Chapter 15 (I)

Chapter 15 (I) - Chapter 15 The heat capacity of a diatomic...

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Chapter 15 The heat capacity of a diatomic gas
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Introduction 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 M-B 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.
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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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Chapter 15 (I) - Chapter 15 The heat capacity of a diatomic...

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