 Saturated vapor column on a dry adiabat

ID: saturated-vapor-column-on-a-dry-adiabat

For a dilute saturated vapour with constant latent heat

L

x = R_{A} / c_{p A}

ϵ = R_{A} / R_{B}

and

β = L / (R_{B} T_{s})

. Its mass path is

W = ϵ e_{s} (T_{s}) e^{β} E_{1} (β) / (gx)

. Substituting

y = β e^{x ζ}

in the log-pressure column integral proves this identity. For

β ≫ 1

W \sim c_{p A} T_{s} e_{s} (T_{s}) / (gL)

with relative correction

- 1/ β + O (β^{- 2})

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