong>OR</strong></em></p>
<p>only <em>F</em> has a non-zero lever arm «about the axis»</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) <em><strong>ALTERNATIVE 1</strong></em><br>use of Newton’s law for linear motion: <em>Mg</em>sin<em>θ</em>-<em>F</em>=<em>Ma</em></p>
<p>use of Newton’s law for rotational motion: <em>FR</em>=<em>Iα</em></p>
<p>combining \(Mg\sin \theta = Ma + \frac{{I\alpha }}{R}\)</p>
<p>substitution of \(I = \frac{1}{2}M{R^2}\) and \(\alpha = \frac{a}{R}\)</p>
<p>to get result</p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>\(Mgh = \frac{1}{2}M{v^2} + \frac{1}{4}M{v^2} \ll {\rm{from}}\frac{1}{2}I{\omega ^2} = \frac{1}{2}\left( {\frac{1}{2}M{R^2}} \right)\frac{{{v^2}}}{{{R^2}}} \gg \)</p>
<p>\({v^2} = \frac{4}{3}gh\)</p>
<p>\({v^2} = 2as = 2a\frac{h}{{\sin \theta }}\)<br><br>manipulation to produce given answer</p>
<p><em>Accept correct use of torques about point of contact.</em></p>
<p>(ii) rearranging \(s = \frac{1}{2}a{t^2}\) to get \(t = \sqrt {\frac{{2s}}{a}} \) </p>
<p>substitution to get \(t = \ll \sqrt {\frac{{2 \times 1.5}}{{\frac{2}{3} \times 9.81 \times \frac{1}{2}}}} \gg = 0.96{\rm{s}}\)</p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="text-decoration: underline;">acceleration</span> of ice is <em>g</em>sin<em>θ</em> whereas for the solid cylinder acceleration is two thirds of this «so speed of ice must always be greater at same point»</p>
<p><em>Allow answers in terms of energies, eg ice does not use energy to rotate and therefore will have a greater translational speed.</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the hollow cylinder has a greater moment of inertia</p>
<p>and hence a smaller acceleration</p>
<div class="question_part_label">d.</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>
<br><hr><br><div class="specification">
<p>Two of the brightest objects in the night sky are the planet Jupiter and the star Vega.<br>The light observed from Jupiter has a similar brightness to that received from Vega.</p>
</div>
<div class="specification">
<p>Vega is found in the constellation Lyra. The stellar parallax angle of Vega is about 0.13 arc sec.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify the mechanism leading stars to produce the light they emit.</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>Outline why the light detected from Jupiter and Vega have a similar brightness, according to an observer on Earth.</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>Outline what is meant by a constellation.</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>Outline how the stellar parallax angle is measured.</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>Show that the distance to Vega from Earth is about 25 ly.</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>«nuclear» fusion</p>
<p><em>Do not accept “burning’’</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>brightness depends on luminosity and distance/<em>b</em> = \(\frac{L}{{4\pi {d^2}}}\)</p>
<p>Vega is much further away but has a larger luminosity</p>
<p><em>Accept answer in terms of Jupiter for MP2</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>a group of stars forming a pattern on the sky <em><strong>AND</strong> </em>not necessarily close in distance to each other</p>
<p><em>OWTTE</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the star’s position is observed at two times, six months apart, relative to distant stars</p>
<p>parallax angle is half the angle of shift</p>
<p><img src="data:image/png;base64,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"></p>
<p><em>Answers may be given in diagram form, so allow the marking points if clearly drawn</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{1}{{0.13}}\) = 7.7 «pc»</p>
<p>so <em>d</em> = 7.7 x 3.26 = 25.1 «ly»</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.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">b.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>A heat engine operates on the cycle shown in the pressure–volume diagram. The cycle consists of an isothermal expansion AB, an isovolumetric change BC and an adiabatic compression CA. The volume at B is double the volume at A. The gas is an ideal monatomic gas.</p>
<p style="text-align: center;"><img 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"></p>
<p>At A the pressure of the gas is 4.00 x 10<sup>6</sup> Pa, the temperature is 612 K and the volume is 1.50 x 10<sup>–4</sup>\(\,\)m<sup>3</sup>. The work done by the gas during the isothermal expansion is 416 J.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Justify why the thermal energy supplied during the expansion AB is 416 J.</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>Show that the temperature of the gas at C is 386 K.</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>Show that the thermal energy removed from the gas for the change BC is approximately 330 J.</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 efficiency of the heat engine.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State and explain at which point in the cycle ABCA the entropy of the gas is the largest.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>Δ<em>U</em> = 0 so <em>Q</em> = Δ<em>U</em> + <em>W</em> = 0 + 416 = 416 «J»</p>
<p> </p>
<p><em>Answer given, mark is for the proof.</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><strong>ALTERNATIVE 1</strong></em></p>
<p>use \(p{V^{\frac{5}{3}}} = c\) to get \(T{V^{\frac{2}{3}}} = c\)</p>
<p>hence \({T_{\text{C}}} = {T_{\text{A}}}{\left( {\frac{{{V_{\text{A}}}}}{{{V_{\text{C}}}}}} \right)^{\frac{2}{3}}} = 612 \times {0.5^{\frac{2}{3}}} = 385.54\)</p>
<p>«<em>T</em><sub>C</sub> ≈ 386K»</p>
<p> <em><strong>ALTERNATIVE 2</strong></em></p>
<p>\({P_{\text{C}}}{V_{\text{C}}}^\gamma = {P_{\text{A}}}{V_{\text{A}}}^\gamma \) giving <em>P</em><sub>C</sub> = 1.26 x 10<sup>6</sup> «Pa»</p>
<p>\(\frac{{{P_{\text{C}}}{V_{\text{C}}}}}{{{T_{\text{C}}}}} = \frac{{{P_{\text{A}}}{V_{\text{A}}}}}{{{T_{\text{A}}}}}\) giving \({T_{\text{C}}} = 1.26 \times \frac{{612}}{2} = 385.54\) «K»</p>
<p>«<em>T</em><sub>C</sub> ≈ 386K»</p>
<p> </p>
<p><em>Answer of 386K is given. Look carefully for correct working if answers are to 3 SF.</em></p>
<p><em>There are other methods:</em></p>
<p><em>Allow use of P</em><sub>B</sub><em> = 2 x 10<sup>6</sup> «Pa» and \(\frac{P}{T}\) is constant for BC.</em></p>
<p><em>Allow use of n = 0.118 and T</em><sub>C</sub><em> = </em>\(\frac{{{P_{\text{C}}}{V_{\text{C}}}}}{{nR}}\)</p>
<p><em><strong>[2 marks]</strong></em> </p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(Q = \Delta U + W = \frac{3}{2}\frac{{{P_{\text{A}}}{V_{\text{A}}}}}{{{T_{\text{A}}}}}\Delta T + 0\)</p>
<p>\(Q = \frac{3}{2} \times \frac{{4.00 \times {{10}^6} \times 1.50 \times {{10}^{ - 4}}}}{{612}} \times \left( {386 - 612} \right)\)</p>
<p>«–332 J»</p>
<p> </p>
<p><em>Answer of 330 J given in the question.</em><br><em>Look for correct working or more than 2 SF.</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>\({\text{e}} = \frac{{{Q_{{\text{in}}}} - {Q_{{\text{out}}}}}}{{{Q_{i{\text{n}}}}}} = \frac{{412 - 332}}{{416}}\)</p>
<p>e = 0.20</p>
<p> </p>
<p><em>Allow </em>\(\frac{{416 - 330}}{{416}}\).</p>
<p><em>Allow e = 0.21.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>entropy is largest at B</p>
<p>entropy increases from A to B because <em>T</em> = constant but volume increases so more disorder <em><strong>or </strong></em>Δ<em>S</em> = \(\frac{Q}{T}\) and <em>Q</em> > 0 so Δ<em>S </em>> 0</p>
<p>entropy is constant along CA because it is adiabatic,<em> Q</em> = 0 and so<em> ΔS = </em>0<em><br><strong>OR</strong><br></em>entropy decreases along BC since energy has been removed, Δ<em>Q</em> < 0<em> so ΔS <</em> 0</p>
<p><em><strong>[3 marks]</strong></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.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">a.iv.</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 cylindrical space probe of mass 8.00 x 10<sup>2</sup> kg and diameter 12.0 m is at rest in outer space.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>Rockets at opposite points on the probe are fired so that the probe rotates about its axis. Each rocket produces a force <em>F</em> = 9.60 x 10<sup>3</sup> N. The moment of inertia of the probe about its axis is 1.44 x 10<sup>4</sup> kg\(\,\)m<sup>2</sup>.</p>
</div>
<div class="specification">
<p>The diagram shows a satellite approaching the rotating probe with negligibly small speed. The satellite is not rotating initially, but after linking to the probe they both rotate together.</p>
<p style="text-align: center;"><img 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"></p>
<p>The moment of inertia of the satellite about its axis is 4.80 x 10<sup>3</sup> kg\(\,\)m<sup>2</sup>. The axes of the probe and of the satellite are the same.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce the linear acceleration of the centre of mass of the probe.</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 resultant torque about the axis of the probe.</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 forces act for 2.00 s. Show that the final angular speed of the probe is about 16 rad\(\,\)s<sup>–1</sup>.</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>Determine the final angular speed of the probe–satellite system.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the loss of rotational kinetic energy due to the linking of the probe with the satellite.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>zero</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the torque of each force is 9.60 x 10<sup>3</sup> x 6.0 = 5.76 x 10<sup>4</sup> «Nm»</p>
<p>so the net torque is 2 x 5.76 x 10<sup>4</sup> = 1.15 x 10<sup>5</sup> «Nm»</p>
<p> </p>
<p><em>Allow a one-step solution.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the angular acceleration is given by \(\frac{{1.15 \times {{10}^5}}}{{1.44 \times {{10}^4}}}\) «= 8.0 s<sup>–2</sup>»</p>
<p><em>ω</em> = «\(\alpha \)<em>t</em> = 8.0 x 2.00 =» 16 «s<sup>–1</sup>»</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1.44 x 10<sup>4</sup> x 16.0 = (1.44 x 10<sup>4</sup> + 4.80 x 10<sup>3</sup>) x <em>ω</em></p>
<p><em>ω</em> = 12.0 «s<sup>–1</sup>»</p>
<p> </p>
<p><em>Allow ECF from (b).</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>initial KE \(\frac{1}{2} \times 1.44 \times {10^4} \times {16.0^2} = 1.843 \times {10^6}\) «J»</p>
<p>final KE \(\frac{1}{2} \times \left( {1.44 \times {{10}^4} + 4.80 \times {{10}^3}} \right) \times {12.0^2} = 1.382 \times {10^6}\) «J»</p>
<p>loss of KE = 4.6 x 10<sup>5</sup> «J»</p>
<p> </p>
<p><em>Allow ECF from part (c)(i).</em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.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.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A hoop of mass <em>m</em>, radius <em>r</em> and moment of inertia <em>mr</em><sup>2</sup> rests on a rough plane inclined at an angle <em>θ</em> to the horizontal. It is released so that the hoop gains linear and angular acceleration by rolling, without slipping, down the plane.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the diagram, draw and label the forces acting on the hoop.</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 the linear acceleration <em>a</em> of the hoop is given by the equation shown.</p>
<p style="text-align: center;"><em>a</em> = \(\frac{{g \times \sin q}}{2}\)</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the acceleration of the hoop when <em>θ</em> = 20°. Assume that the hoop continues to roll without slipping.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the relationship between the force of friction and the angle of the incline.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The angle of the incline is slowly increased from zero. Determine the angle, in terms of the coefficient of friction, at which the hoop will begin to slip.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>weight, normal reaction and friction in correct direction</p>
<p>correct points of application for at least two correct forces</p>
<p><em>Labelled on diagram.</em></p>
<p><img 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"></p>
<p><em>Allow different wording and symbols</em></p>
<p><em>Ignore relative lengths</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE</strong> <strong>1</strong></em></p>
<p><em>ma</em> = <em>mg</em> sin <em>θ</em> – <em>F</em><sub>f</sub></p>
<p><em>I</em>\(\alpha \) = <em>F</em><sub>f</sub> x <em>r</em></p>
<p><em><strong>OR</strong></em></p>
<p><em>mr </em>\(\alpha \) = <em>F</em><sub>f</sub></p>
<p>\(\alpha \) = \(\frac{a}{r}\)</p>
<p><em>ma</em> = <em>mg</em> sin <em>θ – mr \(\frac{a}{r}\) → </em>2<em>a</em> = <em>g</em> sin <em>θ</em></p>
<p><em>Can be in any order</em></p>
<p><em>No mark for re-writing given answer<br></em></p>
<p><em>Accept answers using the parallel axis theorem (with I = 2mr<sup>2</sup>) only if clear and explicit mention that the only torque is from the weight<br></em></p>
<p><em>Answer given look for correct working</em></p>
<p><strong><em>ALTERNATIVE 2</em></strong></p>
<p><em>mgh = </em>\(\frac{1}{2}\)<em>Iω</em><sup>2</sup> + \(\frac{1}{2}\) <em>mv</em><sup>2</sup></p>
<p>substituting <em>ω =</em> \(\frac{v}{r}\) «giving <em>v</em> = \(\sqrt {gh} \)»</p>
<p>correct use of a kinematic equation</p>
<p>use of trigonometry to relate displacement and height «<em>s</em> = <em>h</em> sin <em>θ</em>»</p>
<p><em>For alternative 2, MP3 and MP4 can only be awarded if the previous marking points are present</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1.68 «ms<sup>–2</sup>»</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p><em>N</em> = <em>mg</em> cos <em>θ</em></p>
<p><em>F</em><sub>f</sub> ≤ <em>μmg</em> cos<em> θ</em></p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p><em>F</em><sub>f</sub> = <em>ma</em> «from 7(b)»</p>
<p>so <em>F</em><sub>f</sub> = \(\frac{{mg\sin \theta }}{2}\)</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>F</em><sub>f</sub> = <em>μmg</em> cos <em>θ</em></p>
<p>\(\frac{{mg\sin \theta }}{2}\) = <em>mg</em> sin <em>θ </em>– <em>μmg</em> cos <em>θ</em></p>
<p><em><strong>OR</strong></em></p>
<p><em>mg</em> \(\frac{{\sin \theta }}{2}\) = <em>μmg</em> cos <em>θ</em></p>
<p>algebraic manipulation to reach tan <em>θ</em> = 2<em>μ</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>The pressure–volume (<em>pV</em>) diagram shows a cycle ABCA of a heat engine. The working substance of the engine is 0.221 mol of ideal monatomic gas.</p>
<p style="text-align: left;"><img 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"></p>
<p>At A the temperature of the gas is 295 K and the pressure of the gas is 1.10 × 10<sup>5</sup> Pa. The process from A to B is adiabatic.</p>
</div>
<div class="specification">
<p>The process from B to C is replaced by an isothermal process in which the initial state is the same and the final volume is 5.00 × 10<sup>–3<sub> </sub></sup>m<sup>3</sup>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the pressure at B is about 5 × 10<sup>5</sup> Pa.</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>For the process BC, calculate, in J, the work done by 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>For the process BC, calculate, in J, the change in the internal energy 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>For the process BC, calculate, in J, the thermal energy transferred to the gas.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain, without any calculation, why the pressure after this change would belower if the process was isothermal.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine, without any calculation, whether the net work done by the engine during one full cycle would increase or decrease.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why an efficiency calculation is important for an engineer designing a heat engine.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>«</strong>\({p_1}V_1^{\frac{5}{3}} = {p_2}V_2^{\frac{5}{3}}\)<strong>»</strong></p>
<p>\(1.1 \times {10^5} \times {5^{\frac{5}{3}}} = {p_2} \times {2^{\frac{5}{3}}}\)</p>
<p><em>p</em><sub>2</sub> <strong>«</strong>= \(\frac{{1.1 \times {{10}^5} \times {5^{\frac{5}{3}}}}}{{{{2.5}^{\frac{5}{3}}}}}\)<strong>»</strong> = 5.066 × 10<sup>5</sup> <strong>«</strong>Pa<strong>»</strong></p>
<p> </p>
<p><em>Volume may be in litres or m<sup>3</sup>.</em></p>
<p><em>Value to at least 2 sig figs, </em><strong><em>OR </em></strong><em>clear working with substitution required for mark.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>«</strong>W = <em>p</em>Δ<em>V</em><strong>»</strong></p>
<p><strong>«</strong>= 5.07 × 10<sup>5</sup> × (5 × 10<sup>–3</sup> – 2 × 10<sup>–3</sup>)<strong>» </strong></p>
<p>= 1.52 × 10<sup>3</sup> <strong>«</strong>J<strong>»</strong></p>
<p> </p>
<p><em>Award </em><strong><em>[0] </em></strong><em>if POT mistake.</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>Δ<em>U</em> = \(\frac{3}{2}\)<em>p</em>Δ<em>V</em> = \(\frac{3}{2}\)5.07 × 10<sup>5</sup> × 3 × 10<sup>–3</sup> = 2.28 × 10<sup>–3</sup> <strong>«</strong>J<strong>»</strong></p>
<p> </p>
<p><em>Accept alternative solution via T</em><sub><em>c</em></sub><em>.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>Q</em><strong> «</strong>= (1.5 + 2.28) × 10<sup>3</sup> =<strong>»</strong> 3.80 × 10<sup>3</sup> <strong>«</strong>J<strong>»</strong></p>
<p> </p>
<p><em>Watch for ECF from (b)(i) and (b)(ii).</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>for isothermal process, PV = constant / ideal gas laws mentioned</p>
<p>since V<sub>C</sub> > V<sub>B</sub>, P<sub>C</sub> must be smaller than P<sub>B</sub></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the area enclosed in the graph would be smaller</p>
<p><span>so</span> the net work done would decrease</p>
<p> </p>
<p><em>Award MP2 only if MP1 is awarded.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>to reduce energy loss; increase engine performance; improve mpg <em>etc</em></p>
<p> </p>
<p><em>Allow any sensible answer.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">d.</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>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A monatomic ideal gas is confined to a cylinder with volume 2.0 x 10<sup>–3</sup> m<sup>3</sup>. The initial pressure of the gas is 100 kPa. The gas undergoes a three-step cycle. First, the gas pressure increases by a factor of five under constant volume. Then, the gas expands adiabatically to its initial pressure. Finally it is compressed at constant pressure to its initial volume.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the volume of the gas at the end of the adiabatic expansion is approximately 5.3 x 10<sup>–3</sup> m<sup>3</sup>.</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>Using the axes, sketch the three-step cycle.</p>
<p><img 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"></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>The initial temperature of the gas is 290 K. Calculate the temperature of the gas at the start of the adiabatic expansion.</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>Using your sketched graph in (b), identify the feature that shows that net work is done by the gas in this three-step cycle.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(500\,000 \times {\left( {2 \times {{10}^{ - 3}}} \right)^{\frac{5}{3}}} = 100\,000 \times {V^{\frac{5}{3}}}\)</p>
<p><em>V</em> = 5.3 x 10<sup>–3</sup> «m<sup>3</sup>»</p>
<p><em>Look carefully for correct use of pV<sup>γ</sup> = constant</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct vertical and horizontal lines</p>
<p>curve between B and C</p>
<p> </p>
<p><em>Allow tolerance ±1 square for A, B and C</em></p>
<p><em>Allow ECF for MP2</em></p>
<p><em>Points do not need to be labelled for marking points to be awarded</em></p>
<p><img 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"></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of <em>PV</em> = <em>nRT</em> <em><strong>OR</strong></em> use of \(\frac{P}{T}\) = constant</p>
<p><em>T</em> = «5 x 290 =» 1450 «K»</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>area enclosed</p>
<p>work is done by the gas during expansion</p>
<p><em><strong>OR</strong></em></p>
<p>work is done on the gas during compression</p>
<p>the area under the expansion is greater than the area under the compression</p>
<div class="question_part_label">d.</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>
<br><hr><br><div class="specification">
<p>An astronomical reflecting telescope is being used to observe the night sky.</p>
<p>The diagram shows an incomplete reflecting telescope.</p>
<p><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Complete the diagram, with a Newtonian mounting, continuing the <strong>two</strong> rays to show how they pass through the eyepiece.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>When the Earth-Moon distance is 363 300 km, the Moon is observed using the telescope. The mean radius of the Moon is 1737 km. Determine the focal length of the mirror used in this telescope when the diameter of the Moon’s image formed by the main mirror is 1.20 cm.</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>The final image of the Moon is observed through the eyepiece. The focal length of the eyepiece is 5.0 cm. Calculate the magnification of the telescope.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The Hubble Space reflecting telescope has a Cassegrain mounting. Outline the main optical difference between a Cassegrain mounting and a Newtonian mounting.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>plane mirror to the left of principal focus tilted anti-clockwise</p>
<p>two rays which would go through the principal focus</p>
<p>two rays cross between mirror and eyepiece <em><strong>AND</strong> </em>passing through the eyepiece</p>
<p><em>eg:</em></p>
<p><em><img src="data:image/png;base64,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"></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{2 \times 1737}}{{363300}} = \frac{{0.0120}}{f}\)</p>
<p><em>f</em> = 1.25 «m»</p>
<p><em>Allow ECF if factor of 2 omitted answer is 2.5m</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>M = \(\frac{{1.25}}{{0.05}}\) = 25</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>parabolic/convex mirror instead of flat mirror</p>
<p>eyepiece/image axis same as mirror</p>
<div class="question_part_label">d.</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>
<br><hr><br><div class="specification">
<p>A train is passing through a tunnel of proper length 80 m. The proper length of the train is 100 m. According to an observer at rest relative to the tunnel, when the front of the train coincides with one end of the tunnel, the rear of the train coincides with the other end of the tunnel.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain what is meant by proper length.</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>Draw a spacetime diagram for this situation according to an observer at rest relative to the tunnel.</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 velocity of the train, according to an observer at rest relative to the tunnel, at which the train fits the tunnel.</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>For an observer on the train, it is the tunnel that is moving and therefore will appear length contracted. This seems to contradict the observation made by the observer at rest to the tunnel, creating a paradox. Explain how this paradox is resolved. You may refer to your spacetime diagram in (b).</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the length of an object in its rest frame</p>
<p><em><strong>OR</strong></em></p>
<p>the length of an object measured when at rest relative to the observer</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>world lines for front and back of tunnel parallel to <em>ct</em> axis</p>
<p>world lines for front and back of train</p>
<p>which are parallel to <em>ct′</em> axis</p>
<p><img src="data:image/png;base64,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"></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>realizes that gamma = 1.25</p>
<p>0.6<em>c</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>indicates the two simultaneous events for <em>t</em> frame</p>
<p>marks on the diagram the different times «for both spacetime points» on the <em>ct′</em> axis «shown as Δ<em>t′</em> on each diagram»</p>
<p><img src="data:image/png;base64,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"></p>
<p><em><strong>ALTERNATIVE 2: (no diagram reference)</strong></em></p>
<p>the two events occur at different points in space</p>
<p>statement that the two events are not simultaneous in the <em>t′</em> frame</p>
<div class="question_part_label">d.</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>
<br><hr><br><div class="specification">
<p>Sirius is a binary star. It is composed of two stars, Sirius A and Sirius B. Sirius A is a main sequence star.</p>
</div>
<div class="specification">
<p>The Sun’s surface temperature is about 5800 K.</p>
</div>
<div class="specification">
<p>The image shows a Hertzsprung–Russell (HR) diagram.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">The mass of Sirius A is twice the mass of the Sun. Using the Hertzsprung–Russell (HR) diagram,</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by a binary star.</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>The peak spectral line of Sirius B has a measured wavelength of 115 nm. Show that the surface temperature of Sirius B is about 25 000 K.</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>The mass of Sirius B is about the same mass as the Sun. The luminosity of Sirius B is 2.5 % of the luminosity of the Sun. Show, with a calculation, that Sirius B is <strong>not</strong> a main sequence star.</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>Determine the radius of Sirius B in terms of the radius of the Sun.</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>Identify the star type of Sirius B.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>draw the approximate positions of Sirius A, labelled A and Sirius B, labelled B.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>sketch the expected evolutionary path for Sirius A.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>two stars orbiting a common centre «of mass»</p>
<p><em>Do not accept “stars which orbit each other”</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«\(\lambda \) x <em>T </em>= 2.9 x 10<sup>–3</sup>»</p>
<p><em>T</em> = \(\frac{{2.9 \times {{10}^{ - 3}}}}{{115 \times {{10}^{ - 9}}}}\) = 25217 «K»</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of the mass-luminosity relationship <em><strong>or</strong></em> \({\left( {\frac{{{M_{{\text{Sirius}}}}}}{{{M_{{\text{Sun}}}}}}} \right)^{3.5}}\) = 1</p>
<p>if Sirius B is on the main sequence then \(\left( {\frac{{{L_{\,{\text{Sirius}}\,{\text{B}}}}}}{{L{\,_{{\text{Sun}}}}}}} \right)\) = 1 «which it is not»</p>
<p><em>Conclusion is given, justification must be stated</em></p>
<p><em>Allow reverse argument beginning with luminosity</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\left( {\frac{{{L_{\,{\text{Sirius}}\,{\text{B}}}}}}{{L{\,_{{\text{Sun}}}}}}} \right)\) = 0.025</p>
<p><em>r </em><sub>Sirius</sub> = «\(\sqrt {0.025 \times {{\left( {\frac{{5800}}{{25000}}} \right)}^4}} \) =» 0.0085 <em>r </em><sub>Sun</sub></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>white dwarf</p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Sirius A on the main sequence above and to the left of the Sun <em><strong>AND</strong> </em>Sirius B on white dwarf area as shown</p>
<p><em>Both positions must be labelled </em></p>
<p><em>Allow the position anywhere within the limits shown.</em></p>
<p><em><img src="data:image/png;base64,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"></em></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>arrow goes up and right and then loops to white dwarf area</p>
<p><img 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"></p>
<div class="question_part_label">e.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.</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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A fixed mass of an ideal monatomic gas undergoes an isothermal change from A to B as shown.<br><img 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" alt><br>The temperature at A is 350 K. An identical mass of the same ideal monatomic gas undergoes an isobaric change from A to C.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Calculate the temperature at C.</p>
<p>(ii) Calculate the change in internal energy for AC.</p>
<p>(iii) Determine the energy supplied to the gas during the change AC.</p>
<p>(iv) On the graph, draw a line to represent an adiabatic expansion from A to a state of volume 4.0×10<sup>−3</sup>m<sup>3</sup> (point D).</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) State the change in entropy of a gas for the adiabatic expansion from A to D.</p>
<p>(ii) Explain, with reference to the concept of disorder, why the entropy of the gas is greater at C than B.</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>(i) 1400 «K»</p>
<p>(ii) \(\frac{3}{2}P\Delta V = \frac{3}{2} \times 4 \times {10^5} \times 3 \times {10^{ - 3}}\)<br>1800 J</p>
<p>(iii) 1800+<em>P</em>Δ<em>V</em>=1800+4×10<sup>5</sup>×3×10<sup>−3</sup> <em><strong>OR</strong></em> use of \(\Delta Q = \frac{5}{2}P\Delta V\)<br>3000 J</p>
<p>(iv) curve starting at A ending on line CB <em><strong>AND</strong></em> between B and zero pressure</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) 0</p>
<p>(ii)<br><em><strong>ALTERNATIVE 1</strong></em><br>C has the same volume as B <em><strong>OR</strong></em> entropy is related to disorder</p>
<p>higher temperature/pressure means greater disorder</p>
<p>therefore entropy at C is greater «because entropy is related to disorder»</p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>to change from B to C, Δ<em>Q</em> > 0</p>
<p>so Δ<em>S</em> > 0</p>
<p>Δ<em>S</em> related to disorder</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 horizontal rigid bar of length 2<em>R</em> is pivoted at its centre. The bar is free to rotate in a horizontal plane about a vertical axis through the pivot. A point particle of mass <em>M</em> is attached to one end of the bar and a container is attached to the other end of the bar.</p>
<p>A point particle of mass \(\frac{M}{3}\) moving with speed <em>v</em> at right angles to the rod collides with the container and gets stuck in the container. The system then starts to rotate about the vertical axis.</p>
<p>The mass of the rod and the container can be neglected.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>A torque of 0.010 N m brings the system to rest after a number of revolutions. For this case <em>R</em> = 0.50 m, <em>M</em> = 0.70 kg and <em>v</em> = 2.1 m s<sup>–1</sup>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an expression, in terms of <em>M</em>, <em>v</em> and <em>R</em>, for the angular momentum of the system about the vertical axis just before the collision.</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>Just after the collision the system begins to rotate about the vertical axis with angular velocity <em>ω</em>. Show that the angular momentum of the system is equal to \(\frac{4}{3}M{R^2}\omega \).</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>Hence, show that \(\omega = \frac{v}{{4R}}\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine in terms of <em>M</em> and <em>v</em> the energy lost during the collision.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the angular deceleration of the system is 0.043 rad\(\,\)s<sup>–2</sup>.</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 number of revolutions made by the system before it comes to rest.</p>
<div class="marks">[3]</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>\(\frac{M}{3}vR\)</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>evidence of use of:</em> \(L = I\omega = \left( {M{R^2} + \frac{M}{3}{R^2}} \right)\omega \)</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>evidence of use of conservation of angular momentum, \(\frac{{MvR}}{3} = \frac{4}{3}M{R^2}\omega \)</p>
<p>«rearranging to get \(\omega = \frac{v}{{4R}}\)»</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>initial KE = \(\frac{{M{v^2}}}{6}\)</p>
<p>final KE = \(\frac{{M{v^2}}}{{24}}\)</p>
<p>energy loss = \(\frac{{M{v^2}}}{8}\)</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\alpha \) «= \(\frac{3}{4}\frac{\Gamma }{{M{R^2}}}\)» = \(\frac{3}{4}\frac{{0.01}}{{0.7 \times {{0.5}^2}}}\)</p>
<p>«to give \(\alpha \) = 0.04286 rad\(\,\)s<sup>−2</sup>»</p>
<p> </p>
<p><em>Working <strong>OR</strong> answer to at least 3 SF must be shown</em></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>\(\theta = \frac{{\omega _i^2}}{{2\alpha }}\) «from \(\omega _f^2 = \omega _i^2 + 2\alpha \theta \)»</p>
<p>\(\theta \) «\( = \frac{{{v^2}}}{{32{R^2}\alpha }} = \frac{{{{2.1}^2}}}{{32 \times {{0.5}^2} \times 0.043}}\)» = 12.8 <em><strong>OR</strong> </em>12.9 «rad»</p>
<p>number of rotations «= \(\frac{{12.9}}{{2\pi }}\)» = 2.0 revolutions</p>
<p><em><strong>[3 marks]</strong></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;">
[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">a.iv.</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="question">
<p>The diagram shows two methods of pedalling a bicycle using a force <em>F</em>.</p>
<p style="text-align: center;"><img 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"></p>
<p>In method 1 the pedal is always horizontal to the ground. A student claims that method 2 is better because the pedal is always parallel to the crank arm. Explain why method 2 is more effective.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>in method 1 the perpendicular distance varies from 0 to a maximum value, in method 2 this distance is constant at the maximum value<br><em><strong>OR<br></strong></em>angle between <em>F</em> and <em>r</em> is 90° in method 2 and less in method 1<br><em><strong>OR<br></strong>Γ</em> = <em>F</em> × perpendicular distance</p>
<p>perpendicular distance/ torque is greater in method 2</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br>