The molar specific heats of an ideal gas at constant pressure and volume are denoted by C_p and C_v respectively. If \(\gamma=\frac{C_P}{C_V}\) and R is the universal gas constant, then C_v is equal to:

\(\frac{R}{\gamma - 1}\)

\(C_P - C_V = R\) -------(1)

and \(\frac{C_P}{C_V} = \gamma \)

Dividing equation (1) by $C_V$, 

$\frac{C_P}{C_V}$ - $\frac{C_V}{C_V}$ = $\frac{R}{C_V}$

\(\gamma\) - 1 =  $\frac{R}{C_V}$

$C_V = \frac{R}{\gamma - 1}$