Starting from van der Waals equation for a gas, deduce expressions for its critical temperature, critical pressure and critical volume.

Derive the expression for the energy distribution of particles according to Bose-Einstein statistics.

Consider the following equation of state for a gas: P = \frac{RT}{v-b} - \frac{a}{Tv^{2}} where a and b are constants and other symbols have their usual meaning. Find the values of P_{c}, T_{c} and V_{c} in terms of a and h at the critical point.

Write a note on Brownian motion and the importance of its study.

Calculate the root-mean-square speed of smoke particles of mass 5\times 10^{-14}\text{ g} in air 0^{\circ}\text{C}.

Write a note on Super fluidity, explaining why it is a quantum phenomenon.

Write a note on Thermal ionization and its application.

Using Maxwell-Boltzmann distribution law prove that there cannot be any negative absolute temperature.