MPH 011 Statistical Mechanics Solved Assignment 2026 is carefully prepared for M.Sc. Physics students as per the latest IGNOU guidelines. This course builds strong conceptual clarity in probability distributions, ensembles, partition functions, quantum statistics, Bose–Einstein condensation, Fermi–Dirac statistics, thermodynamic fluctuations, virial theorem, and cluster integrals. Our solutions are written in clear, step-wise format with proper derivations, logical explanations, and neat mathematical presentation so that you can confidently submit your assignment and score well.
MPH 011 Assignment Questions (As Per IGNOU TMA/2026)
PART A
a) Show under what condition Poisson distribution tends to Normal distribution. (10)
b) A monthly demand for a commodity is a continuous random distribution with probability distribution function given as:
p(x) = { 3N(x² − 1), 1 < x < 2
0, elsewhere }
where N is normalization constant. Obtain the value of N so that the function is normalized and hence, find the mean and the variance. (10)
c) N particles obey Maxwell–Boltzmann distribution. They are distributed among three states with energies: E₁ = 0, E₂ = k_B T, and E₃ = 4k_B T. If the equilibrium energy of the system is approximately 3000 k_B T, calculate the total number of particles. (5)
a) Obtain the phase space area enclosed by a classical harmonic oscillator for energies ranging from 0 to E. (5)
b) The Hamiltonian for the non-relativistic, non-interacting, monoatomic ideal gas is given by: H(q, p) = ∑ᵢ₌₁³ᴺ pᵢ²/(2m) + U(qᵢ) where m is the mass of the particle and U(qᵢ) is the potential energy. Obtain an expression of the phase space volume of the energy shell and hence obtain an expression of number of microstates. (10)
c) Obtain expression for average energy U (≡ ⟨E⟩) for the canonical ensemble in terms of partition function Z. (5)
d) For the grand canonical ensemble, obtain an expression for the ensemble average energy and ensemble average particle numbers. (5)
PART B
3. a) (i) A proton (mass = 1.67 × 10⁻²⁷ kg) inside a nucleus (radius = 10⁻¹⁴ m) may have speed up to 2.0 × 10⁸ m s⁻¹. How many quantum states are available to it?
(ii) The time evolution of the quantum state, ψ(q,t), is given by the Schrödinger wave equation: iħ ∂ψ/∂t = Ĥ ψ Using this equation, obtain the time evolution of the wave function when the energy eigenvalue is E.
b) State and prove quantum Liouville equation.
c) Using the relation of thermodynamic probability:
W = ∏_(i=1)^N [ g_i! / (N_i! (g_i − N_i)! ) ]
Obtain an expression of Fermi-Dirac distribution function.
Show a plot of f(ε) (the occupation index of a state corresponding to energy εᵢ) versus ε for different temperatures and discuss it.
What is the physical interpretation of Fermi energy?
d) Show that the probability that a state with energy δ above the Fermi level ε_F is filled is equal to the probability of a state with energy δ below the Fermi level ε_F is empty.
e) What is the Bose-Einstein condensation? Write an expression for number of particles in excited state (N_ex) in terms of Bose-Einstein condensation temperature (T_c), total number of bosons (N) in an assembly and temperature T. Show a plot of distribution of bosons as a function of temperature below and above the T_c.
4. a) State the Virial theorem and prove Boyle’s law using it.
b) What is meant by Cluster Integrals? Express B₂ and B₃ in terms of Cluster Integrals.
c) Using entropy as a function of temperature and pressure, obtain the first Ehrenfest’s equation.
d) Discuss the concept of thermodynamic fluctuations in the canonical ensemble. Define energy fluctuations and derive an expression for the mean square fluctuation of energy. Using the classical ideal gas, show that the relative fluctuation in energy varies as: δE / E ≈ 1 / √N and hence justify why thermodynamic calculations are valid for ordinary macroscopic systems.
MPH 011 Assignments Details
This Tutor Marked Assignment (TMA) carries 100 marks and contributes 30% weightage in final evaluation. Minimum 40 marks are required to pass. All questions are compulsory. Solutions must be written clearly with proper derivations and submitted to your Study Centre.
MPH 011 Assignment Submission End Date
For students enrolled in January 2026 – Submit before 31st December 2026 to the Coordinator of the Learner Support Centre.
Why Choose Our MPH 011 IGNOU Solved Assignments?
- Step-wise derivations with proper mathematical clarity so you don’t lose marks due to missing logical steps in proofs and calculations.
- All statistical mechanics concepts explained in simple academic language for better understanding of ensembles and quantum distributions.
- Exact alignment with IGNOU TMA 2026 pattern including marks distribution and structured presentation format.
- Neatly formatted equations, proper symbols, and logical flow suitable for handwritten rewriting without confusion.
- Detailed explanations for Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein statistics for conceptual strength.
- Carefully error-checked solutions ensuring accurate calculations and correct thermodynamic expressions.
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FAQs – MPH 011 Solved Assignment
1. Is MPH 011 difficult?
MPH 011 is conceptually intensive because it combines probability theory, thermodynamics, and quantum mechanics. Many students find it challenging mainly due to mathematical derivations. However, if you understand the logic behind partition functions, ensembles, and distribution laws, the subject becomes manageable. Structured practice and stepwise derivations make scoring much easier.
2. How should I write long derivation questions?
Always begin with definitions and assumptions. Write each mathematical step clearly without skipping intermediate reasoning. Mention formulas used and explain transitions logically. IGNOU examiners value clarity over lengthy writing. A neat structure—introduction, derivation, conclusion—helps secure better marks.
3. Are diagrams and graphs important in this assignment?
Yes, especially for Fermi-Dirac and Bose-Einstein distributions, Ehrenfest equations, and thermodynamic fluctuations. Properly labeled graphs improve presentation quality and demonstrate conceptual clarity, which can positively influence evaluation.
4. What happens if I fail in assignment?
If you score below 40 marks, you must reappear by submitting the next valid assignment as per IGNOU schedule. Assignment submission is mandatory before filling examination form, so timely submission is extremely important.
5. How much weightage does MPH 011 assignment carry?
The assignment carries 30% weightage in final evaluation. Even if you perform well in the term-end examination, poor assignment marks can reduce your overall grade. Writing well-structured, correct, and complete answers is crucial for a strong final percentage.
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