For one mole of an ideal gas, the relationship between molar heat capacity at constant pressure ($C_p$) and constant volume ($C_v$) is derived from the first law of thermodynamics: $\Delta H = \Delta U + \Delta(PV)$. Since $\Delta H = C_p\Delta T$, $\Delta U = C_v\Delta T$, and $PV = RT$, we get $C_p\Delta T = C_v\Delta T + R\Delta T$, which simplifies to $C_p - C_v = R$.