Description
BACHELOR’S DEGREE PROGRAMME
(BSCG/BSCM)
THERMAL PHYSICS AND STATISTICAL MECHANICS
Valid from 1st January, 2026 to 31st December, 2026
Tutor Marked Assignment
THERMAL PHYSICS AND STATISTICAL MECHANICS
Course Code: BPHCT-135
Assignment Code: BPHCT-135/TMA/2026
Max. Marks: 100 Note: Attempt all questions.
The marks for each question are indicated against it.
PART A
a) Calculate rms v for helium atoms at 300K. At what temperature will oxygen molecules have the same value of vrms ? Take mHe 67 .6*10-27 kg.
b) 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.
c) Define mean free path? Obtain an expression of mean free path for zeroth order approximation
d) What is Brownian motion? Write its two examples. Show that during sedimentation, particles concentration decreases exponentially as height increases
e)
a) A mass of an ideal gas )5.1 ( =g at C 27° is suddenly compressed to four times its original pressure. Calculate the final temperature of the gas.
b) 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.
c) State the zeroth law of thermodynamics. Explain how the zeroth law introduces the concept of temperature.
d) Obtain the expressions of work done for an ideal gas (i) in an isothermal expansion (ii)) in an adiabatic process.
e) Obtain an expression of coefficient of volume expansion for one mole of van der Waals’ gas
PART B
a) 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.
b) Draw p-V diagram of the Carnot Cycle and hence obtain an expression of efficiency.
c) Using the Maxwell’s relations of thermodynamics, obtain the first and second TdS equations.
d) Derive Clausius-Clayperon equation of phase transition. Draw phase diagram of water.
e) What is Joule-Thomson effect? Write any four findings of Joule- Thomson experiment.
a) 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.
d) What is Fermi-energy? Obtain an expression for Fermi energy for a system of N Fermions enclosed in a volume V. What will be the value of Fermi-energy ) eV in( of gold at Fermi-temperature 6.42*104 K
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