Statistical ensembles-b.subha
- 2. Methodology of Thermodynamics and Statistical Mechanics Thermodynamics study of the relationships between macroscopic properties Volume, pressure, compressibility, … Statistical Mechanics (Statistical Thermodynamics) how the various macroscopic properties arise as a consequence of the microscopic nature of the system Position and momenta of individual molecules (mechanical variables) Statistical Thermodynamics (or Statistical Mechanics) is a link between microscopic properties and bulk (macroscopic) properties
- 3. A collection of particles - system A collection systemts – ensembles The systems may have same macroscopic proterties and may have different microscopic properties.
- 5. represents states of a mechanical system in thermal equilibrium with a heat bath at a fixed temperature. system can exchange energy with the heat bath, so that the states of the system with differ in total energy.
- 6. Canonical Ensemble Large reservoir (constant T) All the ensemble members have the same (n, V, T) Energy can be exchanged but particles cannot Number of Systems : N N ∞
- 7. Grand Canonical Ensembles represents the possible states of a mechanical system of particles that are in thermo-dynamic equilibrium (thermal & chemical) with a reservoir. system is said to be open in sense that the system can exchange energy and particles with a reservoir. So that the system can differ in bath their total energy and total no. of particles.
- 8. Large reservoir (constant T ) All the ensemble members have the same (V, T, mi ) Energy and particles can be exchanged Number of Systems : N N ∞
- 9. Micro canonical ensembles represents the possible states of a mechanical system whose total energy is exactly specified. System is assumed to be isolated in the sense the energy of the system does not change with time.
- 10. Micro Canonical Ensembles EVN EVN EVN impermeable All the ensemble members have the same (E, V, N) there is no transfer of Energy and mass isolated
- 11. Gibbs,Josiah willard(1902). Elementary principles in Statistical Mechanics.New York: Charles Scribner’s Sons. Cercignani,Carlo,(1998). Ludwig Boltzmann: The Man Who Trusted Atoms. Oxford University Press. IsBN 9780198501541. Huang, Kerson(1967). Statistical Mechanics. John Wiley & Sons. Srivastava, R.K; Ashok, J.(2005). Statistical Mechanics. New Delhi: PHI Learning Pvt.Ltd. ISBN 9788120327825.
- 12. Thank you