In the text, two Einstein solids with oscillators shared energy units, and the most…

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 Microstates, multiplicity and the statistical entropy

Problem

In the text, two Einstein solids with

N_A = N_B = 3

oscillators shared

q = 6

energy units, and the most probable split was the even one. Now keep the two solids the same, weakly coupled in a rigid insulating box, and raise the shared total to

q = 8

units of size

h\nu

. Each oscillator holds a whole number of units above its lowest level, every accessible microstate of the pair is equally likely, and

\Omega(N,q) = \binom{q+N-1}{q}

. ((a)) Tabulate

\Omega_A\Omega_B

for every

q_A

from

0

8

and state the most probable value of

q_A

. ((b)) Find the probability of that most probable macrostate, to three significant figures. ((c)) Compute the same probability for the

q = 6

case and say how raising

q

at fixed

N

has changed it.

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