Q7: An extreme relativistic gas of indistinguishable particles in a volume V is characterized by the single particle energy states.
ωd = (d)3
where c is the speed of light. Assume the particles can leave the volume to the reservoir and back so that the chemical potential of the system-reservoir remains constant.
1. Calculate the grand partition function and the q-potential of the system.
From the grand partition function, find out:
2. Average number of particles for given V, T.
3. Internal energy of the system. Prove that U = 3kT.
4. Pressure in the system. Prove that PV = kT.