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Adiabatic Lapse Rate, Dry


from the first law of thermodynamics
dQ = dU + deltaW = n · cv dT + P dV = 0
where cv is given in units of erg/K/mole and n is the number of moles. The derivative of the ideal gas law, P · V = n R T, is
V dP + P dV = n R dT
equating P dV and noting that R = cp - cv yields
dQ = n cv dT - V dP + n (cp-cv) dT
dQ = n cp dT - V dP = 0 for adiabatic
Cp = cp/<mw> and rho = n · <mw>/V so that
dT/dP = V/(n · cp) = 1 /(Cp · rho)
From hydrostatic equilibrium and the gas law we can convert from pressure to height coordinates:
dP = - g rho dz
dT/dz|a = -g/Cp
Gammaa ident -dT/dz|a = g/Cp


<g>
cm/s2
Cp
J/gm/K		Adiabatic
Lapse Rate
K/Km
Rg
J/gm/K		Autoconvective
Lapse Rate
K/Km
Venus889.890.850110.4680.1889247.104
Earth979.861.00409.7600.2871034.130
Mars374.100.83124.5000.1889219.802
Jupiter2425.6112.35911.9633.745186.477
Saturn1000.0914.01290.7143.892462.569
Uranus880.0713.01370.6763.614912.435
Neptune1110.4613.01370.8533.614913.072
Titan135.801.04401.3010.290004.683