HL Paper 2
The electrical circuit shown is used to investigate the temperature change in a wire that is wrapped around a mercury-in-glass thermometer.
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 S1 is closed and, a few seconds later, opened. Then switch S2 is closed.
The capacitance of the capacitor is 22 mF. Calculate the energy stored in the capacitor when it is fully charged.
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.
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.
Suggest one other energy loss in the experiment and the effect it will have on the value for the specific heat capacity of the wire.
0.46 mole of an ideal monatomic gas is trapped in a cylinder. The gas has a volume of 21 m3 and a pressure of 1.4 Pa.
(i) State how the internal energy of an ideal gas differs from that of a real gas.
(ii) Determine, in kelvin, the temperature of the gas in the cylinder.
(iii) The kinetic theory of ideal gases is one example of a scientific model. Identify two reasons why scientists find such models useful.
The first scientists to identify alpha particles by a direct method were Rutherford and Royds. They knew that radium-226 () decays by alpha emission to form a nuclide known as radon (Rn).
At the start of the experiment, Rutherford and Royds put 6.2 x 10–4 mol of pure radium-226 in a small closed cylinder A. Cylinder A is fixed in the centre of a larger closed cylinder B.
The experiment lasted for 6 days. The decay constant of radium-226 is 1.4 x 10–11 s–1.
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.
Write down the nuclear equation for this decay.
Deduce that the activity of the radium-226 is almost constant during the experiment.
Show that about 3 x 1015 alpha particles are emitted by the radium-226 in 6 days.
The wall of cylinder A is made from glass. Outline why this glass wall had to be very thin.
The experiment was carried out at a temperature of 18 °C. The volume of cylinder B was 1.3 x 10–5 m3 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.
A closed box of fixed volume 0.15 m3 contains 3.0 mol of an ideal monatomic gas. The temperature of the gas is 290 K.
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–1 K–1.
A closed box of fixed volume 0.15 m3 contains 3.0 mol of an ideal monatomic gas. The temperature of the gas is 290 K.
Determine, in kJ, the total kinetic energy of the particles of the gas.
Explain, with reference to the kinetic model of an ideal gas, how an increase in temperature of the gas leads to an increase in pressure.
Liquid oxygen at its boiling point is stored in an insulated tank. Gaseous oxygen is produced from the tank when required using an electrical heater placed in the liquid.
The following data are available.
Mass of 1.0 mol of oxygen = 32 g
Specific latent heat of vaporization of oxygen = 2.1 × 105 J kg–1
An oxygen flow rate of 0.25 mol s–1 is needed.
Distinguish between the internal energy of the oxygen at the boiling point when it is in its liquid phase and when it is in its gas phase.
Calculate, in kW, the heater power required.
Calculate the volume of the oxygen produced in one second when it is allowed to expand to a pressure of 0.11 MPa and to reach a temperature of –13 °C.
State one assumption of the kinetic model of an ideal gas that does not apply to oxygen.
A square loop of side 5.0 cm enters a region of uniform magnetic field at t = 0. The loop exits the region of magnetic field at t = 3.5 s. The magnetic field strength is 0.94 T and is directed into the plane of the paper. The magnetic field extends over a length 65 cm. The speed of the loop is constant.
Show that the speed of the loop is 20 cm s−1.
Sketch, on the axes, a graph to show the variation with time of the magnetic flux linkage in the loop.
Sketch, on the axes, a graph to show the variation with time of the magnitude of the emf induced in the loop.
There are 85 turns of wire in the loop. Calculate the maximum induced emf in the loop.
The resistance of the loop is 2.4 Ω. Calculate the magnitude of the magnetic force on the loop as it enters the region of magnetic field.
Show that the energy dissipated in the loop from t = 0 to t = 3.5 s is 0.13 J.
The mass of the wire is 18 g. The specific heat capacity of copper is 385 J kg−1 K−1. Estimate the increase in temperature of the wire.
A container of volume 3.2 × 10-6 m3 is filled with helium gas at a pressure of 5.1 × 105 Pa and temperature 320 K. Assume that this sample of helium gas behaves as an ideal gas.
A helium atom has a volume of 4.9 × 10-31 m3.
The mass of a helium atom is 6.6 × 10-27 kg. Estimate the average speed of the helium atoms in the container.
Show that the number of helium atoms in the container is 4 × 1020.
Calculate the ratio .
Discuss, by reference to the kinetic model of an ideal gas and the answer to (c)(i), whether the assumption that helium behaves as an ideal gas is justified.
An ideal monatomic gas is kept in a container of volume 2.1 × 10–4 m3, temperature 310 K and pressure 5.3 × 105 Pa.
The volume of the gas in (a) is increased to 6.8 × 10–4 m3 at constant temperature.
State what is meant by an ideal gas.
Calculate the number of atoms in the gas.
Calculate, in J, the internal energy of the gas.
Calculate, in Pa, the new pressure of the gas.
Explain, in terms of molecular motion, this change in pressure.
Titan is a moon of Saturn. The Titan-Sun distance is 9.3 times greater than the Earth-Sun distance.
The molar mass of nitrogen is 28 g mol−1.
Show that the intensity of the solar radiation at the location of Titan is 16 W m−2.
Titan has an atmosphere of nitrogen. The albedo of the atmosphere is 0.22. The surface of Titan may be assumed to be a black body. Explain why the average intensity of solar radiation absorbed by the whole surface of Titan is 3.1 W m−2.
Show that the equilibrium surface temperature of Titan is about 90 K.
The mass of Titan is 0.025 times the mass of the Earth and its radius is 0.404 times the radius of the Earth. The escape speed from Earth is 11.2 km s−1. Show that the escape speed from Titan is 2.8 km s−1.
The orbital radius of Titan around Saturn is and the period of revolution is .
Show that where is the mass of Saturn.
The orbital radius of Titan around Saturn is 1.2 × 109 m and the orbital period is 15.9 days. Estimate the mass of Saturn.
Show that the mass of a nitrogen molecule is 4.7 × 10−26 kg.
Estimate the root mean square speed of nitrogen molecules in the Titan atmosphere. Assume an atmosphere temperature of 90 K.
Discuss, by reference to the answer in (b), whether it is likely that Titan will lose its atmosphere of nitrogen.
Plutonium-238 (Pu) decays by alpha (α) decay into uranium (U).
The following data are available for binding energies per nucleon:
plutonium 7.568 MeV
uranium 7.600 MeV
alpha particle 7.074 MeV
The energy in b(i) can be transferred into electrical energy to run the instruments of a spacecraft. A spacecraft carries 33 kg of pure plutonium-238 at launch. The decay constant of plutonium is 2.50 × 10−10 s−1.
Solar radiation falls onto a metallic surface carried by the spacecraft causing the emission of photoelectrons. The radiation has passed through a filter so it is monochromatic. The spacecraft is moving away from the Sun.
State what is meant by the binding energy of a nucleus.
Draw, on the axes, a graph to show the variation with nucleon number of the binding energy per nucleon, . Numbers are not required on the vertical axis.
Identify, with a cross, on the graph in (a)(ii), the region of greatest stability.
Some unstable nuclei have many more neutrons than protons. Suggest the likely decay for these nuclei.
Show that the energy released in this decay is about 6 MeV.
The plutonium nucleus is at rest when it decays.
Calculate the ratio .
Estimate the power, in kW, that is available from the plutonium at launch.
The spacecraft will take 7.2 years (2.3 × 108 s) to reach a planet in the solar system. Estimate the power available to the spacecraft when it gets to the planet.
State and explain what happens to the kinetic energy of an emitted photoelectron.
State and explain what happens to the rate at which charge leaves the metallic surface.
Three identical light bulbs, X, Y and Z, each of resistance 4.0 Ω are connected to a cell of emf 12 V. The cell has negligible internal resistance.
When fully charged the space between the plates of the capacitor is filled with a dielectric with double the permittivity of a vacuum.
The switch S is initially open. Calculate the total power dissipated in the circuit.
The switch is now closed. State, without calculation, why the current in the cell will increase.
The switch is now closed. .
The cell is used to charge a parallel-plate capacitor in a vacuum. The fully charged capacitor is then connected to an ideal voltmeter.
The capacitance of the capacitor is 6.0 μF and the reading of the voltmeter is 12 V.
Calculate the energy stored in the capacitor.
Calculate the change in the energy stored in the capacitor.
Suggest, in terms of conservation of energy, the cause for the above change.
Potassium-40 decays by two processes.
The first process is that of beta-minus (β−) decay to form a calcium (Ca) nuclide.
Potassium-40 decays by a second process to argon-40. This decay accounts for 11 % of the total decay of the potassium-40.
Rocks can be dated by measuring the quantity of argon-40 gas trapped in them. One rock sample contains 340 µmol of potassium-40 and 12 µmol of argon-40.
Write down the equation for this decay.
Show that the initial quantity of potassium-40 in the rock sample was about 450 µmol.
The half-life of potassium-40 is 1.3 × 109 years. Estimate the age of the rock sample.
Outline how the decay constant of potassium-40 was determined in the laboratory for a pure sample of the nuclide.
The diagram shows the gravitational field lines of planet X.
Outline how this diagram shows that the gravitational field strength of planet X decreases with distance from the surface.
The diagram shows part of the surface of planet X. The gravitational potential at the surface of planet X is –3V and the gravitational potential at point Y is –V.
Sketch on the grid the equipotential surface corresponding to a gravitational potential of –2V.
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 × 1021 kg and its radius is 1.2 × 106 m. The planet has no atmosphere. Calculate the speed at which the meteorite will hit the surface.
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 × 105 J kg–1.