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

Solution :
As we know that $${C_p} - {C_V} = R$$
$$\eqalign{ & {C_p} = R + {C_V} \cr & {\text{and}}\,\,\frac{{{C_p}}}{{{C_V}}} = \gamma \,\,\left( {{\text{given}}} \right) \cr & {\text{So,}}\,\,\frac{{R + {C_V}}}{{{C_V}}} = \gamma \cr & \Rightarrow \gamma {C_V} = R + {C_V} \cr & \Rightarrow \gamma {C_V} - {C_V} = R \cr & \Rightarrow {C_V} = \frac{R}{{\gamma - 1}} \cr} $$