Molecular Physics | Thermodynamics Answers

a) What do you understand by mean free path of gas molecules? Derive an expression for the law of distribution of free paths. (1,4)
b) What is Brownian motion? Give three examples of such a motion. Using Einstein’s theory, obtain an expression for Einstein’s formula for mean square displacement of a Brownian particle. (2,3,5)
c) What is the transport phenomenon in gases? Obtain an expression for coefficient of viscosity of a gas if the average number of molecules crossing an area is given by vnn41=∆ and molecules make their last collision before crossing an imaginary surface at a distance of λ32above or below it.

What is adiabatic demagnetisation? Explain how low temperatures are produced using adiabatic demagnetisation?

1/A cylinder containing n mol of an ideal gas undergoes an adiabatic process.
(a) Show that the work done on the gas is
(b) Starting with the first law of thermodynamics in differential form, prove that the work done on the gas is also equal to . Show that this result is consistent with the equation in part (a).
2/ A vertical cylindrical tank contains 1.80 mol of an ideal gas under a pressure of 1.00 atm at 20.0oC. The round part of the tank has a radius of 10.0 cm, and the gas is supporting a piston that can move up and down in the cylinder without friction.
(a) What is the mass of this piston?
(b) How tall is the column of gas that is supporting the piston?

Poisson's ratio is 0.4, longitudinal strain is 2*10^3, so what will be the volume percentage?

1. a vessel contains non linear triatomic gas. if 50% of gas dissociates into individual atom then find the new degree of freedom by ignoring the vibrational mode and further dissociation.(Ans-3.75)

2.A narrow glass tube 80 cm long and opened at both ends is half immersed in mercury and now the top of the tube is closed and is taken out of mercury. A column of mercury 20 cm long remains in the tube. Find atm pressure(ans-60 cm of Hg column)

3.The mean free path of a molecule of He gas is A. Its mean free path along any arbitary cordinate axis will be?(ans-A/3)

4.Two container A and B are partly filled with water and closed. The volume of A is twice of B and it contains half the amount of water in B. IF both are at same temperature the water vapour in the container will have pressure ratio? (ans-1:1)

A cylinder of radius r and of thermal conductivity K1 is

surrounded by a cylindrical shell of inner radius r and outer radius 2r made of a material of thermal conductivity K2. The effective thermal conductivity of the system is??

Show that the partition function of an N-particle system is given by the expression:

Zn=Z^N=V^N/h^3N(2πm/ β)^3N/2
Obtain expressions for (i) heat capacity at constant volume, (ii) average pressure exerted
by the gas, and (iii) Helmholtz free energy F.

Derive an expression for ground state energy of a completely degenerate FD gas. For
copper, take N/V =8.5 x10^28 m^-3 , h=6.62x 10^-34 Js and Me = 9.1x 10^-31 kg to calculate Fermi
energy

What is the transport phenomenon in gases? Obtain an expression for coefficient of viscosity of a gas if the average number of molecules crossing an area is given by Δn=1/4nv and molecules make their last collision before crossing an imaginary surface at a distance of 2/3λ above or below it.

What is Brownian motion? Give three examples of such a motion. Using Einstein’s theory, obtain an expression for Einstein’s formula for mean square displacement of a Brownian particle.