5. Consider a lattice gas of N particles distributed cells (with N < V). Suppose that each cell may be either empty or occupied by a single particle. The number of microscopic states of this system will be given by among V! N (V, N) = N! (V – N)! Obtain an expression for the entropy per particle, s = s where v = V/N. From this fundamental equation, obtain an expression for the equation of state p/T. Write an expansion of p/T in terms of the density p = 1/v. Show that the first term of this expansion gives the Boyle law of the ideal gases. Sketch a graph of µ/T, where µ is the chemical potential, in terms of Whetia the

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5. Consider a lattice gas of N particles distributed
cells (with N < V). Suppose that each cell may be either empty
or occupied by a single particle. The number of microscopic
states of this system will be given by
among
V!
N (V, N) =
N! (V – N)!
Obtain an expression for the entropy per particle, s = s
where v =
V/N. From this fundamental equation, obtain an
expression for the equation of state p/T. Write an expansion of
p/T in terms of the density p = 1/v. Show that the first term
of this expansion gives the Boyle law of the ideal gases. Sketch
a graph of u/T, where u is the chemical potential, in terms of
the density p. What is the behavior of the chemical potential in
the limits p →
0 and p → 1?
Transcribed Image Text:5. Consider a lattice gas of N particles distributed cells (with N < V). Suppose that each cell may be either empty or occupied by a single particle. The number of microscopic states of this system will be given by among V! N (V, N) = N! (V – N)! Obtain an expression for the entropy per particle, s = s where v = V/N. From this fundamental equation, obtain an expression for the equation of state p/T. Write an expansion of p/T in terms of the density p = 1/v. Show that the first term of this expansion gives the Boyle law of the ideal gases. Sketch a graph of u/T, where u is the chemical potential, in terms of the density p. What is the behavior of the chemical potential in the limits p → 0 and p → 1?
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