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Ideal gas inside a sphere under the influence of gravitational field

  1. Oct 16, 2011 #1
    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:

  2. jcsd
  3. Oct 16, 2011 #2

    vela

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    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.
     
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