Question

The ratio $\frac{C_p}{C_v}$ of the specific heats at a constant pressure and at a constant volume of any perfect gas

• A. cant be greater than $\frac{5}{4}$
• B. cant be greater than $\frac{3}{2}$
• C. cant be greater than $\frac{9}{7}$
• D. can have any value

Answer 1

The correct option is C cant be greater than $\frac{9}{7}$

$C_p$ and $C_v$ are specific heats at constant pressure and volume respectively.

$\frac{C_p}{C_v}=\frac{f+2}{f}$ where $f$ is the number of degrees of freedom for the gas.

For a perfect monoatomic gas $f=3$ where there areonly 3 translational degrees of freedom.

$\therefore$ $\frac{C_p}{C_v}=\frac{3+2}{3}=\frac{5}{3}$

For a diatomic molecule, $f=7$ since there are 3 degrees of translational, 2 rotational and 2 vibration degrees of freedom.

$\therefore$ $\frac{C_p}{C_v}=\frac{7+2}{7}=\frac{9}{7}$

Hence, the correct option is (C), max value is for a mono-atomic gas.