1. Answer any three parts

Calculate the thermal conductivity of a gas using the following data p =1·6 kg v =480 A. X M 32, 1.4 and R 8.31 kJkmol^-1

Calculate the change in temperature when oxygen gas at 27°C is made to undergo adiabatic throttling and the pressure is reduced by 50 atm. Given:
a 13·2x10^-2Nm^4,b=31·2 x10^-6m^3 8.3 J and Cp =3.5 R.

A student is working in a physics laboratory on sonometer, whose wire has cross-sectional area 0.85 x m^2. A tension of 20 N is applied at the free end. The wire is stretched between two rigid supports 1.2 m apart. If the temperature is reduced by 12°C, calculate the final tension in the wire. The coefficient of linear expansion and isothermal Youngs modulus may be assumed to be constant at the values 1·5 x and 2·0 x 10^11 Nm^-2.

Consider a one level system having energy E -kBT ln where V is the volume and Vo is a constant. Obtain an expression for pressure for this system. Discuss the significance of your result.

2. What is thermocouple How is it used to measure temperature Discuss its merits and limitations.
OR
State zeroth law of thermodynamics and write parametric as well as exact equation of state for one mole of a real gas and a paramagnetic substance.

What do you understand by the term. second order phase transition? Show that for a second order phase transition:

dp/dT=(CP2 -CP1 [Tv (132

Define entropy and show that entropy increases when two gases mix.

4. Write van der Waals' equation for one mole of a real gas. Show that the critical coefficient is independent of the nature of gas.
OR
State two characteristics of Brownian motion. Write down the equation of motion of a free Brownian particle moving along a particular direction using Langevin's arguments. Why do we work with mean squared displacement rather than mean displacement?

Calculate the diameter of a molecule of helium using the following data van der Waals' constant b 2.42 x m^3 mol^-1.

Show that the phase space of a linear harmonic oscillator is an ellipse.

Obtain an expression for BE condensation temperature.
OR
Write down Planck's formula for black body radiation and show that it contains Wien's law, Rayleigh-Jeans law and Stefan-Boltzmann law.

Plot Fermi-Dirac, Bose-Einstein and Maxwell-Boltzmann distribution functions at a finite temperature as a function of energy on the same graph.

Physical constants:

NA =6·02 x 10^23 mol^-1

kB 1.38 x 10^-23

R =8·31 kJ kmol^-l