Question

Each molecules of a gas has $f$ degree of freedom. The ratio $\frac{C_p}{C_v}=\gamma$ for the gas is

• A. $1+\frac{f}{2}$
• B. $1+\frac{1}{f}$
• C. $1+\frac{2}{f}$
• D. $\frac{f}{2}$

Answer 1

The correct option is C $1+\frac{2}{f}$

The specific heat at constant pressure for gas,

$C_P=(\frac{f}{2}+1)R$

where, $R=$ universal gas constant

$f=$ degree of freedom

The specific heat at constant volume for gas,

$C_V=\frac{f}{2}R$

$\gamma =\frac{C_P}{C_V}$

$\gamma =\frac{(\frac{f}{2}+1)R}{\frac{f}{2}R}$

$\gamma =\frac{f+2}{f}$

$\gamma =1+\frac{2}{f}$

The correct option is C.