Statistical Mechanics and Thermodynamics of Simple Systems We know that the tota

Question

Statistical Mechanics and Thermodynamics of Simple Systems

We know that the total energy U and the pressure P are identically the same for an assembly of distinguishable particles as for molecules of the classical ideal gas while S is different. Please explain why this makes sense. All you have to do is write in words and explain why it makes physical sense using heuristic reasoning or your physicist's intuition, that's all.

We are working under the assumption that the independent-particle approximation holds. So, why would this be the case?

The answer to this Chegg question is wrong: http://www.chegg.com/homework-help/questions-and-answers/statistical-mechanics-thermodynamics-simple-systems-know-total-energy-u-pressure-p-identic-q29448787

Explanation / Answer

In statistical mechanics we come across two very important terms 'macrostates' and 'microstates'. Macroscopic variables of a thermodynamic system describes the collective behaviour of the system for example pressure, energy, temperature etc. Whereas a microstate describes the properties of the individual constituent particles present in the system. Now for distinguishable particles the number of microstates is much much higher compared to indistinguishable particles (because say, the number of ways you can permute their positions is much higher than that of indistinguishable particles).

Since entropy is proportional to the number of microstates of the system hence the entropy is different for the case of distinguishable and indistinguishable particles although the other macroscopic parameters such as pressure, energy which determines the collective behaviour of the system remains same in both the cases.

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