The exhaustive list of topics in Advanced Thermodynamics in which we provide **Help with Homework Assignment** and **Help with Project** is as follows

- Thermodynamics and statistical mechanics
- Internal energy
- First law of thermodynamics
- Intensive and extensive properties.
- Concept of entropy
**Second law of thermodynamics :**- Extremum principles of Energy and Entropy.
- Legendre transforms of energy and reformulation of second law in terms of the Legenedre transforms
- Maxwell relations
- Maximum work theorem.
- Conditions of phase equilibrium and Its applications
- Gibbs Duhem relations
- Gibbs phase rule
- Cojugate variables
- Criteria for stability and its implications.

**Chemical reactions:**- Condition of equilibrium for a reaction mixture
- Equilibrium constants
- Heat of reaction.

**Thermodynamics of fluid-fluid interfaces:**- Dividing surface
- Surface excess quantities
- Condition of equilibrium at interfaces
- Kelvin equation
- Gibbs adsorption isotherm

**Thermodynamics of fluid-solid interfaces :**- Condition of equilibrium with respect to dissolution and growth of solids.

**Classical mechanics:**- Lagrangian formulation
- Constants of motion
- Hamilton's principle
- Phase space
- Concept of statistical ensemble
- Statistical independence of macroscopic bodies
- Liouville equation
- Measurements and ensemble averages.
- Microcanonical
- Canonical and Grand-canonical ensembles
- Gibbs entropy formula and Boltzmann entropy formula
- Partition functions
- Fluctuations and stability.

**Ideal gas :**- Analytical derivations of the partition functions of ideal gas in various ensembles and thermodynamic properties,

**Ideal solid :**- Analytical derivation of partition function
- Heat capacity
- Non-ideal gases
- Virial equation of state
- Second virial coefficient.

**Liquids :**- Distribution functions
- Pair correlation function g(r) and experimental measurement of g(r) by diffraction
- Mean-field theory and perturbation theory.

**Dilute solutions and colligative properties:**- Derivation of Raoults law
- Henry's law
- Van't Hoff 's formula for osmotic pressure.
- Boiling point elevation
- Freezing point depression.

**Introductory Quantum Statistical mechanics :**- Schrödinger Wave equation
- Degeneracy
- Partition functions.
- Ideal gas of polyatomic particles
- Molecular partition functions
- Einstein and Debye theory of perfect crystals.