**Course Objectives:** The learners should be able to apply principles and laws of equilibrium thermodynamics to multicomponent systems. In addition, they should be able to use spectroscopic data to calculate thermodynamic properties of ideal gases, real gases, solids and metals using the principlesand techniques of statistical thermodynamics.

**Learning Outcomes:** At the end of the course, the learners should be able to:

** Calculate** change in thermodynamic properties, equilibrium constants, partial molar quantities, chemical potential. Identify factors affecting equilibrium constant.

**Apply** phase rule and, draw phase diagrams for one, and two component systems,

**identify** the dependency of temperature and pressure on phase transitions, and

**identify** first/second order phase transitions.

**Solve** problems based on Debye-Huckel limiting law. Calculate excess thermodynamic properties.

**Calculate** the absolute value of thermodynamic quantities (U, H, S, A, G) and

equilibrium constant (K) from spectroscopic data.

**Predict** heat capacity (Cv, Cp) of an ideal gas of linear and non-linear molecules

from the number of degrees of freedom, rotational and vibrational wave numbers.

**Derive** the temperature dependence of the second Virial coefficient (real gases) from

interatomic potentials.

**Explain** T3 dependence of heat capacity of solids at low temperatures (universal

feature) using Debye and Einstein theory of heat capacity of solids.

**Explain** the concept of Fermi energy in metals and use it to calculate the chemical

potential of conduction

**Course Contents:**

Classical Thermodynamics

Phase behavior of one and two component systems: Fundamental equations for open systems, Partial molar quantities and chemical potential, Chemical equilibrium, Phase behavior of one and two component systems, Ehrenfest classification of phase transitions.

Thermodynamics of mixtures: Thermodynamics of ideal and non-ideal solutions: Liquid-liquid solutions, liquid-solid solutions, multicomponent systems and excess thermodynamic properties, Activity of ideal, regular and ionic solutions.

**Statistical Thermodynamics**

Introduction: Concept of ensembles, partition functions and distributions, microcanonical, canonical and grand canonical ensembles, canonical and grand canonical partition functions, Boltzmann, Fermi-Dirac and Bose-Einstein distributions.

**Ideal gases:** Canonical partition function in terms of molecular partition function ofnon-interacting particles, Translational, rotational and vibrational partition functions. Absolute values of thermodynamic quantities (U,H,S,A,G) for ideal monoatomic and diatomic gases, heat capacity (Cv, Cp) of an ideal gas of linear and nonlinear molecules, chemical equilibrium.

**Real gases:** Canonical partition function for interacting particles, intermolecular potential (Lennard-Jones, Hard-sphere and Square-well) and virial coefficients. Temperature dependence of the second virial coefficient.

**Solids:** Thermodynamics of solids – Einstein and Debye models. T3 dependence of heat capacity of solids at low temperatures (universal feature).

**Metals:** Fermi function, Fermi energy, free electron model and density of states, chemical potential of conduction electrons.

**Text Books:**

1. P. Atkins and J. Paula, Physical Chemistry, 10th Edition, Oxford University Press,

Oxford 2014

2. D. A. McQuarrie and J. D. Simon, Molecular Thermodynamics, University Science

Books, California 2004

3. R. S. Berry, S. A. Rice and J. Ross, Physical Chemistry, 2nd Edition, Oxford

University Press, Oxford, 2007

4. D. A. McQuarrie, Statistical Mechanics, University Science Books, California 2005

5. B. Widom, Statistical Mechanics – A Concise Introduction for Chemists,

Cambridge, University Press, 2002