Cp is always greater than Cv for a gas, which of the following statements provide, partly or wholly, the reason for this ?

Q: C_p is always greater than C_v for a gas, which of the following statements provide, partly or wholly, the reason for this ?
(i) No work is done by a gas at constant volume
(ii) I When a gas absorbs heat at constant pressure, its volume must change
(iii) For the same change in temperature, the internal energy of a gas changes by a smaller amount at constant volume than at constant pressure
(iv) The internal energy of an ideal gas is a function only of its temperature

(a) (i), (ii)

(b) (ii), (iii)

(c) (iii), (iv)

(d) all

Ans: (a)

Sol:(a) When heat Q is supplied at constant volume

Q = Q_v = ∆U = nC_v∆T

When heat Q is supplied at constant pressure

Q = Q_p = ∆U’ + ∆W

= n C_v (∆T)’ + ∆W

$\large C_v = \frac{Q}{n \Delta T} $

$\large C_p = \frac{Q}{n \Delta T’} $

(∆T)’ < (∆T) Hence, C_p > C_v