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Which specific heat applies when a gas is heated at constant volume?

  • A.About 1005 joules per kilogram per kelvin, which is the corresponding value when the pressure is held fixed
  • B.About 287 joules per kilogram per kelvin
  • C.About 4186 joules per kilogram per kelvin, which is the value appropriate to liquid water at room temperature
  • D.About 718 joules per kilogram per kelvin for dry air

Answer: D

At constant volume no work is done, so all the heat supplied raises the internal energy, and the specific heat is 718 joules per kilogram per kelvin for dry air. At constant pressure the gas must also do work of expansion, so more heat is needed for the same temperature rise, giving 1005. The difference of exactly 287 is the specific gas constant. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

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