An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter 8.1, Problem 12P
To determine
Verification of the statement that second virial coefficient
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You are studying a gas known as "gopherine" and looking in the literature you find that someone has
reported the partition function for one molecule of this gas,
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q(V, T) = )
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Assume that the molecules are independent and indistinguishable. Derive the expressions for the
energy, (E), for this gas. Give your answers in terms of N, kg, T. V and the constants A and B.
O (E) = NkaT
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Consider a system with 1000 particles that can only have two energies, ɛ, and
with
ɛ, > E,. The difference between these two values is Aɛ = ɛ, -& . Assume that gi = g2 = 1. Using the
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equation for the Boltzmann distribution graph the number of particles, ni and m, in states &
n2,
E
and
E, as a
function of temperature for a Aɛ = 1×10-2' J and for a temperature range from 2 to 300 K. (Note: kg =
1.380x10-23 J K-!.
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Two systems A and B, of identical composition, are brought together and allowed to exchange both
energy and particles, keeping volumes VA and VB constant. Show that the minimum value of the
quantity (dEA/dNA) is given by
HATB – HBTA
TB – TA
where the u's and the T's are the respective chemical potentials and temperatures.
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