In a lattice gas, atoms occupy sites with energy and there is zero energy when t

Question

In a lattice gas, atoms occupy sites with energy and there is zero energy when the site is unoccupied. At most one atom can occupy a site. Assume a lattice gas of cubic symmetry with occupancy of M sites, and with N cells.

a) Using the energy expression U = M for a microstate, develop an expression for the temperature of the lattice gas.

b) Consider two subsystems of size N/2 each, system A with MA atoms, and system B with MB atoms, with M=MA+MB These subsystems are brought into contact. For very large N,M, show that P(N,MA) is sharply peaked about MA = M/2. Namely, prove (i) the max is at M/2, and (ii) the distribution falls off for

|MA – M/2| ~ N -1/2.

Explanation / Answer

Take the derivative and solve for zero, my brother.

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