Two plates A and B have thermal conductivities and respectively. They have same surface area and same thickness. [2023]

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Solution

Q.
Two plates A and B have thermal conductivities ${84 W m}^{- 1} K^{- 1}$ and ${126 W m}^{- 1} K^{- 1}$ respectively. They have same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of A and B are kept at $100 ° C$ and $0 ° C$ respectively, then the temperature of the surface of contact in steady state is ________ ${}^{\circ}C$ . [2023]

Ans.
(40)

Let the temperature of the contact surface is T, then

$H_{A} = H_{B}$

$\frac{K_{A} A (T_{A} - T)}{L} = \frac{K_{B} A (T - T_{B})}{L}$

$84 (100 - T) = 126 (T - 0)$

$2 (100 - T) = 3 T$

$\Rightarrow T = 40 ° C$

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