Write a short note on Clausius-Clapeyron equation.

Write a short note on Adiabatic demagnetisation.

Explain the evaporation of a liquid at a temperature below its boiling point on the basis of kinetic theory of matter.

What is the most probable distribution of speeds in a large number of molecules of a gas and indicate the steps for its derivation.

What is an adiabatic process? Give three engineering examples of adiabatic processes which are in common use.

Explain how very low temperatures can be produced by adiabatic demagnetisation.

The specific heat of a substance is found to vary with temperature in the following way c(T) = aT + bT^2 where c(T) is the specific heat at the temperature T and 'a' and 'b' are constants. Compare the average specific heat of the substance in the temperature range 0-T to the specific heat at the mid-temperature T/2.

Explain the concept of internal energy of a system. Formulate mathematically the first law of thermodynamics. Calculate the work done in an isothermal compression of a gas.

Mention the assumptions made & by Einstein in explaining the variation of specific heat of solids with temperature. Show how these assumptions were used to derive the formula for the specific heat of solids. How and why Einstein's theory fails at very low temperatures.

Write a short note on Carnot cycle.

Write a short note on Thermodynamic potentials.

At the N.T.P., the mass of one litre of Hydrogen is 0.09 gm. Calculate the (i) RMS (ii) Mean and (iii) Most Probable Speed at 27^\circ\text{ C}.

The RMS speed of oxygen molecules at 0^\circ\text{ C} is 460\text{ ms}^{-1}. What would be the RMS speed of Argon molecules (Mol. wt. = 40 gm/mole) at 40^\circ\text{ C} and at what temperature this speed would be double than at N.T.P.?

Write a short note on Brownian motion.

The molecules of a gas are made up of four non coplanar atoms. Enumerate the translational, vibrational and rotational degrees of freedom of each molecule. Hence obtain the specific heat at constant volume C_V of the gas. Does the value so obtained agree with the observed value in general? If not why?

Prove the latent heat equation \left(\frac{\delta L}{\delta T}\right)_{sv} - \frac{L}{T} = C_s - C_p where C_s and C_p are specific heats of saturated vapour aid the liquid in contact with it respectively. Given the following values referring to 1\text{ gm} of water at 100^\circ\text{C} L = 539\text{ Cal/gm} \left(\frac{\delta L}{\delta T}\right)_{sv} = -0.64\text{ Cal K}^{-1}\text{ gm}^{-1} C_p = 1.01\text{ Cal K}^{-1}\text{ g}^{-1} Calculate C_s. Explain why the specific heat takes a negative value.

Prove that \int_A^B \delta Q / T evaluated along a reversible path joining the states A and B does not depend on the path chosen. Hence define the entropy function S. Calculate the entropy change in an ideal gas undergoing a state change from (V, P) to (2V, P/2) for three suitably chosen different paths and show that the result turns out to be the same all the cases.

Write a short note on Clausius Calpeyron equation.

State the basic assumptions of Debye theory of specific heat of solids and write the expression for C_V derived from this theory. Show that this expression yields the famous T^3 law of specific heat at low temperature. Discuss the extent to which the theory agrees (or disagrees) with observation on specific heat through the variation of the Debye characteristic temperature \Theta_D with temperature, in general.

The two atoms is a molecule of a gas interact according to the potential \phi(r) = \frac{A}{r^6} + \frac{B}{r^{12}} r being the separation distance between the two atoms. Determine A and B if the potential energy \phi(r) = \phi(r_0) at the equilibrium separation r = r_0.