Home · A-Level 9702 · Temperature · Thermal equilibrium · Practice
A2 · Practice questions · Thermal equilibrium

Equal temperature means no net flow.

Six original Cambridge-style questions on the direction of thermal energy transfer, the meaning of thermal equilibrium, and the final temperature when two bodies are brought into contact.

Original questions All questions on this page are original work, written in the Cambridge AS & A Level style. They are not from past papers. They test the same concepts and skills the syllabus rewards.
Keep these straight

Temperature sets the direction, not the amount.

01
Analysis
[2 marks]

Body A is in thermal equilibrium with body B, and body B is in thermal equilibrium with body C. State what can be deduced about bodies A and C, and explain your reasoning.

  • A and C are at the same temperature, so they would be in thermal equilibrium with each other if placed in contact, with no net transfer of thermal energy between them. ✓
  • Thermal equilibrium means equal temperature: A has the same temperature as B, and C has the same temperature as B, so A and C share one temperature. ✓
02
Calculation
[3 marks]

In a well-lagged container, 0.30 kg of water at 70 °C is mixed with 0.30 kg of water at 10 °C. Calculate the final temperature of the mixture and the thermal energy transferred between the two samples. The specific heat capacity of water is 4200 J kg⁻¹ K⁻¹.

  • Equal masses of the same substance: energy lost by the hot water equals energy gained by the cold water, so the temperature changes are equal and the final temperature is the mean, (70 + 10) / 2 = 40 °C. ✓
  • Energy transferred Q = mcΔθ = 0.30 × 4200 × (70 − 40) = 3.8 × 10⁴ J. ✓
  • This energy passes from the hotter sample to the colder one until both are at 40 °C and in thermal equilibrium. ✓
03
Analysis
[3 marks]

A small steel ball bearing at 400 °C is dropped into a large swimming pool at 20 °C. The pool contains far more internal energy than the ball. State the direction of the net transfer of thermal energy, explain why the amount of internal energy stored does not decide this direction, and describe the final state of the ball and the pool.

  • Net thermal energy is transferred from the ball to the pool, because the ball is at the higher temperature. ✓
  • Temperature, not internal energy, determines the direction of net flow; the pool stores more internal energy only because it contains vastly more particles, while its particles have lower mean kinetic energy than those of the ball. ✓
  • The transfer stops when the ball and the pool are at the same temperature (thermal equilibrium), which is barely above 20 °C because the pool's heat capacity is so large. ✓
04
Calculation
[3 marks]

A copper block of mass 0.50 kg at 95 °C is lowered into 0.80 kg of water at 20 °C in an insulated container of negligible heat capacity. Calculate the temperature at which the block and the water reach thermal equilibrium. Specific heat capacity of copper = 390 J kg⁻¹ K⁻¹, of water = 4200 J kg⁻¹ K⁻¹.

  • At equilibrium both are at the same temperature θ, and energy lost by the copper equals energy gained by the water: 0.50 × 390 × (95 − θ) = 0.80 × 4200 × (θ − 20). ✓
  • 195(95 − θ) = 3360(θ − 20), so 18 525 + 67 200 = 3555θ. ✓
  • θ = 85 725 / 3555 = 24 °C; the water's much larger heat capacity keeps the final temperature close to its own starting value. ✓
05
Analysis
[2 marks]

A liquid-in-glass thermometer is placed in a beaker of warm water. Explain why the reading must be allowed to settle before it is recorded, and state why the thermometer should have a much smaller heat capacity than the water.

  • Thermal energy flows from the water to the cooler thermometer until the two reach thermal equilibrium; only then is the thermometer at the water's temperature and its reading meaningful. ✓
  • With a small heat capacity the thermometer takes very little energy from the water, so the water's temperature is almost unchanged by the measurement. ✓
06
Calculation
[4 marks]

An aluminium block of mass 2.0 kg at 150 °C is placed in contact with an iron block of mass 3.0 kg at 20 °C. The pair is isolated from the surroundings. Specific heat capacity of aluminium = 900 J kg⁻¹ K⁻¹, of iron = 450 J kg⁻¹ K⁻¹.

(a) State the direction of the net transfer of thermal energy, and when it stops. (b) Calculate the final temperature of the blocks. (c) Calculate the thermal energy transferred. (d) State whether the two blocks have equal internal energies at equilibrium.

  • (a) Net energy is transferred from the aluminium (higher temperature) to the iron, and it stops when the two blocks reach the same temperature. ✓
  • (b) 2.0 × 900 × (150 − θ) = 3.0 × 450 × (θ − 20), so 270 000 + 27 000 = 3150θ and θ = 94 °C. ✓
  • (c) Q = 2.0 × 900 × (150 − 94.3) = 1.0 × 10⁵ J, which is also the energy gained by the iron, 3.0 × 450 × 74.3. ✓
  • (d) No: equilibrium means equal temperatures, but the internal energies differ because the blocks have different masses and materials. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.