N particles obey MB distribution. They are distributed among three states with energies  and . If the equilibrium energy of the system is 2000 k_BT, calculate the total number of particles, N. 

Derive an expression of the partition function for a single particle monatomic ideal gas. Write the expression for a monatomic gas consisting of N-identical yet distinguishable and non-interacting particles.

What is Joule-Thomson effect? Write any four findings of Joule- Thomson experiment. 

Derive Clausius-Clayperon equation of phase transition. Draw phase diagram of water.

Using the Maxwell's relations of thermodynamics, obtain the first and second TdS-equations. 

Draw p-V diagram of the Carnot Cycle and hence obtain an expression of efficiency. 

Consider that two ideal gases having n₁ moles are n₂ moles are enclosed in two separate containers at constant temperate T and pressure P. It these two gases mix, obtain an expression for the entropy of mixing per mole of mixture. 

Obtain an expression of coefficient of volume expansion for one mole of van der Waals’ gas. 

Obtain the expressions of work done for an ideal gas (i) in an isothermal expansion (ii)) in an adiabatic process. 

State the zeroth law of thermodynamics. Explain how the zeroth law introduces the concept of temperature.

i) What are intensive and extensive variables for thermodynamic systems? Write two examples of each.
ii) Represent an (a) isobaric (b) isochoric (c) isothermal and (d) a cyclic process on p-V indicator diagram.

A mass of an ideal gas  at  is suddenly compressed to four times its original pressure. Calculate the final temperature of the gas.

Write the expressions of an ideal gas and van der Waals’ equation. 10 moles of nitrogen gas occupy a volume of  in a vessel at . Calculate the pressure exerted by the molecules, if it is assumed to obey van der Waals’ equation. Compare this Value with that obtained using ideal gas law.
Given: ,

and . 

What is Brownian motion? Write its two examples. Show that during sedimentation, particles concentration decreases exponentially as height increases. 

Define mean free path? Obtain an expression of mean free path for zeroth order approximation. 

What is most probable speed? Using the expression of the number of molecules in a Maxwellian gas in the range v to v + dv as
$
Obtain an expression for most probable speed. 

Calculate v_rms for helium atoms at 300K. At what temperature will oxygen molecules have the same value of v_rms? Take  . 

The refractive indices of the core and cladding materials of an optical fibre are 1.51 and 1.39, respectively. Calculate the numerical aperture and light gathering capacity of the fibre.

Two energy levels of an atomic system are separated by energy corresponding to frequency . Assume that all atoms are in one or the other of these two energy levels, compute the fraction of atoms in the upper energy level at temperature . Take  and . 

An atomic system consisting of two energy levels, with population of higher energy level less than that of the lower level, is in thermal equilibrium. Show that the absorption of radiation dominates stimulated emission if radiation of appropriate frequency is introduced into the system. Comment on the consequences of this fact for laser action.