Consider a one-component gas of non-interacting classical structureless particles of mass m at a temperature T .   (a)   Calculate exactly the grand canonical partition function,   for this system as...

Consider a one-component gas of non-interacting classical structureless particles of mass m at a temperature
T.

(a)   Calculate exactly the grand canonical partition function,
  for this system as a function of volume,
V
, temperature, and chemical potential, μ. Your result should look like

            Where z is a function of
T
 and μ.

(b)   From the result of part (a) determine the pressure, p, as a function of
T
and the average particle density,
p.

(c)   For 1 cc of gas at STP, compute the relative root mean square of the density fluctuations, [(δp)²] /p²] ½.

(d)   Calculate the probability of observing a spontaneous fluctuation in 1cc of gas at STP for which the instan-taneous density differs from the mean by one part in 10⁶.