Write a short note on Brownian motion.

Write a short note on Concept of negative temperature.

Write the expressions obtained from Einsteins’s and Debye’s theories for the specific heat of solids. What is the basic difference between the two theories? Calculate the heat required to raise the temperature of a solid of mass m from T_1 to T_2 in the low temperature region.

State Nernst’s heat theorem. Taking the example of adiabatic demagnetisation show that no adiabatic process initiated at non-zero-temperature can lead to zero temperature.

Show that done in a reversible expansion of an ideal gas from volume V_1 to V_2 is greater than the corresponding work done in an irreversible expansion against a constant pressure P_2.

What is an adiabatic demagnetisation cycle? Discuss the cycle in terms of M, H indicator diagram.

Derive expressions for the Maxwellian distribution of

(i) One component of velocities

(ii) one component of momenta, in the molecules of an ideal gas.

Write a short note on Thermal ionization.

Write a short note on Equipartition of energy.

Establish the following relation using Carnot's principle. \frac{dp}{dT} = \frac{JL}{T(V_2 - V_1)} The symbols have usual meanings.

Calculate the Joule-Thomson coefficient for nitrogen gas at 293 K and 100 atm. pressure taking C_p = 8.21\text{ cal deg}^{-1}\text{ mole}^{-1} a = 1.39\text{ liter}^2\text{ atm-mole}^{-2} and b = 3.92 \times 10^{-2}\text{ liter mole}^{-1}

A 10 ohm resistor carrying 3 ampere current is cooled by running water so as to keep the temperature at 300 K. Discuss the change in entropy per second (i) of the resistor (ii) of the universe.

Derive an expression for the specific heat of solids in Einstein model. Explain Einstein temperature T_E. Find the value of specific heat when. (i) T \gg T_E (ii) T \ll T_E (iii) T = T_E/2

Derive an expression for the pressure exerted by an ideal gas on the walls of the walls of the chamber in terms of concentration of molecules (n), gas temperature (T) and a universal constant. Specifically discuss how T comes into the picture.

Assuming Clausius inequality, show that working between two given temperatures, all the engines of irreversible cycle are less efficient than a Carnot cycle and that all reversible cycles have the same efficiency as Carnot cycle.

Define thermodynamic temperature of a magnetic system. Making use of Gibb's equation, derive an expression for cooling produced due to adiabatic demagnetization process. Why is the method use only after pre-cooling to a low temperature?

Under standard temperature and pressure a gas has density P = 1.29\text{mg/cc}, and the velocity (v) of sound propagation in it is 330\text{ m/s}. Calculate the number of degrees of freedom, the gas molecules may possess.

Write a short note on Thermal ionization.

Write a short note on Equipartition of energy.

Define entropy. Write a general expression for the elemental entropy change dS for 1 mole of an ideal gas. How would this become for cases where the change is (i) isothermal, (ii) isochoric, (iii) isobaric? Deduce expression for S_2 - S_1 for each of these cases, where (i) and (ii) refer to the initial and final stage entropies respectively. Constants C_p, C_v, R may be used, as needed, to express the results.