Q1
• Explain how the internal energy of an ideal gas is related to its temperature. In your answer, you should use appropriate technical terms spelled correctly.
A weather balloon is designed to be inflated to a maximum volume of 1.4 ×104 m3.
To launch the balloon, it is partially inflated with 80 kg of helium at a pressure of
1.0 ×105 Pa and a temperature of 21 °C.
molar mass of helium = 0.004 kg mol−1
• Calculate the volume of the partially inflated balloon.
To limit the maximum height that the balloon can reach, helium is allowed to leak out through a control valve.
• Determine the number of moles of helium that need to escape for the weather
balloon to reach its maximum volume when the pressure is 1.2 ×103 Pa and the
The space probe, Curiosity, roaming on the surface of Mars, is powered by a radioisotope thermoelectric generator (RTG). The generator transforms thermal energy into electrical energy. The thermal energy comes from the radioactive decay of plutonium-238. The diagram shows an image of Curiosity.
• Complete the following reaction.
• Complete the following reaction.
Plutonium-238 is an alpha-emitter with a half-life of 88 years. The kinetic energy
produced during each decay is 9.0 ×10−13 J. The RTG on Curiosity produces 120 W of
electrical power from 2000 W of thermal power.
• Calculate the mass of plutonium-238 on board Curiosity.
molar mass of plutonium-238 = 0.238 kg mol−1
Q3
The unit of magnetic flux density is the tesla, T. • Express this unit in terms of kg, C and s.
The diagram shows the circular path travelled by electrons in a region of uniform magnetic field in a vacuum.
The direction of the magnetic field is perpendicular to the plane of the paper.
The electrons have a speed of 7.0 ×106 m s−1 and travel in a circular path of diameter
5.0 cm.
• Calculate the magnetic flux density B.
• Calculate the period T of the electrons in their circular orbit.
This question is about electric fields. The diagram shows the electric field pattern drawn by a student for two oppositely charged plates.
• State two errors made by the student in this drawing of the field pattern.
At a distance r from the centre of a radioactive nucleus the electric field strength is E.
The diagram shows the graph of the electric field strength E against 1/r2.
The electric field strength is given by the equation:
The radioactive nucleus emits an alpha particle.
• State the change, if any, to the graph shown above for the resultant (daughter) nucleus. Explain your answer.
A negatively charged droplet of oil is held stationary between two horizontal plates. The potential difference between the plates is 1.50 kV. The diagram shows the two forces acting on this charged droplet.
The droplet is spherical and has a radius of 1.27 ×10−6 m.
The density of oil is 950 kg m−3. The separation between the plates is 2.10 cm.
• Show that the magnitude of the charge on the droplet is about 1.1 ×10−18 C.
A charged capacitor is connected across the ends of a negative temperature coefficient (NTC) thermistor kept at a fixed temperature. The capacitor discharges through the thermistor. The potential difference V across the capacitor is maximum at time t = 0.
• On the axes, carefully sketch a graph to show how the potential difference V across the capacitor varies with time t. Label this graph L.
The temperature of the thermistor is increased to a higher fixed value.
• Sketch another graph to show the variation of V with t when the same charged capacitor is discharged across the ends of the hotter thermistor.
Label this graph H.
• Explain how you can show that the graph sketched in (i) has a constant-ratio property (exponential decay).
The diagram shows an electrical circuit.
The cell has e.m.f. 1.4 V and negligible internal resistance. The values of the capacitors and the resistor are shown in above. A mechanical switch vibrates between contacts X and Y at a frequency of 120 Hz.
• Calculate the time constant of the circuit.
• Calculate the value of the average current I in the resistor. Assume that the capacitors are fully discharged between each throw of the switch.
• The frequency of vibration of the mechanical switch is doubled. Explain why the average current in the circuit is not doubled.
Q6
• Explain what is meant by the binding energy of a nucleus.
The fusion of protons occurs in a star when the temperature within the core is greater than about 107 K. It takes the fusion of 4 protons to form a helium-4 (4-He) nucleus. In this process, known as the proton–proton cycle, energy is released.
The net energy released in producing a single helium-4 nucleus is 4.53 ×10–12 J.
• Calculate the binding energy per nucleon of the helium-4 nucleus.
The fusion of helium nuclei to make heavier elements occurs in red giants at temperatures above 108 K.
• Explain why fusion of helium requires higher temperatures than the fusion of hydrogen (protons).
• Estimate the mean speed of helium nuclei at a temperature of 108 K.
Q7
The diagram shows a horizontal current-carrying wire placed in a uniform magnetic field.
The magnetic field of flux density 0.070 T is at right angles to the wire and into the
plane of the paper. The weight of a 1.0 cm length of the wire is 6.8 ×10–5 N. The current
I in the wire is such that the vertical upward force on the wire due to the magnetic field is equal to the weight of the wire.
• Calculate the current I in the wire.
• Suggest why it would be impossible for overhead cables carrying an alternating current to float in the Earth’s magnetic field.
A charged particle enters a region of uniform magnetic field. The diagram shows the path of this particle.
The direction of the field is perpendicular to the plane of the paper. The magnetic field has flux density B. The particle has mass m, charge Q and speed v. The particle travels in a circular arc of radius r in the magnetic field.
• Derive an equation for the radius r in terms of B, m, Q and v.
A thin aluminium plate is now placed in the magnetic field. The diagram shows the path of an unknown charged particle.
The particle loses some of its kinetic energy as it travels through the plate. The initial radius of the path of the particle before it enters the plate is 4.8 cm. After leaving the plate the final radius of the path of the particle is 1.2 cm.
Q8
The diagram shows a negatively charged metal sphere close to a positively charged metal plate.
• On the diagram draw a minimum of five field lines to show the electric field pattern between the plate and the sphere.
The diagram shows two positively charged particles A and B.
At point X, the magnitude of the resultant electric field strength due to the particles A and B is zero.
distance d from the particle A.
The diagram below shows a stationary positively charged particle.
This particle creates both electric and gravitational fields in the space around it. Explain why the ratio of the electric field strength E to the gravitational field strength g at any point around this charge is independent of its distance from the particle.
