Question

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 C_Aand C_B be the molar heat capacities for the two processes,

Options

• C_A = C_B

• C_A < C_B

• C_A > C_B

•  C_A and C_B cannot be defined.

Answer 1

C_A > C_B
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. ΔU_A = ΔU_B.

But as , ΔW_A =ΔW_B this gives ΔQ_A = 2ΔQ_B. 

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 ΔQ_A = 2ΔQ_B, C_A > C_B.