Two plates each of area A, thickness `L_1 and L_2` thermal conductivities `K_1 and K_2` respectively are joined to form a single plate of thickness `(L_1+L_2)`. If the temperatures of the free surfaces are `T_1 and T_2`. Calculate.

(a) rate of flow of heat
(b) temperature of interface and
(c) equivalent thermal conductivity.

Options

A. `(K_(1)K_(2))/(K_(1)+K_(2))`
B. `(2K_(1)K_(2))/(K_(1)+K_(2))`
C. `((K_(1)^(2)+K_(2)^(2))^(3//2))/(K_(1)K_(2))`
D. `((K_(1)^(2)+K_(2)^(2))^(3//2))/(2K_(1)K_(2))`

Answer

B

Explanation

Equivalent thermal circuit
`R_(eq)=R_(1)+R_(2)=(2l)/(KA)=l/(K_(1)A)+l/(K_(2)A) rArr K=(2K_(1)K_(2))/(K_(1)+K_(2))`