Derive the expression for the second virial coefficient B₂ in terms of the intermolecular potential  using the approximation  Use the Lennard-Jones potential to outline its calculation.

Consider a single classical 1-D non-relativistic harmonic oscillator. Obtain x(t) and p(t) as a function of time t. Assume that initially at t = 0, the oscillator is at the maximum displacement  .Plot its phase space trajectory for fixed total energy E

Obtain Fermi-Dirac distribution function. Draw it for  What is its physical significance? 

Obtain an expression of probability of finding the system in the microstate k corresponding to energy E_{k i}n canonical ensemble. Also, write the expression of canonical partition function.

What is Gibb’s paradox? Derive Sackur-Tetrode equation of entropy for a classical, ideal gas.

Using the Mayer f-function, show that the second virial coefficient B₂ for  gas

   is the

diameter of the sphere. Here  

State Ising model and obtain the partition function (ln Z) for 1D in the absence of an external magnetic field up to second order perturbation. Explain the physical significance of each term in the Hamiltonian and discuss the role of the coupling constant J.