CSIR NET Physical Sciences Thermodynamic and Statistical Physics Syllabus

Thermodynamic and Statistical Physics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Thermodynamic and Statistical Physics in CSIR NET Physical Sciences, not a summary of it.

1. 1

   Laws of Thermodynamics and Their Consequences

   3 topics

   • First Law of Thermodynamics
   • Second Law of Thermodynamics
   • Third Law of Thermodynamics
2. 2

   Thermodynamic Potentials and Maxwell Relations

   3 topics

   • Internal Energy, Enthalpy, and Helmholtz Free Energy
   • Gibbs Free Energy
   • Maxwell Relations
3. 3

   Chemical Potential and Phase Equilibria

   2 topics

   • Chemical Potential
   • Phase Equilibria
4. 4

   Phase Space, Micro- and Macro-States

   2 topics

   • Phase Space
   • Micro-States and Macro-States
5. 5

   Ensembles and Partition Functions

   4 topics

   • Micro-Canonical Ensemble
   • Canonical Ensemble
   • Grand-Canonical Ensemble
   • Partition Functions
6. 6

   Free Energy and Thermodynamic Quantities

   1 topic

   • Connection between Free Energy and Thermodynamic Quantities
7. 7

   Classical and Quantum Statistics

   2 topics

   • Classical Statistics
   • Quantum Statistics
8. 8

   Ideal Bose and Fermi Gases

   2 topics

   • Ideal Bose Gas
   • Ideal Fermi Gas
9. 9

   Principle of Detailed Balance

   1 topic

   • Detailed Balance in Statistical Mechanics
10. 10

    Blackbody Radiation and Planck's Distribution Law

    2 topics

    • Blackbody Radiation
    • Planck's Distribution Law

Thermodynamic and Statistical Physics flashcards for CSIR NET Physical Sciences

21 of 50 cards from the Thermodynamic and Statistical Physics deck — real questions with worked answers.

1. What defines a first-order phase transition in terms of the Gibbs free energy?

   A transition in which the first derivatives of the Gibbs free energy $G$ (such as entropy $S = -\left(\frac{\partial G}{\partial T}\right)_{P}$ and volume $V = \left(\frac{\partial G}{\partial P}\right)_{T}$) are discontinuous. $G$ itself is continuous but has a kink.

2. What is latent heat and to which order of phase transition is it associated?

   Latent heat $L = T\,\Delta S$ is the heat absorbed or released during a phase change at constant temperature. It is nonzero in first-order transitions because of the discontinuity in entropy $\Delta S$.

3. State the Clausius-Clapeyron equation for the coexistence curve of a first-order transition.

   $$\frac{dP}{dT} = \frac{L}{T\,\Delta V} = \frac{\Delta S}{\Delta V}$$ where $L$ is the latent heat, $T$ the transition temperature, and $\Delta V$ the volume change.

4. What characterizes a second-order (continuous) phase transition?

   The first derivatives of $G$ (entropy, volume) are continuous, but second derivatives (specific heat $C_P$, compressibility $\kappa_T$, thermal expansion) are discontinuous or diverge. There is no latent heat.

5. What is an order parameter in the theory of phase transitions?

   A quantity that is zero in the disordered (high-temperature) phase and nonzero in the ordered (low-temperature) phase, e.g. magnetization $M$ for a ferromagnet or the condensate fraction. It rises continuously from zero in a second-order transition.

6. Define the critical exponents $\alpha$, $\beta$, $\gamma$, and $\delta$ near a continuous phase transition.

   With reduced temperature $t = \frac{T - T_c}{T_c}$: specific heat $C \sim |t|^{-\alpha}$; order parameter $M \sim (-t)^{\beta}$; susceptibility $\chi \sim |t|^{-\gamma}$; and at $T_c$, $M \sim H^{1/\delta}$.

7. What is the Ehrenfest classification of phase transitions?

   Phase transitions are classified by the lowest order $n$ of the derivative of the free energy that is discontinuous: a first-order transition has discontinuous first derivatives, an $n$-th order transition has discontinuous $n$-th derivatives. (Modern usage distinguishes only first-order vs. continuous.)

8. What is the relationship between magnetic susceptibility $\chi$, magnetization $M$, and field $H$?

   $$\chi = \frac{\partial M}{\partial H}$$ For linear response, $M = \chi H$. Diamagnets have $\chi < 0$, paramagnets have $\chi > 0$ (small), ferromagnets have large positive $\chi$.

9. What is diamagnetism and what is the sign of its susceptibility?

   Diamagnetism is the property whereby an applied magnetic field induces magnetic moments opposing the field (Lenz's law on orbital electrons). It gives a small negative susceptibility, $\chi_{dia} < 0$, and is present in all materials.

10. State the Langevin formula for diamagnetic susceptibility.

    $$\chi_{dia} = -\frac{n\mu_0 Z e^{2}}{6m}\langle r^{2}\rangle$$ where $n$ is the number density of atoms, $Z$ the number of electrons, $\langle r^{2}\rangle$ the mean square orbital radius. It is temperature-independent.

11. What is Landau diamagnetism?

    The diamagnetic contribution of conduction (free) electrons arising from the quantization of their orbital motion into Landau levels in a magnetic field. Its magnitude is $-\frac{1}{3}$ of the Pauli paramagnetic susceptibility for free electrons.

12. What is paramagnetism and the sign of its susceptibility?

    Paramagnetism arises from permanent atomic magnetic moments that align with an applied field, giving a small positive susceptibility $\chi_{para} > 0$. Thermal agitation opposes alignment, so $\chi$ decreases with temperature.

13. State the Curie law for paramagnetic susceptibility.

    $$\chi = \frac{C}{T}, \qquad C = \frac{n\mu_0 \mu^{2}}{3k_B}$$ where $C$ is the Curie constant, $\mu$ the magnetic moment per atom, $n$ the number density. Valid in the high-temperature / low-field limit.

14. Give the classical Langevin function for paramagnetic magnetization.

    $$M = n\mu\, L(x), \quad L(x) = \coth x - \frac{1}{x}, \quad x = \frac{\mu B}{k_B T}$$ For small $x$, $L(x) \approx \frac{x}{3}$, recovering the Curie law.

15. What is the Brillouin function and its role in quantum paramagnetism?

    $$B_J(x) = \frac{2J+1}{2J}\coth\!\left(\frac{2J+1}{2J}x\right) - \frac{1}{2J}\coth\!\left(\frac{x}{2J}\right)$$ It gives the magnetization $M = ng\mu_B J\, B_J(x)$ of a quantum paramagnet with angular momentum $J$, where $x = \frac{g\mu_B J B}{k_B T}$.

16. What is Pauli paramagnetism?

    The weak, nearly temperature-independent paramagnetism of conduction electrons in a metal, arising from the spin alignment of electrons near the Fermi surface. $\chi_{Pauli} = \mu_0 \mu_B^{2} g(\varepsilon_F)$, where $g(\varepsilon_F)$ is the density of states at the Fermi level.

17. What is ferromagnetism and what is the Curie temperature?

    Ferromagnetism is the spontaneous alignment of atomic magnetic moments producing net magnetization even without an applied field, due to the exchange interaction. The Curie temperature $T_c$ is the temperature above which spontaneous magnetization vanishes and the material becomes paramagnetic.

18. State the Curie-Weiss law for a ferromagnet above $T_c$.

    $$\chi = \frac{C}{T - T_c}$$ valid for $T > T_c$, where $C$ is the Curie constant and $T_c$ the Curie (paramagnetic) temperature. The susceptibility diverges as $T \to T_c^{+}$.

19. What is the Weiss molecular field theory of ferromagnetism?

    A mean-field theory in which each magnetic moment experiences an effective internal field $B_{eff} = B + \lambda M$ proportional to the magnetization. Self-consistent solution $M = M(B_{eff})$ predicts spontaneous magnetization below $T_c = \frac{C\lambda}{\mu_0}$ (or $\lambda C$).

20. Distinguish ferromagnetism, antiferromagnetism, and ferrimagnetism.

    Ferromagnetism: neighboring moments align parallel, large net $M$. Antiferromagnetism: neighboring moments align antiparallel and cancel, zero net $M$ (orders below the Neel temperature $T_N$). Ferrimagnetism: antiparallel moments of unequal magnitude give a nonzero net $M$.

21. What is the exchange interaction and why is it essential for ferromagnetism?

    A quantum-mechanical interaction arising from the Pauli exclusion principle and Coulomb repulsion, favoring parallel (or antiparallel) spin alignment. It is far stronger than magnetic dipole interactions and is what produces ordering at room-temperature scales.

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