N atoms are in two boxes, box A: volume=V, and box B: volume=3V. (Assume a atoms make up a low density perfect gas).
1) How many ways can n be chosen, where n=(number of atoms in box A)?
2) Each atom if allocated a spatial state. Assuming that the number of available states within a volume V is proportional to that volume, write down an expression for the total number of microstates (Ω) present in the macrostate specified by n.
3) By optimising Ω determine the most likely number of gas atoms present in A and B. What are these values when N = 100?
4) Find the probability of the most likely distribution.
The attempt at a solution
1) 2^N right? (N binary choices)
3) Clearly 25 in A, 75 in B. But need to answer 2) to derive it their way.