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Conduction

A 10 cm lon...

Question

A $10$ cm long copper rod is welded to $20$ cm long steel rod each having cross-section A. If their thermal conductivities are $386 J m^{- 1} s^{- 1}^{o} C^{- 1}$ and $46 J m^{- 1} s^{- 1}^{o} C^{- 1}$ the temperature of junction will be _____.
Given : Copper end is at $100^{o} C$ and steel rod end is at $0^{0} C$

A

{87.5}^{o} C

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B

{79.3}^{o} C

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C

75^{o} C

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D

{71.5}^{o} C

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Solution

The correct option is D ${71.5}^{o} C$
$T h e t h e r m a l r e s i s t a n c e R o f r o d o f l e n g t h L,$
$a r e a o f c r o s s s e c t i o n A a n d t h e r m a l c o n d u c t i v i t y K i s g i v e n b y R = \frac{L}{K A} T h e t h e r m a l r e s i s t a n c e o f c o p p e r r o d R_{C u} = \frac{20}{386 \times A} T h e t h e r m a l r e s i s t a n c e o f s t e e l r o d R_{s t e e l} = \frac{10}{46 \times A} L e t t e m p e r a t u r e o f t h e j u n t i o n b e T C u r r e n t t h r o u g h c o p p e r r o d = C u r r e n t t h r o u g h s t e e l r o d \frac{100 - T}{R_{C u}} = \frac{T - 0}{R_{S t}} P u t t i n g t h e v a l u e s a n d s o l v i n g w e g e t T = 71.5 ℃$

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