Statistical ensembles-b.subha

statistical Ensembles- presentation

1. E.M.G. YADAVA WOMEN’S COLLEGE, MADURAI – 625 014. (An Autonomous Institution – Affiliated to Madurai Kamaraj University) Re-accredited (3 rd Cycle) with Grade A + and CGPA 3.51 by NAAC STATISTICAL MECHANICS ENSEMBLES Mrs.B.Subha Assistant Professor Department of Physics E.M.G Yadava Women’s College, Madurai .

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 Introduction

3. A collection of particles - system A collection systemts – ensembles The systems may have same macroscopic proterties and may have different microscopic properties. Ensembles

4. Ensembles Three types of Ensembles Canonical Ensembles Grand Canonical Ensembles Micro Canonical Ensembles

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. Canonical Ensembles

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 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. Grand Canonical Ensemble Large reservoir (constant T ) All the ensemble members have the same (V, T, m i ) 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. Micro Canonical Ensembles

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. References

12. Thank you