1. 1
   A cylinder fitted with a frictionless piston contains 0.50 mol of a monatomic ideal gas. The gas is heated slowly so that its pressure stays at 1.0 × 10⁵ Pa while its temperature rises from 300 K to 400 K and the piston moves outwards.

   (a)

   What is the change in internal energy of the gas?

   [1 mark]

   • A623 J
   • B415 J
   • C1040 J
   • D208 J

   (b)

   Which term describes this process?

   [1 mark]

   • AIsovolumetric
   • BIsobaric
   • CIsothermal
   • DAdiabatic

   (c)

   Calculate the energy supplied to the gas as heat.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A 0.20 kg block of ice at 0 °C is left on a tray in a large room whose air stays at 25 °C. The ice slowly melts into water at 0 °C, absorbing all the energy it needs from the room. The specific latent heat of fusion of ice is 3.34 × 10⁵ J kg⁻¹.

   (a)

   What is the change in entropy of the ice as it melts?

   [1 mark]

   • A0 J K⁻¹
   • B224 J K⁻¹
   • C2.67 × 10³ J K⁻¹
   • D245 J K⁻¹

   (b)

   Which statement about the entropy changes is correct?

   [1 mark]

   • AThe entropy of the room increases
   • BThe total entropy of the ice and the room stays constant because energy is conserved
   • CThe entropy of the room decreases by less than the entropy of the ice increases
   • DThe entropy of the ice decreases because it absorbs energy

   (c)

   Using the equation S = kB ln Ω, explain why the entropy of the water increases as it melts.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   An engine test gives these results for each cycle. The working gas absorbs 2.4 kJ as heat from a hot reservoir at 900 K and releases 1.7 kJ as heat to the surroundings at 300 K, returning to its initial state at the end of the cycle.

   (a)

   Determine the efficiency of the engine and compare it with the maximum possible efficiency for these reservoir temperatures.

   [3 marks]

   (b)

   A company claims a new design would absorb 2.4 kJ and release only 0.60 kJ per cycle, between the same reservoirs. Evaluate this claim using the second law of thermodynamics.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   In a model of a diesel engine's compression stroke, a monatomic ideal gas starts at a pressure of 1.0 × 10⁵ Pa, a volume of 2.4 × 10⁻³ m³ and a temperature of 300 K. It is compressed rapidly and adiabatically to a volume of 0.30 × 10⁻³ m³. For an adiabatic process in a monatomic ideal gas, PV^(5/3) is constant.

   (a)

   Determine the final pressure and temperature of the gas and the work done on it during the compression.

   [6 marks]

   (b)

   Compare this adiabatic compression with an isothermal compression of the same gas between the same two volumes, and discuss how such processes are combined in a heat engine, with reference to the Carnot cycle.

   [6 marks]

   Total for question 4: 12 marks

End of questions