JEE Main · 2023 · 13 Apr 2023 · Shift 2 · Heat & Thermodynamics

Two plates A and B have thermal conductivities

84 Wm^{- 1} K^{- 1}

and

126 Wm^{- 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

10 0^{\circ} C

and

0^{\circ} C

respectively, then the temperature of the surface of contact in steady state is

____

^{\circ} C

Answer: 40

Solution

In steady state, the rate of heat flow through both plates is equal:

H_{A} = H_{B}

\frac{K _{A} A ( T _{A} - T )}{L} = \frac{K _{B} A ( T - T _{B} )}{L}

where

T

is the contact surface temperature.

Simplifying:

K_{A} (100 - T) = K_{B} (T - 0)

84 (100 - T) = 126 T

8400 - 84 T = 126 T

8400 = 210 T

T = 4 0^{\circ} C

JEE Main · 2023 · 13 Apr 2023 · Shift 2 · Integer answer

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