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Two materials having coefficients of thermal conductivity '3k' and 'k' and thickness 'd' and '3d' respectively, are joined to form a slab as shown in the figures. The temperatures of the outer surfaces are `theta_(2)` and `theta_(1)` respectively `(theta_(2) gt theta_(2))`. The temperature at the interface is :

A

`(theta_(1))/(6) + (5 theta_(2))/(6)`

B

`(theta_(1))/(10) + (9 theta_(2))/(10)`

C

`(theta_(2) + theta_(1))/(2)`

D

`(theta_(1))/(3) + (2 theta_(2))/(3)`

Text Solution

Verified by Experts

The correct Answer is:
B

`d (dQ)/(dt) = (3KA(theta_(2) - theta))/(d) = (KA(theta - theta_(1)))/(3d)`
`theta = (theta_(1))/(10) + (9 theta_(2))/(10)`
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