For an ideal gas, the relationship between the molar heat capacities at constant pressure ($C_{p,m}$) and constant volume ($C_{v,m}$) is given by Mayer's relation: $C_{p,m} - C_{v,m} = R$, where $R$ is the universal gas constant .

The question specifies that $C_p$ and $C_v$ are specific heats per unit mass. The relationship between molar heat capacity and specific heat capacity is: $\text{Molar Heat Capacity} = \text{Specific Heat Capacity} \times \text{Molecular Weight} (M)$. Substituting this into Mayer's relation: $(M C_p) - (M C_v) = R$ $M(C_p - C_v) = R$ $C_p - C_v = \frac{R}{M}$.