Two bodies of specific heats S1 and S2 having same heat capacities are combined to form a single composite body. Prove that the specific heat of the composite body is 2 S1 S2/S1 + S2

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Solution

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$l e t M 1 b e t h e m a s s o s S 1 s p e c i f i c h e a t c a p a c i t y . M 2 b e t h e m a s s o f S 2 s p e c i f i c h a e t c a p a c i t y . i t i s g i v e n t h a t h e a t c a p a c i t y o f b o t h a r e s a m e . M 1 S 1 = M 2 S 2 \Rightarrow \frac{M 1}{M 2} = \frac{S 2}{S 1} f o r ∆ T r i s e i n t e m p b o t h r e q u i r e d s a m e h r a t a s h e a t c a p a c i t y i s s a m e . Q = M 1 S 1 ∆ T = M 2 S 2 ∆ T i f b o t h a r e c o m b i n e d t h e n 2 Q = (M 1 + M 2) S ∆ T; S i s t h e c o m b i n e d s p e c i f i c h e a t c a p a c i t y . M 1 S 1 ∆ T + M 2 S 2 ∆ T = (M 1 + M 2) S ∆ T S = \frac{M 1 S 1 + M 2 S 2}{M 1 + M 2} = \frac{\frac{M 1}{M 2} S 1 + S 2}{\frac{M 1}{M 2} + 1} = \frac{2 S 2 S 1}{S 1 + S 2} R e g a r d s$

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