# Ideal gas inside a sphere under the influence of gravitational field

1. Oct 16, 2011

### Thunderbird88

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

We have an ideal gas consisted of N classical particles, each having mass m. The system is inside a spherical bottle of radius R and is inside the gravitational field of the earth. The system is also in thermal equilibrium with a heat reservoir which has temperature T. I have to find the partition function and the energy of the system.

2. The attempt at a solution

The problem I face is finding the energy of a single particle. I'm confused regarding the potential energy. My solution is in the pdf file. Is there something wrong with the spherical coordinates?

#### Attached Files:

• ###### solution.pdf
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2. Oct 16, 2011

### vela

Staff Emeritus
I'm assuming you're placing the origin of the coordinate system in the middle of the sphere and directing the z-axis upward. The potential energy depends on how high the particle is, not how far it is from the origin, so U=mgr isn't correct.