I am aware of the derivation for the dry adiabatic lapse rate using the enthalpy approach: nc(adsbygoogle = window.adsbygoogle || []).push({}); _{p}dT+VdP=0, but I can't seem to spot the error in my own derivation. If anyone sees it, I would be especially grateful.

dU=[tex]\delta[/tex]Q-[tex]\delta[/tex]W

nc_{v}dT=0 - PdV

[tex]\frac{dT}{dV}[/tex]=-[tex]\frac{P}{nc_{v}}[/tex]

[tex]\frac{dT}{dV}[/tex] [tex]\frac{dV}{dz}[/tex]= -[tex]\frac{P}{nc_{v}}[/tex] [tex]\frac{dV}{dz}[/tex]=-[tex]\frac{P}{nc_{v}}[/tex] [tex]\frac{dV}{dP}[/tex] [tex]\frac{dP}{dz}[/tex] by the chain rule

[tex]\frac{dT}{dz}[/tex] = [tex]\frac{-P}{nc_{v}}[/tex] [tex]\frac{-nRT}{P^{2}}[/tex] [tex]\frac{-MPg}{RT}[/tex] = [tex]\frac{-Mg}{c_{v}}[/tex]

I obtained [tex]\frac{dV}{dP}[/tex] by differentiating PV = nRT and [tex]\frac{dP}{dz}[/tex] from the hydrostatic equation, substituting

density = mass/volume = MP/RT, where M is molar mass in g/mol.

For some reason, I obtain c_{v}in my derivation instead of the correct c_{p}.

Any thoughts?

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# Dry adiabatic lapse rate

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