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 $100^{\circ}\,C$ and $0{ }^{\circ}\,C$ respectively, then the temperature of the surface of contact in steady state is $..........\,{ }^{\circ} C$.
JEE MAIN 2023, Medium
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Let the temperature of contact surface is $T$, then
$H _{ A }= H _{ B }$
$\frac{ K _{ A } A\left(T_A-T\right)}{L}=\frac{ K _{ B } A \left( T - T _{ B }\right)}{ L }$
$84(100-T)=126( T -0)$
$2(100-T)=3\,T$
$200-2\,T =3\,T$
$T =40^{\circ}\,C$
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