An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter 6.2, Problem 25P
The analysis of this section applies also to linear polyatomic molecules, for which no rotation about the axis of symmetry is possible. An example is
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In this and following questions, we develop a model for spontaneous
emission of a photon by a diatomic molecule AB (a model molecule),
which rotates and vibrates. In intermediate calculations, atomic units
(a.u.) will be used: unit of mass = the mass of electron, unit of charge
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electron is -e). The initial state of the molecule is an excited
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molecule with the reduced mass µ = 10,000 a.u. (it is similar to the
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V(r)
=
C6
p12
C12
p6
"
where r is the distance between A and B in the molecule, C6 and C12
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The diatomic molecule N2 has a rotational constant B(~) = 2.0 cm-1 and a vibrational constant v(~) = 2400 cm-1. The symmetry number for the molecule is 2. Sorry that I cannot write the symbols properly here for the wavenumber versions of the spectroscopic constants.
(a) Calculate the rotational partition function and the vibrational partition function for N2 at T = 298 K assuming the high-temperature limit is valid in both cases.
(b) Suppose that a high-temperature limit for a partition function gives the value q = 0.34. Comment on the value and whether the high-temperature limit is valid.
N 2 has a molecular weight of 28.02 g/mol a bit larger than that of a Ne atom, 20.18 g/mol.
(a) At a particular temperature, Z trans= 1.90 x 10 26 for Ne in a specific container. What is the translational partition function for a N2 molecule in this container at the same temperature?
(b) At 100 K, the rotational partition function for N2is found to be 17.39. What would you expect it to be at 500 K?
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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