Microcanonical Ensemble | Statistical Mechanics | CSIR NET Physics June 2026 | L4 | IFAS

Statistical Mechanics CSIR NET Physics lecture on Microcanonical Ensemble (Lec 04) for CSIR NET June 2026. Covers statistical physics for CSIR NET, PYQ insights, and concepts for physical science preparation. Ideal for CSIR NET physics June 2026 aspirants targeting strong fundamentals.

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⏳ Lecture Timeline:
[00:00:00] – Introduction To Microcanonical Ensemble
[00:05:04] – Density of States Definition
[00:07:14] – Phase Space: 1D Microstates
[00:09:40] – 2D & 3D Phase Space Volume
[00:12:33] – Configurational Volume (L³)
[00:13:38] – Momentum Space Sphere (Radius √2mE)
[00:15:40] – Net Phase Space Volume
[00:16:15] – Single Cell Volume (h³)
[00:19:51] – Formula: Number of Microstates (3D)
[00:20:45] – Density of States: g(E) = dΩ/dE
[00:24:33] – g(E) for 1D, 2D, 3D Free Particle
[00:28:48] – Trick: General Dispersion E ∝ p^s
[00:30:27] – General Ω ∝ E^{d/s}
[00:31:48] – General g(E) ∝ E^{d/s - 1}
[00:33:25] – Question: Density of States (E ∝ k^s)
[00:40:34] – Microcanonical: Isolated System (N,V,E fixed)
[00:46:12] – Postulate: Equal Probability (1/Ω)
[00:50:07] – Macrostate Probability (Ω_i / Ω)
[00:52:13] – Boltzmann Entropy: S = k_B ln Ω
[00:56:31] – Bridge: Statistical to Thermodynamics
[01:00:27] – Complete Session (Microcanonical Ensemble)
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📖 Topics Covered in This Lecture:
Density of States (1D,2D,3D free particle), Microcanonical Ensemble (N,V,E fixed), Equal Probability Postulate, Boltzmann Entropy Formula & General DOS: g(E) ∝ E^(d/s − 1)
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📚 Lecture Summary:
In this session, IFAS Expert Faculty focuses on the Microcanonical Ensemble – an isolated system with fixed N, V, E. Key concepts: density of states g(E)=dΩ/dE for continuous energy bands, derived for 1D (g∝E⁻¹/²), 2D (g∝E⁰), 3D (g∝E¹/²). General formula: Ω∝E^(d/s) → g(E)∝E^(d/s−1). Equal probability postulate and Boltzmann’s entropy S = k_B ln Ω bridges statistical mechanics to thermodynamics. Essential for CSIR NET Physics, GATE Physics & SET Physics.
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🎓 This lecture is highly beneficial for students preparing for:
✅ CSIR NET Physical Science ✅ GATE Physics ✅ JEST Physics
✅ TIFR Physics ✅ BARC / DRDO / ISRO Exams ✅ SET / PhD Entrance Exams

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