Derivation of Adiabatic Lapse Rate

AI Thread Summary
In the derivation of the adiabatic lapse rate using the first law of thermodynamics, the neglect of gravitational potential energy is questioned. It is noted that the work done by the air parcel, represented as PdV, is balanced by the change in internal energy, cvdT. However, the discussion highlights that gravitational potential energy is inherently included through the pressure P(z) due to the hydrostatic condition, suggesting that it should not be overlooked in the analysis. This indicates a need for clarity on the role of potential energy in the context of thermodynamic processes in the atmosphere.
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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, cvdT.

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

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