1. Consider a container of volume V that contains N non-interacting particles and that is in thermal equilibrium with it

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1 Consider A Container Of Volume V That Contains N Non Interacting Particles And That Is In Thermal Equilibrium With It 1 (118.68 KiB) Viewed 35 times

1. Consider a container of volume V that contains N non-interacting particles and that is in thermal equilibrium with its environment at a temperature T, where you may assume that N » 1, and hence the Stirling formula In N! = N In N - N. The partition function of a single particle (with zero spin) is given by V Z₁ A3 th (a) What does Ath refer to in this expression? In a few words, [2] state the consequences of the average inter-particle distance being » Ath and of it being Ath. [3] (b) Use the Gibbs entropy S and the canonical distribution to show that 1 S = 7(E) + KB In Z, where Z refers to the partition function of the system and (E) is the mean energy of the system. [3] (c) Using the results above, determine the entropy Sdist and Sindist in terms of (E), N, V and Ath, for the cases of the particles being distinguishable and indistinguishable, respectively. Explain your answer. (d) Show that Sindist is an extensive variable and that Sdist is not. [5] Explain why this is so. =