Gibbs Paradox and Indistinguishability of Particles

P.K. Ahluwalia

1. Learning Outcomes

After studying this module, you shall be able to

• Comprehend the logical consequences of violation of extensiveness of a thermodynamic physical quantity while applying statistical methods.
• Appreciate paradoxical situation which arises on mixing of same type of ideal gases together, namely Gibbs Paradox.
• Infer the importance of indistinguishability of particles even in a classical system.
• Correct the expression of entropy of an ideal gas by applying so called correct Boltzmann counting rule.
• Learn that quantum statistical mechanics reduces to classical statistical mechanics results only when correct enumeration rules are applied in the classical limit.

References:-

1. Pathria R.K. and Beale P. D., Statistical Mechanics, 3rd ed. (Elsevier, 2011).
2. Landau L.D., Lifshitz E.M., “ Statistical Physics Part 1,” 3rd Edition, Oxford: Pergamon Press., 1982
3. Pal P.B., “An Introductory Course of Statistical Mechanics”, New Delhi: Narosa Publishing House Pvt. Ltd., 2008.
4. Panat P.V., “Thermodynamics and Statistical Mechanics,” New Delhi: Narosa Publishing House Pvt. Ltd., 2008
5. Yoshioka D., “Statistical Physics An Introduction,” Berlin Heidelberg: Springer-Verlag, 2007