The ratio of the molar heat capacities of a diatomic gas at constant pressure to that at constant volume is

Question

The ratio of the molar heat capacities of a diatomic gas at constant pressure to that at constant volume is (A) (7/5) (B) (3/2) (C) (3/5) (D) (5/2)

Tardigrade Admin · Accepted Answer

For a diatomic gas, Molar heat capacity at constant pressure, CP = (7/2) R Molar heat capacity at constant volume, CV = (5/2) R ∴ (CP/CV) = (7/2 R/5 /2 R) = 7/5

Q. The ratio of the molar heat capacities of a diatomic gas at constant pressure to that at constant volume is

$\frac{7}{5}$

$\frac{3}{2}$

$\frac{3}{5}$

$\frac{5}{2}$

For a diatomic gas,
Molar heat capacity at constant pressure, $C_{P} = \frac{7}{2} R$
Molar heat capacity at constant volume, $C_{V} = \frac{5}{2} R$
$∴ \frac{C _{P}}{C _{V}} = \frac{7/2 R}{5/2 R} = 7/5$