Question

$C_v$ and $C_p$ denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then,

• A. $C_p-C_v$ is larger for a diatomic ideal gas than for a monatomic ideal gas.
• B. $C_p+C_v$ is larger for a diatomic ideal gas than for a monatomic ideal gas.
• C. $\frac{C_p}{C_v}$ is larger for a diatomic ideal gas than for a monatomic ideal gas.
• D. $C_p.C_v$ is larger for a diatomic ideal gas than for a monatomic ideal gas.

Answer 1

Answer: (B), (D)

The correct options are
B $C_p+C_v$ is larger for a diatomic ideal gas than for a monatomic ideal gas.
D $C_p.C_v$ is larger for a diatomic ideal gas than for a monatomic ideal gas.

For a diatomic gas, $C_p+C_v=\frac{7R}{2}+\frac{5R}{2}=6R$
For a mono atomic gas, $\frac{5R}{2}+\frac{3R}{2}=4R$
$C_p.C_v$ for diatomic gas $=\frac{35R^2}{4}$
And for monatomic gas $=\frac{15R^2}{4}$
$\frac{C_p}{C_v}=\gamma =1+\frac{2}{f}$ is smaller for diatomic gas than for monatomic gas.
$C_p-C_v=R$