Adiabatic Atmosphere · F=ma 2019 #20

Physics · ideal-gases · first-law

Problem

In a simplified model of Earth's atmosphere, temperature decreases with altitude hh as T(h)=T0−ΛhT(h) = T_0 - \Lambda h, where Λ\Lambda is the lapse rate. Assuming the atmosphere is in adiabatic equilibrium and the air behaves as an ideal diatomic gas (γ=7/5\gamma = 7/5), derive the lapse rate Λ\Lambda in terms of gg, MM (molar mass of air), RR (gas constant), and γ\gamma.

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