Question

The heat capacity of a certain amount of a particular gas at constant pressure is greater than that at constant volume by 29.1 J/K. Match the items given in Column I with the items given in Column II.

List 1	List 2
If the gas is monatomic, heat capacity at constant volume	131 J/K
If the gas monatomic, heat capacity at constant pressure	43.7 J/K
If the gas is rigid diatomic, heat capacity at constant pressure	72.7 J/K
If the gas is vibrating diatomic, heat capacity at constant pressure	102 J/K

• A. A$\to$2, B$\to$3, C$\to$4, D$\to$1
• B. B$\to$1, C$\to$3, D$\to$4, A$\to$1
• C. C$\to$1, D$\to$3, A$\to$4, B$\to$1
• D. D$\to$1, A$\to$3, B$\to$4, C$\to$1

Answer 1

The correct option is A A$\to$2, B$\to$3, C$\to$4, D$\to$1

Given:
$C_p-C_v=29.1$ ....(1)
For monoatomic gas, $\frac{C_p}{C_v}=\frac{5}{3}$ ...(2)
Substituting for $C_p$ in (1), we get $\frac{2}{3}{C}_v=29.1$
$\therefore C_v=43.7J{K}^{-1}$
$C_p=43.7+29.1=72.9J{K}^{-1}$
If the gas is diatomic $C_v=\frac{5}{7}{C}_p$
$\therefore \frac{2}{7}{C}_p=29.1$
$\therefore CP=102J{K}^{-1}$
If the gas is vibrating di-atomic $C_v=\frac{7}{9}{C}_p$
$\therefore \frac{2}{9}{C}_p=29.1$
$\therefore C_p=131J{K}^{-1}$