Worksheet: Heat Capacity

In this worksheet, we will practice calculating the heat capacity of an object from the amount of heat exchanged and the change in temperature.


The heat capacity of a substance can be measured under either constant-volume or constant-pressure conditions. Which of the following sets of relationships between 𝐶 𝑣 (heat capacity under constant-volume conditions) and 𝐶 𝑝 (heat capacity under constant-pressure conditions) are always true?

  • A 𝐶 𝑣 (gas) > 𝐶 𝑣 (liquid) > 𝐶 𝑣 (solid) and 𝐶 > 𝐶 𝑣 𝑝 in all phases
  • B 𝐶 𝑣 (gas) 𝐶 𝑣 (solid) and 𝐶 𝑝 (liquid) 𝐶 𝑣 (liquid)
  • C 𝐶 𝑝 approaches a value of 0 as the sample temperature approaches 0 K but increases without bound as the sample temperature is increased.
  • D 𝐶 𝑝 (gas) > 𝐶 𝑣 (gas); 𝐶 𝑝 (solid) 𝐶 𝑣 (solid); and 𝐶 𝑝 (gas) 𝐶 𝑝 (solid)


Suppose 2 moles of water at 333 K are added to 4 moles of water at 293 K. What would be the entropy change associated with this process, assuming that there is no exchange of heat with the surroundings? (The heat capacity of water is 𝐶 = 7 5 . 3 / 𝑝 , 𝑚 J K m o l and may be considered to be independent of temperature.)


Two 1-mole blocks of aluminium, one at 273 K and the other at 373 K, are brought into thermal contact. What will be the temperature of the two blocks when they have reached thermal equilibrium, and what will be the total entropy change ( Δ 𝑆 ) t o t that accompanies the thermal equilibration process? (Assume that the two blocks of aluminium are in a container with walls that keep them completely isolated from outside surroundings, and take the heat capacity of the aluminium blocks to be 𝐶 = 2 4 . 3 5 / 𝑝 , 𝑚 J K m o l .)

  • A 𝑇 = 3 2 3 e q u i l K and Δ 𝑆 = 0 . 5 9 / t o t J K
  • B 𝑇 = 3 2 3 e q u i l K and Δ 𝑆 = 0 t o t
  • C 𝑇 = 3 7 3 e q u i l K and Δ 𝑆 = 6 . 2 1 / t o t J K
  • D 𝑇 = 3 2 3 e q u i l K and Δ 𝑆 = 0 . 5 9 / t o t J K

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