Considering an extreme relativistic ideal gas in volume V in equilibrium with the environment of temperature T. The gas is consisting of N non-interacting monatomic molecules with the single particle energy &-pc, where c is the speed of light. The single-particle energy state in the range of p to (p+dp) is 4nVp² dp. a) Find the partition function. b) Show PV=U/3, where U is the internal energy. c) Show y=4/3, where y is defined as the ratio of heat capacities Cp/Cv.

Considering an extreme relativistic ideal gas in volume V in equilibrium with the environment of temperature T. The gas is consisting of N non-interacting monatomic molecules with the single particle energy &-pc, where c is the speed of light. The single-particle energy state in the range of p to (p+dp) is 4nVp² dp. a) Find the partition function. b) Show PV=U/3, where U is the internal energy. c) Show y=4/3, where y is defined as the ratio of heat capacities Cp/Cv.