The first law of thermodynamics and the dry adiabatic lapse rate

[karen_lorr]

Say there is a parcel of air rising and cooling, what is going?

Is it that the net kinetic energy (Temperature) of the parcel is distributed over the (new and larger) area/volume?
Or
Is it that the parcel is undertaking work as it presses outwards and so looses a corresponding amount of kinetic energy to the area outside the parcel?

Sorry but I’m confused. It may be a mixture of both.

Has anyone got a simple to understand explanation of why, as a parcel of air raises and expands (either vertically, horizontally or some of both, it will cool

 

[D H]

The key point here is the assumption of an adiabatic process. The parcel of air is not exchanging heat or mass with the environment. The parcel of air is however expanding. That means it is doing work on the environment, and that in turn means the parcel of air is losing energy. The temperature drops. The wikipedia article on adiabatic processes, http://en.wikipedia.org/wiki/Adiaba...ous_formula_for_adiabatic_heating_and_cooling, contains a nice derivation of the relevant equations for an ideal gas.

 

[karen_lorr]

Hi
Thanks for the answer.

I am trying to understand exactly what is going on. If no heat/energy is lost to the environment, then (I can't think of another way to put this) where has it gone?

I assume the net temp (avg kinetic energy) is still the same - as no energy has been lost.

So is it just that the energy is spread over a larger volume, thus reduce the local temp?
or
As work has been performed - what is the work and where has the energy gone, if none has been lost?

I have looked all over the web for this and can't find an answer.

Thanks

 

[D H]

Emphasis mine:

I am trying to understand exactly what is going on. If no heat/energy is lost to the environment, then (I can't think of another way to put this) where has it gone?

I assume the net temp (avg kinetic energy) is still the same - as no energy has been lost.

This is the heart of your misunderstanding. You are viewing the parcel of air as either isolated or undergoing a free expansion. This is not the case. The parcel of air has to push the surrounding air aside to make room for the expansion. It is doing work on the external environment. Work is one of the three major mechanisms via which a system can transfer energy to or from the external environment. The other two are mass flow and heat flow. The latter two do not occur here, by the assumption of an adiabatic process. Adiabatic processes do not preclude energy transfer via work.

 

[karen_lorr]

Thank you.
You have explained it wonderfully.