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27 Nov 2019
In a lattice gas, atoms occupy sites with energy ε and there iszero energy when the site is unoccupied. At most one atom canoccupy a site. Assume a lattice gas of cubic symmetry withoccupancy of M sites, and with N cells.
a) Using the energy expression U = Mε for a microstate, develop anexpression for the temperature of the lattice gas.
b) Consider two subsystems of size N/2 each, system A withMA atoms, and system B with MB atoms, withM=MA+MB These subsystems are brought intocontact. For very large N,M, show that P(N,MA) issharply peaked about MA = M/2. Namely, prove (i) the maxis at M/2, and (ii) the distribution falls off for
|MA â M/2| ~ N -1/2.
In a lattice gas, atoms occupy sites with energy ε and there iszero energy when the site is unoccupied. At most one atom canoccupy a site. Assume a lattice gas of cubic symmetry withoccupancy of M sites, and with N cells.
a) Using the energy expression U = Mε for a microstate, develop anexpression for the temperature of the lattice gas.
b) Consider two subsystems of size N/2 each, system A withMA atoms, and system B with MB atoms, withM=MA+MB These subsystems are brought intocontact. For very large N,M, show that P(N,MA) issharply peaked about MA = M/2. Namely, prove (i) the maxis at M/2, and (ii) the distribution falls off for
|MA â M/2| ~ N -1/2.
Deanna HettingerLv2
25 Jan 2019
