OCR A-Level Physics: Thermal Physics and Ideal Gases

A fixed mass of an ideal gas is held in a rigid sealed container. The gas exerts a steady pressure on the container walls.

Explain, using the molecular model of kinetic theory, how the random motion of the gas molecules gives rise to the pressure on the walls of the container. In your answer you should refer to the change of momentum of the molecules at a wall, the rate (frequency) of the collisions, and at least two of the assumptions made about an ideal gas in this model.

(6 marks)

A student investigates the specific heat capacity of a metal by the method of mixtures. A 0.250 kg block of the metal is heated in boiling water to 100.0 °C and then quickly transferred into an insulated calorimeter containing 0.400 kg of water at 18.0 °C. The mixture is stirred and the highest steady temperature reached is recorded. The heat capacity of the calorimeter itself and any heat losses may be neglected.

Quantity	Value
Mass of metal block, $m_{\text{m}}$mm​	0.250 kg
Initial temperature of metal	100.0 °C
Mass of water, $m_{\text{w}}$mw​	0.400 kg
Initial temperature of water	18.0 °C
Final (mixture) temperature	24.5 °C
Specific heat capacity of water, $c_{\text{w}}$cw​	4180 J kg⁻¹ K⁻¹

(a) Calculate the thermal energy gained by the water as it warms to the final temperature. (2 marks)

(b) Hence determine the specific heat capacity of the metal, stating the principle you use. (4 marks)

A solid sample of a pure substance is heated by an electric immersion heater that delivers thermal energy at a constant rate of 60.0 W. The temperature of the sample is logged every 30 s as it warms, melts, and then continues to warm as a liquid. The mass of the sample is 0.120 kg.

Time / s	0	30	60	90	120	150	180
Temperature / °C	20	44	68	80	80	80	104

(a) Identify the time interval over which the sample is melting, and explain how the data show this. (2 marks)

(b) Explain, in terms of the molecules, why the temperature stays constant during this interval even though energy is still being supplied. (1 mark)

(c) Use the data for the constant-temperature interval to determine the specific latent heat of fusion of the substance. (2 marks)

A scuba diver carries a rigid steel cylinder of fixed internal volume $1.20 \times 10^{-2} \ \text{m}^3$1.20×10−2 m3 (12.0 litres). On the boat, before the dive, the air in the cylinder is at a pressure of 2.10 × 10⁷ Pa and a temperature of 27 °C. The air may be treated as an ideal gas. Use $R = 8.31 \ \text{J mol}^{-1}\,\text{K}^{-1}$R=8.31 J mol−1K−1.

(a) Calculate the amount of gas, in moles, sealed inside the cylinder. (3 marks)

(b) The diver descends into water at 7 °C, and the cylinder cools until the air inside reaches this temperature. The cylinder is rigid, so its volume is unchanged. Calculate the new pressure of the air. (2 marks)

Helium gas is held at a temperature of 290 K. A single helium atom has a mass of 6.64 × 10⁻²⁷ kg. The gas behaves ideally. Use the Boltzmann constant $k = 1.38 \times 10^{-23} \ \text{J K}^{-1}$k=1.38×10−23 J K−1.

(a) Calculate the mean translational kinetic energy of a helium atom at this temperature. (2 marks)

(b) Hence calculate the root-mean-square (rms) speed of the helium atoms. (2 marks)

The internal energy of a substance and the concept of absolute zero are central to thermal physics.

(a) State what is meant by the internal energy of a substance. (2 marks)

(b) State what is meant by absolute zero of temperature, and give its value on the Celsius scale. (1 mark)