Calculate the net change in entropy when 10\text{ g} water at 60^\circ\text{C} is mixed with 30\text{ g} water at 20^\circ\text{C}.

State Dulong-Petit's law and discuss its limitations in explaining heat capacities of solids. How were these efficiencies overcome by Debye ?

Discuss the significance of Saha's ionisation formula in classification of stars.

For a completely degenerate BE gas, discuss the condition for onset of BE condensation.

Establish Van der Waals equation of state for a real gas. Deduce expressions for critical constants and show that critical coefficient is independent of the nature of gas.

Explain the thermodynamic behaviour of an ideal Fermi gas. What are fermions ?

Find the efficiency of a Carnot's engine working between 127^\circ\text{C} and 27^\circ\text{C}.

Derive the gas equation when it undergoes adiabatic process.

Show that if an ideal gas is compressed isothermally its compressibility is \frac{1}{p}, whereas if it is compressed adiabatically its compressibility is \frac{1}{\gamma p} where \gamma = C_p / C_v.

A motor car tyre has a pressure of 2\text{ atmospheres} at the room temperature of 27^\circ\text{C}. If the tyre suddenly bursts, find the resulting temperature.

What are bosons ? Based on Bose-Einstein statistics, derive the expression for Bose-Einstein condensation.

Show that the elemental quantity of heat \delta Q is not a total differential.

Write down the expression for the Bose-Einstein distribution function and explain the meaning of the symbols used.

Consider a gas of photons in equilibrium and contained in a volume V at a temperature T. Using the Bose-Einstein statistics, calculate the total energy of the photon gas.

N particles are distributed among three states having energies E = 0, E = kT and E = 2kT. If the total equilibrium energy of the system is 1000 kT, what is the value of N?

Explain why the distribution of speeds of molecules emerging through a small hole in an effusive molecular beam source is not a Maxwellian distribution.

(ii) -\left(\dfrac{\partial f}{\partial E}\right) is symmetric about the Fermi level.

Let f be the Fermi-Dirac distribution function, then show that--- (i) -\left(\dfrac{\partial f}{\partial E}\right) is a maximum at the Fermi level;