42 - Evaporation

Material Balance: \[\begin{aligned} F &= L + V \\ F\;x_F &= L\;x_L \end{aligned}\]

Energy Balance: \[\begin{aligned} FH_F + SH_S &= LH_L + VH_V + SH_C \\ FH_F + S(H_S-H_C) &= LH_L + VH_V \\ FH_F + S\lambda_S &= LH_L + VH_V \\ By taking reference temperature as that of boiling point of solution, we get\\ FC_P(T_F-T_1) + S\lambda_S &= L\times0 + V\lambda_V \\ S\lambda_S &= V\lambda_V - FC_P(T_F-T_1) \end{aligned}\] where \(\lambda_V\) is the latent heat of vaporization of water vapor at \(T_1\).

If feed is at \(T_1\) (i.e., at the boiling point of solution), then, \[S\lambda_S = V\lambda_V\]