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.

 

[Huyen401]

Hi there,

The reason for neglecting potential energy in the derivation of the adiabatic lapse rate is because we are assuming a vertically stable atmosphere in which the air parcel is not changing its altitude. In this case, there is no change in potential energy, so it can be neglected in the overall energy balance.

Additionally, the adiabatic lapse rate is derived assuming that the air parcel is only exchanging heat with its surroundings through compression and expansion, not through any other processes. In this scenario, the work done by the air parcel (PdV) is balanced by the change in internal energy (cvdT), as you mentioned.

If we were to consider potential energy in this scenario, it would introduce an additional source of energy exchange and would complicate the derivation of the adiabatic lapse rate. Therefore, for the sake of simplicity and to focus on the main processes at play, potential energy is typically neglected in this context.

I hope this helps to clarify the reasoning behind neglecting potential energy in the derivation. Let me know if you have any further questions or concerns.