Calculate the pressure of a Fermi gas in its ground state.

Check that the energy of the ground state of a Fermi gas is correct by calculating the chemical potential from it.

A long series of calculations can be used to derive the entropy of the Fermi gas, and the result is σ = π²N. From this, calculate the heat capacity at constant volume.

It turns out that the energy of a Bose gas is given by: U = Aτ where A is a constant that depends only on the volume. From this, calculate the heat capacity at constant volume.

Using the knowledge that the entropy goes to zero as the temperature goes to zero, calculate the entropy from the heat capacity.