obtain the ratio cp/cvfor a hydrogen gas using the law of equipartition of energy

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Solution

$T h e e q u i p a r t i t i i o n t h e o r m s t a t e s t h a t e a c h d e g r e e o f f r e e d o m c o n r i b u t e s \frac{1}{2} k t t o t h e m o l a r e n e r g y o f a g a s . I i n t e r n a l e n e r g y = f \times \frac{1}{2} R T w h e r e f i s t h e d e g r e e o f f r e e d o m S p e c i f i c h e a t a t c o n s \tan t v o l u m e = C_{v} = \frac{d U}{d T} = \frac{d}{d T} (f \times \frac{1}{2} R T) C_{v} = \frac{f R}{2} w e k n o w s p e c i f i c h e a t a t c o n s \tan t p r e s s u r e C_{p} = C v + R C_{P} = \frac{f R}{2} + R = \frac{R}{2} (f + 2) \frac{C_{p}}{C_{v}} = \frac{\frac{R}{2} (f + 2)}{\frac{f R}{2}} = 1 + \frac{2}{f}$

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