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Question

two rods having thermal conductivity in the ratio of 5:3 and having equal length and equal cross sectional area, are joined face to face.If the temperature of free end of first rod is 100 C and temperature of free end second rod is 20 C. Temperature of junction will be?

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Solution

For one dimensional heat flow we know that flow of heat is

$Q = \frac{}{} \frac{K A (θ_{1} - θ_{2}) t}{l} w h e r e K = c o e f f e c i e n t o f t h e r m a l c o n d u c t i v i t y (θ_{1} - θ_{2}) = t e m p e r a t u r e d i f f e r e n c e b e t w e e n t w o f a c e s A c r o s s - s e c t i o n a l a r e a; l i s l e n g t h o f s l a b; t i s t i m e C o n s i d e r i n g s t e a d y s t a t e (r a t e o f f l o w o f h e a t i s c o n s \tan t) s o l e t θ b e t h e j u n c t i o n t e m p e r a t u e \frac{Q}{t} = \frac{5 K \times A \times (100 - θ)}{l} = \frac{3 K \times A \times (θ - 20)}{l} S o l v i n g w e θ = 70 ° C$

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