Model Question Paper PHYSICS:

PHYSICS: MP 2.3- Thermal Physics and Statistical Mechanics

Time: 3 Hours Max. Marks: 80

Instructions: Questions from 1 to 8 carry 15 marks each. Question No. 9 carries 20 marks

1. (a) What are thermodynamic variables? Derive Maxwell’s relations. (10)

(b) What are thermodynamic potentials? Explain. (5)

OR

2. (a) Explain the Seebeck, Joule, Peltier and Thomson effects of a

thermocouple.

(10)

(b) State and explain Fourier’s law, Fick’s law and Ohm’s law. (5)

3 .(a) Define phase space of a molecule. State and explain the postulate of

equal apriori probability.

(10)

(b) Write a note on equipartition of energy. (5)

OR

4 .(a) Obtain the Boltzmann distribution at equilibrium for an isolated system

of N distinguishable particles capable of occupying non-degenerate

energy levels using Lagrange’s method of undetermined multipliers.

(10)

(b) Show that chemical potential is constant throughout a system in the

equilibrium. (5)

5. (a) State and explain the basic postulates of quantum statistical mechanics. (10)

(b) Express the average value of observable using density matrix

formalism. (5)

OR

6 .(a) Deduce BE and FD distributions starting with a grand canonical

ensemble. (10) (b) Discuss about the Rotational partition function. (5)

7. (a) Describe the Landau levels in diamagnetism. (10)

(b) Discuss Boss-Einstein condensation. (5)

OR

8. (a) Apply Bose-Einstein statistics to the photon gas and derive Planck’s

formula. (10)

(b) Show that in the long wavelength limit the Planck‘s law leads to

Rayleigh-Jean‘s law. (5)

9. Answer any four of the following ( 4X5=20)

(a) Find the work done in an isothermal expansion of an ideal gas when its

volume increases by a factor of two.

(b) Obtain an expression for the internal energy of a Vander Waal’s gas

using Maxwell’s relations.

(c) Justify the Stirling approximation for ln (n!) by the graphical method.

(d) Calculate the probability of head and tails in tossing a coin ten times.

(e) Given two particles and three cells: How do you arrange them in

various states according to M-B, B-E and F-D statistics?

(f) The atomic weight of Lithium is 6.94 and its density 0.53 g/cm3

.

Calculate Fermi energy and Fermi temperature.

(g) Find the mean energy of particles at absolute zero for a system obeying

Fermi-Dirac statistics.

(h) A body at 1500 K emits maximum energy at a wavelength 1800 nm. If

the sun emits maximum energy at a wavelength of 560 nm, what is the

temperature of the sun?

*

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