Work done by a sample of an ideal gas in a process A is double the work done in another process B. The temperature rises through the same amount in the two processes. If CAand CB be the molar heat capacities for the two processes,

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CA > CB According to the first law of thermodynamics, ΔQ = ΔU + ΔW, where Δ Q is the heat supplied to the system when ΔW work is done on the system and ΔU is the change in internal energy produced. Since the temperature rises by the same amount in both processes, change in internal energies are same, i.e. ΔUA = ΔUB. But as , ΔWA =ΔWB this gives ΔQA = 2ΔQB. Now, molar heat capacity of a gas, C = (triangleQ) /(ntriangleT), where Δ Q/n is the heat supplied to a mole of gas and ΔT is the change in temperature produced. As ΔQA = 2ΔQB, CA > CB.

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