Explain why two objects made of different materials but with the same mass, initially at the same high temperature, cool down to room temperature at different rates when placed in identical surroundings.

IB DP Physics Higher Level (2023 syllabus) — B.1 Thermal energy transfers · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

Two metal blocks, one made of aluminium and one made of lead, each with a mass of 500 g and initially at 200 °C, are placed on a thermally insulating surface in a room at 20 °C.

Model answer (4 marks)

Both blocks lose heat to the surroundings at a rate that depends on the temperature difference with the room and on their surface properties, which are the same for the two blocks. The rate of temperature change of each block is given by \(\frac{dT}{dt}=\frac{Q̇}{m c}\), where \(Q̇\) is the heat loss rate, \(m\) the mass and \(c\) the specific heat capacity. Aluminium has a much larger specific heat capacity (c≈900 J kg⁻¹ K⁻¹) than lead (c≈130 J kg⁻¹ K⁻¹). Therefore, for the same heat loss rate, the aluminium block’s temperature decreases more slowly than the lead block’s. Consequently, the lead block reaches room temperature faster while the aluminium block takes longer to cool.

Examiner tips

  • Mention the heat loss rate depends on temperature difference and surface properties
  • State the cooling equation dT/dt=Q̇/(m c)
  • Compare the specific heat capacities of aluminium and lead
  • Explain the effect on cooling rate

Common mistakes

  • Confusing specific heat capacity with thermal conductivity
  • Assuming the same temperature change for both blocks
  • Ignoring that the heat loss rate is identical for both

Mark scheme (4 marks)

  1. Both blocks lose thermal energy to the surroundings at a rate that depends on their temperature difference with the surroundings and on surface properties, which are identical here.
  2. The temperature change of each block depends on its specific heat capacity; a material with a larger specific heat capacity requires more thermal energy to change its temperature by 1 K per unit mass.
  3. Aluminium has a much greater specific heat capacity than lead, so for the same rate of energy loss, aluminium's temperature decreases more slowly.
  4. Therefore the lead block reaches room temperature faster / the aluminium block takes longer to cool because its temperature decreases by a smaller amount for each unit of energy transferred away.

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