BPHCT-135 Solved Assignment January 2026 | THERMAL PHYSICS AND STATISTICAL MECHANICS | IGNOU BSCG

Q: Attempt all sub-questions from Part B, Question 4.

This response comprehensively addresses the various aspects of statistical mechanics and blackbody radiation, drawing upon fundamental principles typically covered in the BPHCT-135 course. It explains the derivation of the partition function for ideal gases, demonstrates the application of Maxwell-Boltzmann statistics to calculate particle distributions and total energy, and meticulously deduces classical radiation laws from Planck's quantum theory. Furthermore, it defines Fermi energy and provi

Q1. Attempt all sub-questions from Part A, Question 1.

(a)) Calculate vrms for helium atoms at 300K. At what temperature will oxygen molecules have the same value of vrms? Take mнe = 6.67×10–27 kg. (200 words)
(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 dNv = 4πΝ (m/2πkBT)^3/2 v² exp (-mv²/2kBT) dv Obtain an expression for most probable speed. (200 words)
(c)) Define mean free path? Obtain an expression of mean free path for zeroth order approximation. (200 words)
(d)) What is Brownian motion? Write its two examples. Show that during sedimentation, particles concentration decreases exponentially as height increases. (200 words)
(e)) Write the expressions of an ideal gas and van der Waals' equation. 10 moles of nitrogen gas occupy a volume of 5×10-3 m³ in a vessel at 27°C. 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: a = 1.39×10-6 atm m6 mol-2, b=39.1×10-6 m³ mol-1 and R = 8.2×10-5 atm m³ K-1mol-1. (200 words)

Key Points:

vrms = √(3kBT/m); O₂ requires ~2390 K to match He's vrms at 300 K.
Most probable speed (vmp) is peak of Maxwellian distribution; vmp = √(2kBT/m).
Mean free path (λ) is average distance between collisions; Zeroth-order: λ = 1/(nπd²).
Brownian motion is random particle movement due to molecular collisions; e.g., pollen in water, smoke in air.

Answer: Here are the comprehensive answers to all sub-questions from Part A, Question 1, adhering to the specified word limits and formatting requirements, drawing upon principles of Thermal Physics and Statistical Mechanics. ### (a) Root Mean Square Speed Calculation The root mean square speed (vrms) is a measure of the average speed of molecules in a gas, defined by the kinetic energy of the particles. It is given by the formula vrms = √(3kBT/m), where kB is the Boltzmann constant (1.38×10⁻²³ J/K), ...

Q2. Attempt all sub-questions from Part A, Question 2.

(a)) A mass of an ideal gas (y = 1.5) at 27°C is suddenly compressed to four times its original pressure. Calculate the final temperature of the gas. (200 words)
(b)(i)) What are intensive and extensive variables for thermodynamic systems? Write two examples of each. (120 words)
(b)(ii)) Represent an (a) isobaric (b) isochoric (c) isothermal and (d) a cyclic process on p-V indicator diagram. (80 words)
(c)) State the zeroth law of thermodynamics. Explain how the zeroth law introduces the concept of temperature. (200 words)
(d)) Obtain the expressions of work done for an ideal gas (i) in an isothermal expansion (ii)) in an adiabatic process. (200 words)
(e)) Obtain an expression of coefficient of volume expansion for one mole of van der Waals' gas. (200 words)

Key Points:

Adiabatic compression temperature change: T₂ = T₁ (P₂/P₁)⁽γ⁻¹⁾/γ.
Intensive variables are independent of system size (e.g., T, P, density).
Extensive variables depend on system size (e.g., mass, volume, energy).
p-V diagrams: Isobaric (horizontal), Isochoric (vertical), Isothermal (hyperbolic), Cyclic (closed loop).

Answer: This comprehensive answer addresses various fundamental concepts in Thermal Physics and Statistical Mechanics, specifically from the BPHCT-135 course. It covers ideal gas processes like adiabatic compression and work done during isothermal and adiabatic expansions, introduces thermodynamic variables, explains the Zeroth Law of Thermodynamics, and delves into the properties of real gases using the van der Waals equation.

Q3. Attempt all sub-questions from Part B, Question 3.

(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. If these two gases mix, obtain an expression for the entropy of mixing per mole of mixture. (200 words)
(b)) Draw p-V diagram of the Carnot Cycle and hence obtain an expression of efficiency. (200 words)
(c)) Using the Maxwell's relations of thermodynamics, obtain the first and second TdS-equations. (200 words)
(d)) Derive Clausius-Clayperon equation of phase transition. Draw phase diagram of water. (200 words)
(e)) What is Joule-Thomson effect? Write any four findings of Joule- Thomson experiment. (200 words)

Key Points:

Entropy of mixing per mole: ΔS/N = -R [x₁ ln(x₁) + x₂ ln(x₂)].
Carnot engine efficiency: η = 1 - T_C / T_H, maximum possible efficiency.
First TdS equation: TdS = C_V dT + T (∂P/∂T)_V dV.
Second TdS equation: TdS = C_P dT - T (∂V/∂T)_P dP.

Answer: This section comprehensively addresses the thermodynamics and statistical mechanics concepts outlined in Part B, Question 3 of BPHCT-135. It covers the entropy of mixing for ideal gases, the Carnot cycle and its efficiency, derivations from Maxwell's relations, the Clausius-Clapeyron equation with water's phase diagram, and the Joule-Thomson effect along with its key findings. Each sub-question is tackled with a focus on fundamental principles, derivations, and practical implications, ensuring ...

Q4. Attempt all sub-questions from Part B, Question 4.

(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. (200 words)
(b)) N particles obey MB distribution. They are distributed among three states with energies E₁ = 0, E2 = kBT and E3 = 3 kBT . If the equilibrium energy of the system is 2000 kBT, calculate the total number of particles, N. (200 words)
(c)) Using the Planck's radiation law: κλάλ = (8πhc/λ^5) (1/(exp(hc/λkBT) - 1)) dλ, deduce (i) Rayleigh-Jean's law, (ii) Wien's law and (iii) Stefan's law. (400 words)
(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 (in eV) of gold at Fermi-temperature 6.42×104 K? (200 words)

Key Points:

Single particle partition function for monatomic ideal gas: q = V * (2πmkBT/h²)^(3/2).
System partition function for N distinguishable, non-interacting particles: Z_N = q^N.
Maxwell-Boltzmann distribution: nᵢ = N * exp(-Eᵢ/kBT) / Z.
Rayleigh-Jeans law: Planck's law in the long wavelength (hc/λkBT << 1) limit, u(λ)dλ = (8πkBT/λ⁴) dλ.

Answer: This response comprehensively addresses the various aspects of statistical mechanics and blackbody radiation, drawing upon fundamental principles typically covered in the BPHCT-135 course. It explains the derivation of the partition function for ideal gases, demonstrates the application of Maxwell-Boltzmann statistics to calculate particle distributions and total energy, and meticulously deduces classical radiation laws from Planck's quantum theory. Furthermore, it defines Fermi energy and provi...

BPHCT-135 Solved Assignment — January 2026 / July 2026

THERMAL PHYSICS AND STATISTICAL MECHANICS | IGNOU Bachelor of Science (General) (CBCS) (BSCG)

BPHCT-135—January 2026 / July 2026

THERMAL PHYSICS AND STATISTICAL MECHANICS

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BPHCT-135 Assignment Questions — January 2026

Q1. Attempt all sub-questions from Part A, Question 1.

Q2. Attempt all sub-questions from Part A, Question 2.

Q3. Attempt all sub-questions from Part B, Question 3.

Q4. Attempt all sub-questions from Part B, Question 4.

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