Two slabs A and B of equal surface area are placed one over the other such that their surface are completely in contact. The thickness of slab A is twice that of B. The coefficient of thermal conductivity of slab A is twice that of B. The first surface of slab a is maintained at `100^(@)C`, while the second surface of slab B is maintained at `25^(@)C`. The temperature at the contact of their surface is

Options

A. `62.5^(@)C`
B. `45^(@)C`
C. `55^(@)C`
D. `85^(@)C`

Answer

A

Explanation

`Q_(A) = Q_(B)`
`(K_(A) A(T_(1) - T)) /t_(A) = (K_(B) A(T - T_(2))) /t_(B)`
` implies (2K_(B) (100 - T))/(2t_(B)) = (K_(B)(T-25))/t_(B)`
` implies 100 - T =T - 25 `
`therefore T = 62.5^(@)`