Chapter 7.6, Problem 75P

(a)

To determine

The Bose Einstein Condensation function can be given as ${\overline{n}}_{BE}=e^{-\left(\epsilon -\mu \right)/kT}\left[1+e^{-\left(\epsilon -\mu \right)/kT}+\mathrm{.....}\right]$ .

(b)

To determine

The expression for chemical potential of bosons.

(c)

To determine

To show that the pressure of gas is given as $P=\left(\frac{kT}{V}\right)\ln Z$ and the logarithm of grand partition function is computed as sum over all modes.

(d)

To determine

Express the pressure of gas as $P=\frac{NkT}{V}\left(1-\frac{N{v}_Q}{4\sqrt{2}V}\right)$ and give the result for low pressure of gas.

(e)

To determine

Express the value of virial coefficient and find the value of virial coefficient for helium.

(f)

To determine

Repeat the problem for spin half particles.