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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>
<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>
<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>
<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>
<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>
<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>
<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>
<br><hr><br><div class="specification">
<p>The diagram shows the gravitational field lines of planet X.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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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>
<br><hr><br>