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Real Gases

Derive K(B) [...

Question

Derive K(B) [Boltzmann's constant] x N(A) [ Avogadro 's No.]

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Solution

$W e k n o w f r o m k i n e t i c t h e o r y o f g a s e s t h a t, \frac{1}{3} M C^{2} = P V o r \frac{1}{3} M C^{2} = R T (\sin c e P V = R T) B u t m a s s o f t h e g a s p e r m o l e i s M / N, t h e r e f o r e, \frac{1}{3} \frac{M}{N} C^{2} = \frac{R}{N} T = k T I n t h e a b o v e f o r m u l a \frac{R}{N} = k, w h e r e R, N a n d k a r e g a s c o n s \tan t, A v o g a d r o' s c o n s \tan t a n d B o l t z m a n n c o n s \tan t r e s p e c t i v e l y . T h e r e f o r e R = k \times N .$

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