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Under some conditions, the amplitudes of vibration of a diatomic molecule may be very large, with a certain degree of anharmonicity. In this case, the vibrational energy levels are given by the approximate expression
where x is the parameter of anharmonicity. To first order in x, obtain an expression for the vibrational specific heat of this system.
Physics
Note that
where
with a= βhw. We then have
from which we calculate the first-order correction to the specific heat,
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