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Chapter 15 The heat capacity
of a diatomic gas
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For a diatomic gas, f=7, the equipartition of energy gives
U=(7/2)NkT, C
v
=(7/2)Nk, C
P
=(9/2)Nk, so that
γ
=C
P
/C
V
=1.28.
This is inconsistent with the experimental observation.
Moreover, the classical kinetic theory predicts that c
V
and c
P
are constant. This is not true for a diatomic gas.
This was
considered as the most challenging problem encountered in
kinetic theory.
In this chapter, we shall see how this problem
was solved.
In Chapter 14, we applied the MB stat. to treat a monatomic
gas, where only the translational motion of molecules is
considered. In contrast, to treat a diatomic gas, we have to
take into account the internal degrees of freedom such as
vibrations, rotations and electronic excitations.
Assuming that contributions from electronic excitations are
negligible small (as we’ll prove), the energy of a diatomic
molecule is the sum of the kinetic energy due to the
translational motion of the center of mass of the molecules, the
vibrational energy due to the vibrational of the two atoms along
the axis joining them and the rotational energy due to the
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This note was uploaded on 02/28/2011 for the course PHYS 359 taught by Professor Dr.asdas during the Winter '10 term at Waterloo.
 Winter '10
 Dr.asdas
 mechanics, Energy, Heat

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