Derivation of Adiabatic Lapse Rate

[pm272]

In the derivation of the adiabatic lapse rate, upon using the 1st law of thermodynamics: Why is potential energy neglected? The parcel of air is doing work PdV which is balanced by the internal energy term, c_vdT.

I can't think of a reason to neglect gravitational potential energy here.

Thanks.

 

[olivermsun]

The gravitational potential energy appears through the pressure P(z) because of the hydrostatic condition.