For an ideal gas, the relationship between the molar heat capacity at constant pressure ($C_P$) and the molar heat capacity at constant volume ($C_V$) is known as Mayer's relation. By definition, enthalpy is given by $H = U + pV$. For one mole of an ideal gas, $pV = RT$. Therefore, $\Delta H = \Delta U + \Delta(RT) = \Delta U + R\Delta T$. Since $\Delta H = C_P\Delta T$ and $\Delta U = C_V\Delta T$, substituting these gives $C_P\Delta T = C_V\Delta T + R\Delta T$. Dividing the entire equation by $\Delta T$ yields $C_P = C_V + R$, which rearranges to $C_P - C_V = R$ .