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</div><h2>HL Paper 2</h2><div class="specification">
<p>The first scientists to identify alpha particles by a direct method were Rutherford and Royds. They knew that radium-226 (\({}_{86}^{226}{\text{Ra}}\)) decays by alpha emission to form a nuclide known as radon (Rn).</p>
</div>
<div class="specification">
<p>At the start of the experiment, Rutherford and Royds put 6.2 x 10<sup>–4</sup> mol of pure radium-226 in a small closed cylinder A. Cylinder A is fixed in the centre of a larger closed cylinder B.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>The experiment lasted for 6 days. The decay constant of radium-226 is 1.4 x 10<sup>–11</sup> s<sup>–1</sup>.</p>
</div>
<div class="specification">
<p>At the start of the experiment, all the air was removed from cylinder B. The alpha particles combined with electrons as they moved through the wall of cylinder A to form helium gas in cylinder B.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the nuclear equation for this decay.</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>Deduce that the activity of the radium-226 is almost constant during the experiment.</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>Show that about 3 x 10<sup>15</sup> alpha particles are emitted by the radium-226 in 6 days.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The wall of cylinder A is made from glass. Outline why this glass wall had to be very thin.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The experiment was carried out at a temperature of 18 °C. The volume of cylinder B was 1.3 x 10<sup>–5</sup> m<sup>3</sup> and the volume of cylinder A was negligible. Calculate the pressure of the helium gas that was collected in cylinder B over the 6 day period. Helium is a monatomic gas.</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>\(_2^4\alpha \)</p>
<p><em><strong>OR</strong></em></p>
<p>\({}_2^4{\text{He}}\)</p>
<p>\({}_{86}^{222}{\text{Rn}}\)</p>
<p> </p>
<p><em>These <strong>must</strong> be seen on the right-hand side of the equation.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>6 days is 5.18 x 10<sup>5</sup> s</p>
<p>activity after 6 days is \({A_0}{e^{ - 1.4 \times {{10}^{ - 11}} \times 5.8 \times {{10}^5}}} \approx {A_0}\)</p>
<p><em><strong>OR</strong></em></p>
<p>A = 0.9999927 <em>A</em><sub>0 </sub><em><strong>or</strong> </em>0.9999927 \(\lambda \)<em>N</em><sub>0</sub></p>
<p><em><strong>OR</strong></em></p>
<p>states that index of e is so small that \(\frac{A}{{{A_0}}}\) is ≈ 1</p>
<p><em><strong>OR</strong></em></p>
<p><em>A – A</em><sub>0</sub> ≈ 10<sup>–15</sup> «s<sup>–1</sup>»</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em><br>shows half-life of the order of 10<sup>11</sup> s or 5.0 x 10<sup>10</sup> s</p>
<p>converts this to year «1600 y» or days and states half-life much longer than experiment compared to experiment</p>
<p> </p>
<p><em>Award <strong>[1 max]</strong> if calculations/substitutions have numerical slips but would lead to correct deduction.</em></p>
<p><em>eg: failure to convert 6 days to seconds but correct substitution into equation will give MP2.</em></p>
<p><em>Allow working in days, but for MP1 must see conversion of \(\lambda \) or half-life to day<sup>–1</sup>.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1 </strong></em><br><br>use of <em>A</em> = \(\lambda \)<em>N</em><sub>0</sub></p>
<p>conversion to number of molecules = <em>nN</em><sub>A</sub> = 3.7 x 10<sup>20</sup></p>
<p><em><strong>OR</strong></em></p>
<p>initial activity = 5.2 x 10<sup>9</sup> «s<sup>–1</sup>»</p>
<p>number emitted = (6 x 24 x 3600) x 1.4 x 10<sup>–11</sup> x 3.7 x 10<sup>20</sup> <em><strong>or</strong> </em>2.7 x 10<sup>15</sup> alpha particles</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em><br>use of <em>N</em> = <em>N</em><sub>0</sub>\({e^{ - \lambda t}}\)</p>
<p><em>N</em><sub>0</sub> = <em>n</em> x <em>N</em><sub>A</sub> = 3.7 x 10<sup>20</sup></p>
<p>alpha particles emitted «= number of atoms disintegrated = <em>N</em> – <em>N</em><sub>0</sub> =» <em>N</em><sub>0</sub>\(\left( {1 - {e^{ - \lambda \times 6 \times 24 \times 3600}}} \right)\) <em><strong>or</strong> </em>2.7 x 10<sup>15</sup> alpha particles </p>
<p> </p>
<p><em>Must see correct substitution or answer to 2+ sf for MP3</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>alpha particles highly ionizing<br><em><strong>OR</strong></em><br>alpha particles have a low penetration power<br><em><strong>OR</strong></em><br>thin glass increases probability of alpha crossing glass<br><em><strong>OR</strong></em><br>decreases probability of alpha striking atom/nucleus/molecule</p>
<p> </p>
<p><em>Do not allow reference to tunnelling.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>conversion of temperature to 291 K</p>
<p><em>p</em> = 4.5 x 10<sup>–9</sup> x 8.31 x «\(\frac{{291}}{{1.3 \times {{10}^{ - 5}}}}\)»</p>
<p><em><strong>OR</strong></em></p>
<p><em>p</em> = 2.7 x 10<sup>15</sup> x 1.3 x 10<sup>–23 </sup>x «\(\frac{{291}}{{1.3 \times {{10}^{ - 5}}}}\)»<br><br>0.83 <em><strong>or</strong> </em>0.84 «Pa»</p>
<p> </p>
<p><em>Allow ECF for 2.7 x 10<sup>15</sup> from (b)(ii).</em></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.</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.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 closed box of fixed volume 0.15 m<sup>3</sup> contains 3.0 mol of an ideal monatomic gas. The temperature of the gas is 290 K.</p>
</div>
<div class="specification">
<p>When the gas is supplied with 0.86 kJ of energy, its temperature increases by 23 K. The specific heat capacity of the gas is 3.1 kJ kg<sup>–1</sup> K<sup>–1</sup>.</p>
</div>
<div class="question">
<p>Determine, in kJ, the total kinetic energy of the particles of the gas.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><strong><em>ALTERNATIVE 1</em></strong></p>
<p>average kinetic energy = \(\frac{3}{2}\)1.38 × 10<sup>–23</sup> × 313 = 6.5 × 10<sup>–21</sup><strong> «</strong><span class="Apple-converted-space">J</span><strong>»</strong></p>
<p>number of particles = 3.0 × 6.02 × 10<sup>23</sup> = 1.8 × 10<sup>24</sup></p>
<p>total kinetic energy = 1.8 × 10<sup>24</sup> × 6.5 × 10<sup>–21</sup> = 12 <strong>«</strong><span class="Apple-converted-space">kJ</span><strong>»</strong></p>
<p> </p>
<p><strong><em>ALTERNATIVE 2</em></strong></p>
<p>ideal gas so <em>U</em> =<em> KE</em></p>
<p><em>KE</em> = \(\frac{3}{2}\)8.31 × 131 × 3</p>
<p>total kinetic energy = 12 <strong>«</strong><span class="Apple-converted-space">kJ</span><strong>»</strong></p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>0.46 mole of an ideal monatomic gas is trapped in a cylinder. The gas has a volume of 21 m<sup>3</sup> and a pressure of 1.4 Pa.</p>
<p>(i) State how the internal energy of an ideal gas differs from that of a real gas.</p>
<p>(ii) Determine, in kelvin, the temperature of the gas in the cylinder.</p>
<p>(iii) The kinetic theory of ideal gases is one example of a scientific model. Identify <strong>two</strong> reasons why scientists find such models useful.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>i<br>«intermolecular» potential energy/PE of an ideal gas is zero/negligible<br><br></p>
<p>ii<br><strong>THIS IS FOR USE WITH AN ENGLISH SCRIPT ONLY</strong><br>use of \(T = \frac{{PV}}{{nR}}\) <em><strong>or</strong></em> \(T = \frac{{1.4 \times 21}}{{0.46 \times 8.31}}\)<br><em>Award mark for correct re-arrangement as shown here not for quotation of Data Booklet version.</em><br><em>Award <strong>[2]</strong> for a bald correct answer in K.</em><br><em>Award <strong>[2 max]</strong> if correct 7.7 K seen followed by –265°C and mark BOD. However, if only –265°C seen, award <strong>[1 max]</strong>.</em><br><br>7.7K<br><em>Do not penalise use of “°K”</em><br><br></p>
<p>ii<br><strong>THIS IS FOR USE WITH A SPANISH SCRIPT ONLY</strong><br>\(T = \frac{{PV}}{{nR}}\)<br><em>Award mark for correct re-arrangement as shown here not for quotation of Data Booklet version.</em></p>
<p>\(T = \frac{{1.4 \times 2.1 \times {{10}^{ - 6}}}}{{0.46 \times 8.31}}\)<br><em>Uses correct unit conversion for volume</em></p>
<p>T = 7.7×10<sup>-6</sup>K<br><em>Award <strong>[2]</strong> for a bald correct answer in K. Finds solution. Allow an ECF from MP2 if unit not converted, ie candidate uses 21m3 and obtains 7.7 K</em><br><em>Do not penalise use of “°K”</em></p>
<p> </p>
<p>iii<br>«models used to»<br>predict/hypothesize / lead to further theories<br><em>Response needs to identify <strong>two</strong> different reasons. (<strong>N.B.</strong> only one in SL).</em></p>
<p>explain / help with understanding / help to visualize<br><em>Do not allow any response that is gas specific. The question is couched in general, nature of science terms and must be answered as such.</em></p>
<p>simulate<br>simplify/approximate</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>This question is about an ideal gas.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe how the ideal gas constant <em>R</em> is defined.</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 the temperature of 0.100 mol of an ideal gas kept in a cylinder of volume 1.40×10<sup>–3 </sup>m<sup>3</sup> at a pressure of 2.32×10<sup>5 </sup>Pa.</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 gas in (b) is kept in the cylinder by a freely moving piston. The gas is now heated at constant pressure until the volume occupied by the gas is 3.60×10<sup>–3 </sup>m<sup>3</sup>. The increase in internal energy of the gas is 760 J. Determine the thermal energy given to the gas.</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>After heating, the gas is compressed rapidly to its original volume in (b). Outline why this compression approximates to an adiabatic change of state of the gas.</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>defined from the equation of state of an ideal gas <em>PV</em>=<em>nRT</em>;<br>all symbols (<em>PVnT</em>) correctly identified;</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>390/391 K;</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>work done\( = \left( {P\Delta V = 2.32 \times {{10}^5} \times 2.20 \times {{10}^{ - 3}} = } \right)510{\rm{J}}\);<br>thermal energy\( = \left( {760 + 510 = } \right)1.27 \times {10^3}{\rm{J}}\);<br><em>Award <strong>[1 max]</strong> if volume is taken as 3.6×10<sup>–3</sup>, giving an answer of 1600 J.</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>an adiabatic change is one in which no (thermal/heat) energy is transferred between system and surroundings / no energy enters/leaves system;<br>a rapid compression means that there is insufficient time (for energy transfer) / <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>The electrical circuit shown is used to investigate the temperature change in a wire that is wrapped around a mercury-in-glass thermometer.</p>
<p style="text-align: center;"><img 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"></p>
<p>A power supply of emf (electromotive force) 24 V and of negligible internal resistance is connected to a capacitor and to a coil of resistance wire using an arrangement of two switches. Switch S<sub>1</sub> is closed and, a few seconds later, opened. Then switch S<sub>2</sub> is closed.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The capacitance of the capacitor is 22 mF. Calculate the energy stored in the capacitor when it is fully charged.</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 resistance of the wire is 8.0 Ω. Determine the time taken for the capacitor to discharge through the resistance wire. Assume that the capacitor is completely discharged when the potential difference across it has fallen to 0.24 V.</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>The mass of the resistance wire is 0.61 g and its observed temperature rise is 28 K. Estimate the specific heat capacity of the wire. Include an appropriate unit for your answer.</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>Suggest <strong>one</strong> other energy loss in the experiment and the effect it will have on the value for the specific heat capacity of the wire.</p>
<div class="marks">[2]</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>«\(\frac{1}{2}C{V^2} = \frac{1}{2} \times 0.22 \times {24^2}\)» = «J»</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{1}{{100}} = {e^{ - \frac{t}{{8.0 \times 0.022}}}}\)</p>
<p>\(\ln 0.01 = - \frac{t}{{8.0 \times 0.022}}\)</p>
<p>0.81 «s»</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>c</em> = \(\frac{Q}{{m \times \Delta T}}\)</p>
<p><em><strong>OR</strong></em></p>
<p>\(\frac{{6.3}}{{0.00061 \times 28}}\)</p>
<p>370 J kg<sup>–1</sup> K<sup>–1</sup></p>
<p> </p>
<p> </p>
<p><em>Allow ECF from 3(a) for energy transferred.</em></p>
<p><em>Correct answer only to include correct unit that matches answer power of ten.</em></p>
<p><em>Allow use of g and kJ in unit but must match numerical answer, eg: 0.37 J kg<sup>–1</sup> K<sup>–1</sup> receives<strong> [1]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>some thermal energy will be transferred to surroundings/along connecting wires/to<br>thermometer</p>
<p>estimate «of specific heat capacity by student» will be larger «than accepted value»</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>not all energy transferred as capacitor did not fully discharge</p>
<p>so estimate «of specific heat capacity by student» will be larger «than accepted value»</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.</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>This question is about internal energy.</p>
<p>Humans generate internal energy when moving, while their core temperature remains approximately constant.</p>
</div>
<div class="question">
<p>Distinguish between the concepts of internal energy and temperature.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><em>internal energy:</em><br>total energy of component particles (in the human);<br>comprises potential energy + (random) kinetic energy;</p>
<p><em>temperature:</em><br>measure of average kinetic energy of particles;<br>indicates direction of (natural) flow of thermal energy;<br>internal energy measured in J and temperature measured in K/°C ; <em>(both needed) </em>{<em>(accept alternative suitable units)</em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<div class="page" title="Page 37">
<div class="layoutArea">
<div class="column">
<p><span style="font-size: 12.000000pt; font-family: 'TimesNewRomanPS'; font-weight: bold;">Part 2 </span><span style="font-size: 12.000000pt; font-family: 'TimesNewRomanPSMT';">Properties of a gas<br> </span></p>
</div>
</div>
</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>With respect to a gas, explain the meaning of the terms thermal energy and internal energy.</p>
<p><img 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" alt></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>The graph shows how the pressure <em>P</em> of a sample of a fixed mass of an ideal gas varies with volume <em>V.</em> The gas is taken through a cycle<strong> ABCD.</strong></p>
<p><strong><img src="data:image/png;base64,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" alt></strong></p>
<p> </p>
<p style="text-align: center;"><em>V / 10<sup>–6</sup> m<sup>3</sup></em></p>
<p style="text-align: left;">(i) Estimate the net work done during the cycle.</p>
<p style="text-align: left;">(ii) Explain whether the net work is done on the gas or by the gas.</p>
<p style="text-align: left;">(iii) Deduce, using the data from the graph, that the change <strong>C</strong> is isothermal.</p>
<p style="text-align: left;">(iv) Isothermal change <strong>A</strong> occurs at a temperature of 450 K. Calculate the temperature at which isothermal change <strong>C</strong> occurs.</p>
<p style="text-align: left;">(v) Describe the changes <strong>B</strong> and <strong>D</strong>.</p>
<div class="marks">[10]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>(Q)</em> energy transferred between two objects (at different temperatures);<br><em>(U)</em> (total) potential energy and (random) kinetic energy of the molecules/particles (of the gas);</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) use of area within cycle;<br>each large square has work value of 250 (J);<br>estimate (16 x 250= )4000 (J); (allow 3600 − 4100)<br><em>Award <strong>[3]</strong> for same outcome with small squares of area 10 (J). </em></p>
<p>(ii) (work is done by the gas because) area under expansion is greater than that under compression/pressure during expansion is greater than during compression;</p>
<p>(iii) clear attempt to compare two <em>PV</em> values;<br>evaluate two <em>PV</em> values correctly <em>eg</em> 75 x 80= 6000 and 200 x 30= 6000; </p>
<p>(iv) use of <em>PV</em> =<em>nRT</em> or equivalent;<br>1350/1330 (K);</p>
<p>(v) both changes are isochoric/isovolumetric/constant volume changes;<br>B: temperature/internal energy increases, D: temperature/internal energy decreases;<br>B: thermal energy/heat input (to system), D: thermal energy/heat output (from system);<br>B: pressure increases, D: pressure decreases;</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Few candidates were able to explain thermal energy was the energy transfer between two objects at different temperatures. Many knew the definition of internal energy but a high percentage omitted to mention the potential energy (probably assuming that the gas was ideal).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) Many candidates appeared to attempt to calculate area without actually saying what they were doing; although this was obvious when they referred to the area of a square, in many case it was not obvious and marks were lost when the candidates technique produced an answer out of tolerance. In examples like this there will be a reasonable tolerance for the area and it is not expected that candidates will waste considerable time in counting the small squares.</p>
<p>(ii) Although some candidates were aware that a clockwise cycle applies to net work done by the gas, this does not explain the choice. Simply saying that the area under the expansion was greater than the area under the compression was all that was needed.</p>
<p>(iii) This part was mostly well done by candidates. It is accepted, in line with SL A1, that showing constancy of two PV values does not prove that the change is isothermal; however in terms of deducing that the change is isothermal this technique is fine – that is, the candidates are told that it is isothermal and they are simply illustrating that this is the case. Often examiners will expect three values to be taken in questions such as this.</p>
<p>(iv) This part was well done by those many candidates who used any appropriate variant of the ideal gas equation to calculate the temperature.</p>
<p>(v) The large majority of candidates did well here although a minority were deducted marks when they used contradictory statements such as isochoric and compression or expansion.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows the gravitational field lines of planet X.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline how this diagram shows that the gravitational field strength of planet X decreases with distance from the surface.</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 diagram shows part of the surface of planet X. The gravitational potential at the surface of planet X is –3<em>V</em> and the gravitational potential at point Y is –<em>V</em>.</p>
<p><img src="data:image/png;base64,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"></p>
<p>Sketch on the grid the equipotential surface corresponding to a gravitational potential of –2<em>V</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A meteorite, very far from planet X begins to fall to the surface with a negligibly small initial speed. The mass of planet X is 3.1 × 10<sup>21</sup> kg and its radius is 1.2 × 10<sup>6</sup> m. The planet has no atmosphere. Calculate the speed at which the meteorite will hit the surface.</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>At the instant of impact the meteorite which is made of ice has a temperature of 0 °C. Assume that all the kinetic energy at impact gets transferred into internal energy in the meteorite. Calculate the percentage of the meteorite’s mass that melts. The specific latent heat of fusion of ice is 3.3 × 10<sup>5</sup> J kg<sup>–1</sup>.</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 field lines/arrows are further apart at greater distances from the surface</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>circle centred on Planet X<br>three units from Planet X centre</p>
<p><img 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"></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>loss in gravitational potential = \(\frac{{6.67 \times {{10}^{ - 11}} \times 3.1 \times {{10}^{21}}}}{{1.2 \times {{10}^6}}}\)</p>
<p>«= 1.72 × 10<sup>5</sup> JKg<sup>−1</sup>»</p>
<p>equate to \(\frac{1}{2}\)<em>v</em><sup>2</sup></p>
<p>v = 590 «m s<sup>−1</sup>»</p>
<p> </p>
<p><em>Allow ECF from MP1.</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>available energy to melt one kg 1.72 × 10<sup>5</sup> «J»</p>
<p>fraction that melts is \(\frac{{1.72 \times {{10}^5}}}{{3.3 \times {{10}^5}}}\) = 0.52 <em><strong>OR</strong></em> 52%</p>
<p> </p>
<p><em>Allow ECF from MP1.</em></p>
<p><em>Allow 53% from use of 590 ms<sup>-1</sup>.</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>