A compound slab is made with two different materials A and B with coefficient of thermal conductivity `K_(A) = 2K_(B)` and thickness `x_(A) = (1)/(2) x_(B)`.
If the face of the A surface is at `100^(@)c` and that of the B surface is at `25^(@)C` the temperature of the common surface will be

Options

A. `85^(@)C`
B. `45^(@)C`
C. `40^(@)C`
D. `15^(@)C`

Answer

A

Explanation

Let, T = temperature of the common surface,
`(K_(A)A(T_(A)-T))/(delta_(A))=(K_(B)A(T-T_(B)))/(delta_(B))`
`(2K_(B)(100-T))/((X_(B)/(2)))=(K_(B)(T-25))/(X_(B))`
`4(100-T) = T-25`
` 400 - 4T = T - 25`
`5T = 425`
`T = 85^(@)C`