# Is there an Altitude Dependence on Helmholtz Free Energy?

1. Dec 3, 2015

1. The problem statement, all variables and given/known data

The density of nitrogen molecules is larger at a sea level than at a higher elevation. Assuming thermal equilibrium, what is the altitude dependence of the (Helmholtz)free energy per particle?

2. Relevant equations
F=U-TS, not sure if anything else is relevant

3. The attempt at a solution
My initial guess is no. Mainly because looking at the equation for free energy, the temperature is the same because of thermal equilibrium, and the internal energy is the same. Since we are talking about free energy per particle, I would imagine density would have nothing to do with it. But at a higher altitude, the pressure would be less, and I am not exactly sure how pressure affects the free energy. Thanks. My options are that the free energy would be:

greater at sea level compared to higher elevation
less than sea level
the same

2. Dec 4, 2015

### Staff: Mentor

In the lower atmosphere, the temperature decreases with altitude. The lapse rate is on the order of about 10 K per km. You can also calculate the average pressure at any altitude from the barotropic equation. Why don't you just calculate the Helmholtz free energy per mole as a function of altitude and see what it comes out to be?

Chet

3. Dec 5, 2015

isnt the fact that the question states it is in thermal equilibrium the temperature will be the same?

4. Dec 5, 2015

### Staff: Mentor

Actually, I don't know what they mean. In the actual atmosphere, the temperature decreases with altitude.