Consider a nonrelativistic free particle in a cubic container of edge length l and volume v = l^3. the system is in thermal equlibrium at temperature t.
1) show the dispersion (ae) of gas energy is related to the disperesion (ap)2 of gas pressure by (ap) (ae) .
2) from the partition function of the gas, and using the relation obtained from 1), show the dispersion (ap)2 is given by (ap) 2kbt op 3v t
3) find the dispersion (ae) of gas energy in the fixed volume du tds, dv = 0) from the fluctuation dissipation theorem and show the above relation.