Thermal Physics: 2 Cases, Ratio V(1)/V(2) for Small T

[Fys]

I had a question about 2 cases

we have a cilinder with 2 Ideal Gases. The volume, mass and the number of particles
is given. So We call it V(1),M(1),N(1) for the first gas and V(2),M(2),N(2) for
the second gas. The two gases are separated by a movable wall

Now what is the Ratio V(1)/V(2) for very small T (almost zero) if

1. both gases consist of fermions
2.the first gas consist of bosons and the other one form fermions


I thought for the both cases I use PV=NKT. And so express V in the other quantities.
Then use the fermi distribution and the bose-distribution. But using this I get all kinds of quantities which I don't have.
Can someone help me with this?

thanks for the help

 

[Count Iblis]

You cannot use PV = NkT for an ideal quantum gas at low temperatures.

In case of the Fermi gas, you know that in the linit of zero temperature, the pressure becomes a nonzero constant. It is given by minus the derivative of the total ground state energy w.r.t. volume.

If you don't exactly remember how this is computed, you should first study this before attempting to solve this problem.

In case of the Bose gas, you know that a macroscopic fraction of the molecules will be in the ground state below the critical temperature for Bose-Einstein condensation. There is a maximum density for the particles that are not in the condensate.

You should first derive an expression for the pressure for the Bose gas from first principles before proceeding with this case.