Download PDF by A M Guénault: Statistical physics

By A M Guénault

ISBN-10: 1402059744

ISBN-13: 9781402059742

ISBN-10: 1402059752

ISBN-13: 9781402059759

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Extra resources for Statistical physics

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Through the quantum region. This problem lies at the heart of a number of the historical paradoxes and controversies of classical statistical mechanics in the pre-quantum age. 16). If one has an assembly of particles, each of which may be in G states with equal probability, then S is readily evaluated. ) Since = G N for this situation, we may write S = kB ln = NkkB ln G. 16), we see that the two give the same answer if G = kB T /hν, the ratio of the two energy scales. This is a pleasingly plausible result.

It also goes to zero, albeit rather more gently as 1/T 2 , at high temperatures. (Prove this last statement? ) Entropy S Finally we obtain the entropy S. Again this is a thermal property only, independent of the zero-point term. 5 before us we have three possible derivations. 2) without recourse to calculus. e. S = 0 (C/T )dT . This is possible but not recommended. Instead let us use method 3. 1) for Z. 5). The entropy is obtained by one differentiation, since S = −(∂F/∂T )V ,N , the differentiation being at constant energy levels and number.

The formula β = −1/kkB T gives a statistical definition of temperature, which agrees with the usual thermodynamic definition. 8. Inclusion of T explicitly in the Boltzmann distribution is often useful in applications in which we specify a (T , V , N ) macrostate. 3 Two examples We now apply the general results of the previous chapter to two specific examples, chosen because they are easily soluble mathematically, whilst yet being of direct relevance to real physical systems. The first example is an assembly whose localized particles have just two possible states.

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Statistical physics by A M Guénault


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