Given the molar specific heat at constant pressure, $C_P = \frac{7}{2}R$.

For an ideal gas, Mayer's relation states: $C_P - C_V = R$

Solving for molar specific heat at constant volume ($C_V$): $C_V = C_P - R$ $C_V = \frac{7}{2}R - R = \frac{7}{2}R - \frac{2}{2}R = \frac{5}{2}R$

The ratio of specific heats ($\gamma$) is defined as: $\gamma = \frac{C_P}{C_V}$

Substituting the values: $\gamma = \frac{\frac{7}{2}R}{\frac{5}{2}R} = \frac{7}{5}$