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A slab consists of two parallel layers o...

A slab consists of two parallel layers of two different materials of same thickness having thermal conductivities `K_(1) and K_(2)`. The equivalent conductivity of the combination is

A

`K_1 - K_2`

B

`(k_1)/(K_2)`

C

`(2k_1 K_2)/( K_1 +K_2)`

D

`(K_1+K_2)/(2K_1 K_2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Rate of flow of heat AT through each layer of slab is same.
`K_1 A(Delta T_1 )/(l ) = K_2 A ( Delta T_2)/(l)`
` =(K (Delta T_1 +Delta T_2 ) A)/(2l)`
`or K_1 Delta T_1 = K_2 Delta T_2`
`=(K(Delta T_1 +Delta T_2))/(2) = C `(say)
` therefore Delta T_1 = (C) /( K_1) , Delta T_2 =(C )/( K_2) ,Delta T_1 +Delta T_1 +Delta T_2 =(2C )/( K )`
` or (C )/(K _1) +(C )/( K_2) =(2C)/(K ) or K =(2K_1 K_2)/( K_1 +K_2)`
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