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Old Mar 4th 2010, 03:27 PM   #1
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Density of State

I have this question given to me in my physics course to help with studying, but I'm a bit stuck on how to tackle it.

The number of microstates in a system with energy between E and E+delE if an isolated system of N particles in a volume V is represented by this:

g(E)delE = c(V-bN)^N * (E+(N^2a)/V)^(3N/2)*delE

a, b, and c are constants, while del is the delta operator.

(a) Determine the entropy of the system as a function of E, V, and N.

(b) Determine the temperature T as a function of E, V, and N

(c) Determine the energy in terms of T, V, and N.

(d) What is the pressure as a function of T and p = N/V?
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Old Apr 8th 2010, 03:38 PM   #2
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It seems to be distribution of real gas (van der Waals model).

From the main equation of statistics
S = k ln g(E)
we get
(1) S = kN ln [ (V-bN)(E+N^2a/V)^3/2 ].

1/T = dS/dE
1/T = (3/2) kN/(E+N^2a/V) and
T = (2/3) (E+N^2a/V)/kN.

From this equation we get E
E = (3/2) kNT - N^2a/V.

From (1) expressing E and
P = -(dE/dV) S=const we get
P = kNT/(V-bN) - N^2a/V^2 or
(P+N^2a/V^2)(V-bN) = kNT.
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density, state

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