 Solution

For constant gravitational acceleration, hydrostatic balance gives the atmospheric column mass $m=p_{\mathrm{sfc}}/g$, with negligible pressure at the top. For the same surface temperature $T_{\ast }<T_{\mathrm{sfc}}<T_c$, the variable latent heat gives a smaller integrated $\ln (p_{\mathrm{sfc}}/p_{\ast })$, and henceMultiplying by the same planetary surface area gives the same comparison for total mass. The models agree for a surface at or below the triple point, where they use the same sublimation branch. The comparison assumes the same surface temperature, rather than the same surface pressure.