AQA A-Level Physics: Thermal Physics

The behaviour of a real gas at low pressure can be modelled using the molecular kinetic theory of an ideal gas. The model rests on a small number of simplifying assumptions about the molecules and their motion.

Explain the main assumptions of the molecular kinetic theory model of an ideal gas, and explain how the collisions of the molecules with the walls of the container give rise to the pressure of the gas. Your answer should refer to the change in momentum of the molecules and to the factors that affect the force exerted on the walls.

(6 marks)

A student determines the specific heat capacity of a 0.80 kg aluminium block using an electrical method. An insulated heater of resistance is embedded in the block and connected to a power supply. The student records the following readings.

Quantity	Value
Mass of aluminium block	0.80 kg
Potential difference across heater	12 V
Current through heater	4.0 A
Time switched on	5.0 min
Temperature rise of block	49 °C

(a) Calculate the electrical energy supplied to the heater. (2 marks)

(b) Use your answer to part (a) to calculate the student's experimental value for the specific heat capacity of aluminium. (2 marks)

(c) The accepted value for the specific heat capacity of aluminium is $900 \ \text{J kg}^{-1}\,\text{K}^{-1}$900 J kg−1K−1. The student's value is higher than this. Calculate the energy that must have been lost to the surroundings during the experiment, assuming the accepted value is correct. (2 marks)

A fixed mass of an ideal gas is compressed slowly at a constant temperature inside a sealed cylinder fitted with a frictionless piston. The pressure and volume are recorded at four stages of the compression.

Pressure / kPa	Volume / dm³
100	2.40
150	1.60
200	1.20
300	?

(a) Use the data to show that the gas obeys Boyle's law over this range, and hence determine the missing volume at a pressure of 300 kPa. (3 marks)

(b) State and explain, in terms of the kinetic theory, what happens to the average kinetic energy of the molecules during this compression, and hence what happens to the temperature of the gas. (2 marks)

A rigid steel cylinder of internal volume $0.020 \ \text{m}^3$0.020 m3 contains compressed nitrogen, which behaves as an ideal gas. When the cylinder is in a workshop at a temperature of 17 °C, the gauge shows the gas to be at a pressure of $1.5 \times 10^{6} \ \text{Pa}$1.5×106 Pa.

Take $R = 8.31 \ \text{J K}^{-1}\,\text{mol}^{-1}$R=8.31 J K−1mol−1 and the Avogadro constant $N_A = 6.02 \times 10^{23} \ \text{mol}^{-1}$NA​=6.02×1023 mol−1.

(a) Calculate the number of nitrogen molecules in the cylinder. (3 marks)

(b) The full cylinder is left in direct sunlight and the gas temperature rises to 77 °C. Assuming the cylinder does not expand, calculate the new pressure of the gas. (2 marks)

A sealed flask contains oxygen gas, which may be treated as an ideal gas, at a temperature of 300 K. The molar mass of oxygen is $0.032 \ \text{kg mol}^{-1}$0.032 kg mol−1.

Take the Boltzmann constant $k = 1.38 \times 10^{-23} \ \text{J K}^{-1}$k=1.38×10−23 J K−1 and the Avogadro constant $N_A = 6.02 \times 10^{23} \ \text{mol}^{-1}$NA​=6.02×1023 mol−1.

(a) Calculate the mean translational kinetic energy of an oxygen molecule at this temperature. (2 marks)

(b) Calculate the root-mean-square (r.m.s.) speed of the oxygen molecules. (2 marks)

A pure solid is heated steadily at a constant rate. Its temperature rises until it reaches the melting point, where it stays constant until all the solid has melted, even though energy is still being supplied.

(a) Define the specific latent heat of fusion of a substance. (1 mark)

(b) Explain, in terms of the energy of the molecules, why the temperature stays constant while the solid melts even though thermal energy is still being supplied. (2 marks)