For an ideal gas, the relationship between the molar heat capacity at constant pressure ($C_P$) and at constant volume ($C_V$) is given by Mayer's relation: $C_P - C_V = R$ . Given the ratio of specific heats is $\gamma = \frac{C_P}{C_V}$, we can substitute $C_P = \gamma C_V$ into Mayer's relation: $\gamma C_V - C_V = R$ $C_V(\gamma - 1) = R$ $C_V = \frac{R}{\gamma - 1}$.