Define Helmholtz free energy F and Gibbs free energy G. What does decrease in F and G signify ? Show that the internal energy U at temperature T is given by U = F - T \left( \frac{\partial F}{\partial T} \right)_V

Write a short note on Debye theory of specific heat of solids.

A gas at a pressure P and temperature T has a density \rho. The velocity of sound in this gas is v. Obtain an expression for the degrees of freedom of the gas molecules. At STP, \rho = 1.3\text{ kg m}^{-3} and \text{v} = 330\text{ ms}^{-1}. Calculate the degrees of freedom.

Using a Carnot cycle obtain the Clausius Clayperon equation. At normal pressure the ratio of densities of ice and water is 9 : 10. When 1 kilo-mole of ice is melted, the change in entropy is 22.2 \times 10^3\text{ JK}^{-1}. If the external pressure is increased by 10^5\text{ Nm}^{-2}, what will be the change in the melting point of ice?

Show the distribution of velocities for temperatures \text{T}_1, \text{T}_2 and \text{T}_3 (\text{T}_1 > \text{T}_2 > \text{T}_3) of gas molecules according to the Maxwell-Boltzmann law. Using this law prove that the most probable velocity is \sqrt{2/3} times the root-mean-square velocity.

Obtain an expression for the mean free path. Mention the correction introduced by Maxwell. Calculate the value of Avogadro's number if the mean free path of nitrogen molecules at STP is 6.85 \times 10^{-8}\text{ m}. The molecular diameter is 3.5\text{ \AA}.

Write a short note on Law of equipartition of energy.

What is population inversion ? Mention the methods of achieving population inversion. Explain the concept of negative temperature.

To what extent the pressure in a cathode ray tube must be reduced so that 90\% of the electrons emitted by the cathode reach the anode which is at a distance of 20\text{ cm} from the cathode? The mean molecular radius of main constituent gases of atmosphere is 2\text{\AA} and the number of molecules at standard pressure (760\text{ mm of Hg}) is 3 \times 10^{25} per \text{m}^3.

Explain the concept of entropy The specific heat C_p of a material depends on temperature T according to the relation: C_p = a + bT + cT^2 \text{ where a, b and c are constants,} Derive an expression for the change in its entropy when the temperature changes from T_1 to T_2.

Write a short note on Specific heat of solids.

A vacuum of the order of 10^{-11}\text{ cm of Hg} is obtained in the laboratory. Estimate the number of molecules of gas per cobic centimeter at 27^\circ \text{C} in that vacuum.

What is Brownian motion? Deduce Einstein's formula for translatory Brownian motion of particles suspended in a liquid and hence determine the avogadro's number.

How is absolute scale of temperature obtained with the help of Carnol cycle? Hence define absolute zero

State the principle of equipartition of energy. What are its limitations? Show that it is applicable only when the energy is a quadratic function of the associated variable.

Using Maxwell's thermodynamic relations show that the internal energy of an ideal gas at a constant temperature is independent of its volume while for a real gas it is a function of Volume also.

Hydrogen and oxygen suffer Joule - Thomson expansion at room temperature. Discuss the results with reasons.

Define entropy, Derive expressions for the entropy of a perfect gas in terms of (i) T and v (ii) T and p The symbols have their usual meanings.

Define thermodynamic temperature of a magnetic system. Discuss how cooling takes place due to adiabatic demagnetisation. Explain, why cooling due to adiabatic demagnetisation is important at low temperatures.

Calculate the most probable speed v_p, the avenge speed \langle v \rangle and the root-mean-square speed \langle v^2 \rangle^{1/2} for hydrogen molecules at 273\text{ K}.