# 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

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 CA and CB be the molar heat capacities for the two processes

(a) CA = CB

(b) CA < CB

(c) CA > CB

(d) None

Ans: (c)

Sol: ∆Q = ∆U + ∆W

In Process A:

∆Q = n CA ∆T = ∆U + ∆W …(i)

In Process B:

∆Q’ = n CB ∆T = ∆U + ∆W/2 …(ii)

Dividing (i) by (ii)

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

CA > CB