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Relation between Cp and Cv

Using the law...

Question

Using the law of equipartition of energy, show that for an ideal gas having f degrees of freedom y=1+2/f.

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Solution

$I n t e r n a l E n e r g y o f 1 m o l e g a s, U = \frac{n}{2} f R T S p e c i f i c h e a t a t c o n s \tan t v o l u m e, C_{V} = \frac{d U}{d t} = \frac{f}{2} R = \frac{R}{γ - 1} C_{P} = C_{V} + R γ = \frac{C_{P}}{C_{V}} = 1 + \frac{2}{f}$

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