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…

Two plates $\displaystyle A$ and $\displaystyle B$ have thermal conductivities $\displaystyle 84 \mathrm{Wm}^{-1} \mathrm{~K}^{-1}$ and $\displaystyle 126 \mathrm{Wm}^{-1} \mathrm{~K}^{-1}$ 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 $\displaystyle 100{ }^{\circ} \mathrm{C}$ and $\displaystyle 0^{\circ} \mathrm{C}$ respectively, then the temperature of the surface of contact in steady state is $\displaystyle \_\_\_\_$ $\displaystyle { }^{\circ} \mathrm{C}$.