The latent heat of vaporization per unit mass of a pure substance at a given temperature, \(\lambda\), is defined as the difference in enthalpy between the saturated vapor and saturated liquid at the given temperature, \(T\). Since enthalpy is a thermodynamic function of state, show that \(\lambda\) can be evaluated from a known value of \(\lambda_{0}\) at a reference temperature \(T_{0}\) from the equation

where \(C_{p, A}\) and \(C_{A, L}\) are, respectively, the average heat capacities of gas and liquid between \(T_{0}\) and \(T\).

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A=+CA (T-T)-CAL (T-TO) 'p,A (8-34)