Two plates of equal areas are placed in contact with each other . Their thickness are `2 cm` and `3 cm` respectively. Temperature of the external surface of the first plate is `-25^(@)C` and that of the external surface of the second plate is `25^(@)C` What will be temperature of contact surface if the plates:-
(i) Are of same material (ii) Have thermal conductivity in ratio `2:3`.

Options

A. (i)`-5^(@)C` (ii) `0^(@)C`
B. (i) `5^(@)C` (ii)`0^(@)C`
C. (i) `0^(@)C` (ii) `-5^(@)C`
D. None of these

Answer

A

Explanation

(i) `overset(**)(Q) = (K_(1)A (theta+25))/(t_(1)) = (K_(2)A(25-theta))/(t_(2))`
`implies (KA(theta+25))/(2) = (KA(25-theta))/(3) implies theta = -5^(@)C`
`overset(**)(Q) = (K_(1)A (theta+25))/(t_(1)) = (K_(2)A(25-theta))/(t_(2))`
`implies (2A(theta+25))/(2) = (3A(25-theta))/(3) implies theta = 0^(@)C`