Dew-point scale height in dry ascent
= Dew-point scale height in dry ascent
{title2=$H=L_vR_d/(gR_v)$}
Fixed <water vapor> <mole fraction> gives $d\ln e_v=d\ln p$. Combining <hydrostatic balance> with the <Clausius-Clapeyron relation> yields $d\ln T_D/dz=-(gR_v/L_vR_d)(T_D/T)$. If $T_D/T\simeq1$, 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.