[Part marks] (e) Two such containers - in thermal equilibrium at temperature T and containing many non-interacting parti

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Part Marks E Two Such Containers In Thermal Equilibrium At Temperature T And Containing Many Non Interacting Parti 1 (128.94 KiB) Viewed 48 times

[Part marks] (e) Two such containers - in thermal equilibrium at temperature T and containing many non-interacting particles are now put into contact, such that they can exchange particles. For convenience, we label their volumes V₁ and V₂, and the numbers of indistinguishable particles in them N₁ and №₂, respectively, with N₁ + N₂ = N = constant. We keep track of how many particles are in V₁ and how many are in V₂. i. Taking into account the number of possible permutations [3] of the particles, provide an expression for the partition function Zv₁+v₂ of this combined system. 1+ [4] ii. By appropriate maximisation of S₁+√₂, show that the particles are distributed such that N₁/N₂ = V₁/V₂. You may assume that N₁, N₂ » 1.