Two walls of thicknes `l_(1)` and `l_(2)` and ther-mal condctivities `K_(1)` and `K_(2)` are in contact In the steady state, if the temperature at the outer faces are `T_(1)` and `T_(2)` find the temperature at the common wall .

Options

A. `(K_(1) T_(1) D_(2) + K_(2) T_(2) d_(1))/(K_(1) D_(2) + K_(2) d_(1))`
B. `(K_(1) T_(1) + K_(2) T_(2))/(d_(1) + d_(2))`
C. `((K_(1) d_(1) + K_(2) d_(2))/(T_(1) + T_(2))) T_(1) T_(2)`
D. `(K_(1) d_(1) T_(1) + k_(2) d_(2) T_(2))/(K_(1) d_(1) + K_(2) d_(2))`

Answer

A

Explanation

(1) `i = (T_(1) - T)/(R_(1)) = (T - T_(2))/(R_(2))`
`(T_(1) - T)/(d_(1) // K_(1) A) = (T - T_(2))/(d_(2) // K_(2) A)`
`(K_(1) (T_(1) - T))/(d_(1)) = (k_(2) (T - T_(2)))/(d_(2))`
`k_(1) d_(2) T_(1) - K_(1) d_(2) T = k_(2) d_(1) T - k_(2) d_(1) T_(2)`
`T = (K_(1) d_(2) T_(1) + K_(2) d_(1) T_(2))/(K_(1) d_(2) + k_(2) d_(1))`