 Dew-point scale height in dry ascent

Fixed water vapor mole fraction gives $d\ln e_v=d\ln p$. Combining hydrostatic balance with the Clausius-Clapeyron relation yields $d\ln T_D/dz=-(g{R}_v/L_v{R}_d)(T_D/T)$. If $T_D/T\simeq 1$, then $T_D(z)\simeq T_D(0)e^{-z/H}$. All ratios use absolute temperature; constant latent heat, fixed composition and approximate parcel–environment temperature equality are required.