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# Fundamentals of Statistical Thermodynamics

NPTEL via Swayam

### Overview

ABOUT THE COURSE:Statistical thermodynamics will establish a link between bulk properties based on classical thermodynamics (which students are presumed to have learnt) with microscopic properties of individual molecules. All the essential thermodynamic quantities and laws will be expressed in terms of relevant partition functions. The knowledge thus gained from the contents of this course will enable students to understand that thermodynamic quantities can also be obtained from spectroscopic measurements.INTENDED AUDIENCE: BS (Chemistry); M Sc (Chemistry)PREREQUISITES: Previous knowledge of Chemical Thermodynamics is preferredINDUSTRY SUPPORT: Chemical and Pharmaceutical Industries

### Syllabus

Weeks 1 and 2 :
• A recap of concepts of chemical thermodynamics and need to study statistical thermodynamics.
• Introducing the concepts of statistical thermodynamics, configurations and weights, Boltzmann distribution.
• Introducing the molecular partition function, discussion on various terms therein, interpretation of partition function and discussion on its applications.
• Connecting partition function with population of molecules in energy states and deriving expression for translational partition function for a molecule free to move in one dimension: discussion on physical meaning of all the terms in translational partition function.
• Deriving partition function for translational motion of particle in 2 and 3-dimensions; applications; tutorial problems based on population of states and partition function.
Weeks 3 and 4 :
• Internal energy in terms of molecular partition function; establishing relationship between β and temperature; associated numerical problems/applications
• Discussion on statistical entropy and derivation of Boltzmann formula S = klnW
• Relationship of entropy with partition function and its applications
• Introducing concepts of ensembles (microcanonical, canonical and grand canonical): dominating configurations, canonical distribution and discussion on canonical partition function
• Obtaining thermodynamic information in partition function: internal energy and entropy
Weeks 5 and 6 :
• Further discussion on entropy; Recovering molecular partition function from canonical partition function: establishing relationship between them for distinguishable and indistinguishable molecules and corresponding numerical problems/applications
• Discussion on partition function for a monoatomic perfect gas, derivation of Sackur-Tetrode equation and discussion on concept/terms involved therein
• Numerical problems based on Sackur-Tetrode equation and comparison of the result with those based on concept of classical thermodynamics
• Thermodynamic functions in terms of canonical partition function: Heltmotz energy, pressure; associated numerical problems/applications
• Enthalpy in terms of canonical partition function; associated applications and obtaining ideal gas equation from the use of the canonical partition function
Weeks 7 and 8 :
• Gibbs energy in terms of canonical partition function and associated applications/problems
• Rotational contribution (for linear and non-linear rotor) to partition function and associated numerical problems/applications
• Vibrational and electronic contributions to partition function; Overview of different contributions to overall partition function, associated numerical problems/applications
• Overview of different contributions to overall partition function, associated numerical problems/applications continued
• Mean energies (translational, rotational and vibrational) in terms of partition function and associated numerical problems/applications
Weeks 9 and 10 :
• Heat capacities in terms of translational, rotational, vibrational contributions and effect of dissociation (with numerical problems/applications)
• Residual entropy (discussion in terms of statistical and chemical thermodynamics with suitable examples)
• Deriving equilibrium constant in terms of partition function and associated numerical problems/applications
• Introduction to gas imperfection; Equations of state; Introduction to virial coefficients
• Configuration integral; Mayer f-function; hard sphere potential; Virial Coefficients
Weeks 11 and 12 :
• Derivation of equations of state with examples
• Radial Distribution Functions and their applications in selected systems
• Interpretation of thermodynamic quantities by Lattice Models
• Fermi-Dirac and Bose-Einstein statistics
• Overall summary on different topics covered in statistical thermodynamics and future perspectives

### Taught by

Prof. Nand Kishore

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