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| # | Chapter Title | Key Problems to Include | | :--- | :--- | :--- | | 1 | Zeroth & First Law | Temperature equilibrium, work in different paths, internal energy as state function | | 2 | Second Law & Entropy | Carnot efficiency, entropy change (reversible/irreversible), Clausius theorem | | 3 | Thermodynamic Potentials | Maxwell relations from $F, G, H$, natural variables, Legendre transforms | | 4 | Phase Transitions | Clausius-Clapeyron equation, latent heat, vapor pressure curve, triple point | | 5 | Kinetic Theory of Gases | Maxwell-Boltzmann speed distribution, mean free path, effusion | | 6 | Classical Statistical Mechanics | Microcanonical ensemble (ideal gas entropy), Liouville theorem, equipartition | | 7 | Canonical Ensemble | Partition function $Z$, average energy, heat capacity (Einstein solid, 2-level system) | | 8 | Grand Canonical Ensemble | Fluctuations in $N$, adsorption isotherms (Langmuir), quantum gases | | 9 | Ideal Quantum Gases | Fermi-Dirac & Bose-Einstein distributions, Fermi energy, Bose-Einstein condensation | | 10 | Interacting Systems | Van der Waals gas (Maxwell construction), Ising model (mean field solution) | | 11 | Non-Equilibrium Thermo | Entropy production, Onsager relations, Fourier/Ohm’s law as examples | | 12 | Appendices | Mathematical tools (Gaussian integrals, Stirling approx, Lagrange multipliers) | Due to copyright constraints, I cannot provide direct
Organize the PDF into 10–12 chapters. Each chapter must have: Organize the PDF into 10–12 chapters
Problem: A paramagnetic solid consists of (N) non-interacting spins (S = \frac12) with magnetic moment (\mu). In a magnetic field (B) at temperature (T), compute the entropy, magnetization, and heat capacity. compute the entropy
Solution (summary):
Single-particle partition function: (z = e^\beta \mu B + e^-\beta \mu B = 2\cosh(\beta \mu B)).
(N)-particle: (Z = z^N).
Helmholtz free energy: (F = -kT \ln Z = -NkT \ln(2\cosh(\beta \mu B))).
Magnetization: (M = -\partial F/\partial B = N\mu \tanh(\beta \mu B)).
Entropy: (S = -\partial F/\partial T = Nk[\ln(2\cosh(x)) - x \tanh(x)]) where (x = \mu B/(kT)).
Heat capacity: (C_B = T \partial S/\partial T = Nk x^2 \textsech^2(x)).
(The PDF would then plot these functions and discuss the Schottky anomaly.)