Equation of state (Question 2 (35 Marks)) — UPSC Physics Optional CSE 2007 Paper I

Derive a relation between the total number of Fermions in terms of Fermi momentum and hence obtain the expression for the total energy E of the system at absolute zero. Combine this expression with the equation of state PV = \frac{2}{3} E to show that the pressure of an ideal Fermi gas at T = 0 is proportional to 5/3 power of its number density.