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Equipartition Theorem

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Question

find the value of internal energy and the ratio of specific heats of monoatomic gas molecule.

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Solution

$M o n o a t o m i c g a s h a s t h r e e d e g r e e o f f r e d o m, s o t h e k i n e t i c e n e r g y o f m o n o a t o m i c g a s w h i c h i s a l s o t h e i n t e r n a l h e a t e n e r g y o f t h e m o n o a t o m i c g s a i s; U = E = \frac{3}{2} R T T h e s p e c i f i c h e a t e n e r g y a t c o n s \tan t v o l u m e i s g i v e n b y; c_{v} = \frac{d U}{d T} = \frac{d E}{d T} = \frac{3}{2} R a n d t h e s p e c i f i c h e a t e n e r g y a t c o n s t a n t v o l u m e i s; c_{p} = c_{v} + R = \frac{3}{2} R + R = \frac{5}{2} R T h e r e f o r e γ = \frac{c_{p}}{c_{v}} = \frac{\frac{5}{2} R}{\frac{3}{2} R} = \frac{5}{3} = 1.67$

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