Derive an expression for the fall in the liquid level during evaporation using a quasi-steadystate approach. Show that

\[\frac{d H}{d t}=\frac{M_{\mathrm{A}}}{ho_{\mathrm{L}}} N_{\mathrm{A}}\]

where \(N_{\mathrm{A}}\) is the instantaneous rate of evaporation, i.e., based on the current height of the vapor space \(H\).

Verify the following expression for the height change:

\[H^{2}-H_{0}^{2}=2 \frac{M_{\mathrm{A}}}{ho_{\mathrm{L}}} D_{\mathrm{A}} C y_{\mathrm{A}, \mathrm{s}} \mathcal{F} t\]

where \(\mathcal{F}\) is the drift correction factor. In this expression we assume that the bulk mole fraction of \(\mathrm{A}\) is zero.