BPHCT-135 EM 2025 SOLVED ASSIGNMENT

Description

Tutor Marked Assignment
THERMAL PHYSICS AND STATISTICAL MECHANICS
Course Code: BPHCT-135
Assignment Code: BPHCT-135/TMA/2025
BACHELOR’S DEGREE PROGRAMME
(BSCG/BSCM)
THERMAL PHYSICS AND STATISTICAL MECHANICS
Valid from 1st January, 2025 to 31st December, 2025
PART A
1. a) Discuss Regnault’s experiments on Hydrogen, nitrogen and carbon dioxide for 273
K. Also discuss the Andrews experiments for CO2 on the p-V diagram at various
temperatures. (5)
b) Write the assumptions made by Maxwell to derive the expression for distribution
function of velocities. Hence derive the expression of Maxwellian distribution
function for molecular speeds. Plot Maxwellian distribution function as a function of
molecular speed. (10)
c) The average speed of hydrogen molecules is 1 ms 1850  . The radius of a hydrogen
molecule is m 10 40 . 1 10   . Calculate (i) Collision cross-section, (ii) collision
frequency, and (iii) mean free path. Take . m 10 3 3 25    n (5)
d) What is Brownian motion? Discuss Perrin’s method for determination of Avogadro
number in Brownian motion. How can this method be used to estimate the mass of
molecule (5)
2. a) Explain the classification of boundaries in a thermodynamic system. (5)
b) State Zeroth law of thermodynamics. How does this law introduces the concept of
temperature. Write parametric as well as exact equation of state for one mole of a
ideal gas and stretched wire. (5)
c) Show that for an ideal gas
and 1
T  
p T
1  

where T  is the isothermal compressibility and  is isobaric coefficient of volume
expansion. (5)
d) Derive Mayer’s formula: R C C V p   where V p C C and are the molar heat
capacity at constant pressure and constant volume respectively. (5)
e) Obtain an expression for work done in expanding a gas from volume i V to f V in an
isobaric process. (5)
PART B
3. a) With the help of entropy – temperature diagram of Carnot cycle, obtain an
expression of efficiency of a Carnot engine. A Carnot engine has an efficiency of
50%. It operates between reservoirs of constant temperature with temperature
difference of 80 K. Calculate the temperature of the low-temperature reservoir in
Celsius.
b) Define thermodynamic potentials. Derive Maxwell’s relations from thermodynamic
potentials.
c) When two phases of a substance coexist in equilibrium at constant temperature
and pressure, their specific Gibb’s free energies are equal. Using this fact, obtain
Clausius-Clapeyron equation.
d) Derive Planck’s law of radiation and hence obtain Rayleigh-Jeans law and Wien’s
law.


4. a) Consider a classical ideal gas consisting of N particles. The energy  of a particle
is given by
cp
where c is a constant and p is the magnitude of the momentum.
Calculate (i) the partition function of the system, (ii) internal energy, and (iii) V
(10)
(5)
(5)
(5)
C . (8)
b)
.
4
10
21
5  electrons are confined in a box of volume
wavelength and Fermi energy.
1
cm
3
. Calculate their Fermi
c) Define thermodynamic probability of a macrostate. Establish the Boltzmann
relation between entropy and thermodynamic probability:
S 
k
ln
B W
.
d) Obtain an expression of Fermi-Dirac distribution function. Plot Fermi function
versus energy at different temperatures.
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