An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Textbook Question
Chapter 6.7, Problem 48P
For a diatomic gas near room temperature, the internal partition function is simply the rotational partition function computed in Section 6.2, multiplied by the degeneracy Z of the electronic ground state.
(a) Show that the entropy in this case is
Calculate the entropy of a mole of oxygen
(b) Calculate the chemical potential of oxygen in earth’s atmosphere near sea level, at room temperature. Express the answer in electron-Volts.
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9.1. Consider the results for ideal gases derived from quantum mechanics. Write an
expression for the function s(T, v) that includes the parameter A(T).
(a) Show that the behavior of the entropy as T0 is unrealistic in a quantum
sense. What approximation in the derivation is responsible for this behavior?
(b) The Sackur-Tetrode equation is valid when the thermal de Broglie wave-
length is much less than the average molecular separation distance, A(T) <
(V/N)13, which is generally the case at high temperatures. Calculate the
temperature at which this inequality is first violated for an ideal gas at
atmospheric pressure and with a mass of 6.6 × 10-26 kg/molecule (which is
typical of argon).
x
The first excited energy level of a hydrogen atom has an energy of10.2 eV, if we take the ground-state energy to be zero. However, the first excited level is really four independent states, all with the same energy. We can therefore assign it an entropy of 8 = kIn 4, since for this given value of the energy, the multiplicity is 4. Question: For what temperatures is the Helmholtz free energy of a hydrogen atom in the first excited level positive, and for what temperatures is it negative?
Let's consider a classical ideal gas whose single-particle partition function of molecules is Z ₁.
statements is true?
Which of the following
Select one:
a. If the gas molecules of N molecules cannot be separated from each other, and the partition function ZN of the
system is written ZN = Z₁N, the entropy of the gas calculated from Z N is obtained, which is an extensive quantity.
1
O b. If the molecules cannot be separated from each other, the partition function of the system can be written in the form
ZN = Z₁N/N!. In this case, the entropy calculated from Z N is obtained, which is an extensive quantity.
1
N
O c. If the gas molecules of N molecules cannot be separated from each other, the partition function Z of the system can
be written Z N = Z₁N.
Chapter 6 Solutions
An Introduction to Thermal Physics
Ch. 6.1 - Prob. 2PCh. 6.1 - Prob. 4PCh. 6.1 - Prob. 5PCh. 6.1 - Prob. 6PCh. 6.1 - Prob. 7PCh. 6.1 - Prob. 8PCh. 6.1 - Prob. 9PCh. 6.1 - Prob. 10PCh. 6.1 - Prob. 11PCh. 6.1 - Prob. 12P
Ch. 6.1 - Prob. 13PCh. 6.1 - Prob. 14PCh. 6.2 - Prob. 15PCh. 6.2 - Prob. 16PCh. 6.2 - Prob. 17PCh. 6.2 - Prob. 18PCh. 6.2 - Prob. 19PCh. 6.2 - Prob. 20PCh. 6.2 - For an O2 molecule the constant is approximately...Ch. 6.2 - The analysis of this section applies also to...Ch. 6.3 - Prob. 31PCh. 6.4 - Calculate the most probable speed, average speed,...Ch. 6.4 - Prob. 35PCh. 6.4 - Prob. 36PCh. 6.4 - Prob. 37PCh. 6.4 - Prob. 39PCh. 6.4 - Prob. 40PCh. 6.5 - Prob. 42PCh. 6.5 - Some advanced textbooks define entropy by the...Ch. 6.6 - Prob. 44PCh. 6.7 - Prob. 45PCh. 6.7 - Equations 6.92 and 6.93 for the entropy and...Ch. 6.7 - Prob. 47PCh. 6.7 - For a diatomic gas near room temperature, the...Ch. 6.7 - Prob. 49PCh. 6.7 - Prob. 50PCh. 6.7 - Prob. 51PCh. 6.7 - Prob. 52PCh. 6.7 - Prob. 53P
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