Question

Two metal cubes $A$ and $B$ of same size are arranged as shown in Fig. The extreme ends of the combination are maintained at the indicated temperature. The arrangement is thermally insulated. The coefficients of thermal conductivity of $A$ and $B$ are $300W/m^{\circ }C$ and $200W/m^{\circ }C$, respectively. After steady state is reached, the temperature $t$ of the interface will be ___________.

Answer 1

The heat temperature through $A$ per second
$Q_1=K_{1}A(100-t)/l$
The heat transferred through $B$ per second
$Q_2=K_{2}A(t-0)/l$
At steady state, $K_{1}A(100-t)/l=K_{2}A(t-0)/l$
$\Rightarrow 300(100-t)=200(t-0)$
$\Rightarrow 300-3t=2t\Rightarrow t={60}^{\circ }C$.