Two sealed cells of identical shape are each divided in imagination into two equal halves
PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Statistical foundations and the equilibrium ensembles · Statistical foundations and the equilibrium ensembles
Thermal Physics, Ch Probability, random walks and the statistics of large numbers
Problem
Two sealed cells of identical shape are each divided in imagination into two equal halves. Cell A contains NA=2.5×1017 gas molecules; cell B has been pumped down and contains NB=2.5×1011 molecules. In each cell every molecule is equally likely to be in either half, independently of the others, so the number n in the left half is binomial with p=21.
((a)) Predict, before calculating, which cell shows the larger spread in the number of molecules in its left half, and which shows the larger relative spread. State your reasoning in one sentence each.
((b)) Compute σn for each cell.
((c)) Compute σn/⟨n⟩ for each cell, and the factor by which one exceeds the other.