Q: 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_{A} and C_{B} be the molar heat capacities for the two processes

(a) C_{A} = C_{B}

(b) C_{A} < C_{B}

(c) C_{A} > C_{B}

(d) None

Ans: (c)

Sol: ∆Q = ∆U + ∆W

In Process A:

∆Q = n C_{A} ∆T = ∆U + ∆W …(i)

In Process B:

∆Q’ = n C_{B} ∆T = ∆U + ∆W/2 …(ii)

Dividing (i) by (ii)

$\large \frac{C_A}{C_B} = \frac{\Delta U + \Delta W}{\Delta U + \Delta W/2} > 1 $

C_{A} > C_{B}