Two identical plates of different metals are joined to form a single plate whose thickness is double the thickness of each plate. If the coefficients of conductivity of each plate are $2$ and $3$ respectively, then the conductivity of composite plate will be

What is the temperature (in $^oC$) of the steel-copper junction in the steady state of the system shown in Figure Length of the steel rod $=15.0\; cm ,$ length of the copper rod $=10.0\; cm ,$ temperature of the furnace $=300^{\circ} C ,$ temperature of the other end $=0^{\circ} C .$ The area of cross section of the steel rod is twice that of the copper rod. (Thermal conductivity of steel $=50.2 \;J s ^{-1} m ^{-1} K ^{-1} ;$ and of copper $\left.=385 \;J s ^{-1} m ^{-1} K ^{-1}\right)$

Ice formed over lakes has

Wires $A$ and $B$ have identical lengths and have circular cross-sections. The radius of $A$ is twice the radius of $B$ $i.e.$ ${r_A} = 2{r_B}$. For a given temperature difference between the two ends, both wires conduct heat at the same rate. The relation between the thermal conductivities is given by

If $K_{1}$ and $K_{2}$ are the thermal conductivities $L_{1}$ and $L _{2}$ are the lengths and $A _{1}$ and $A _{2}$ are the cross sectional areas of steel and copper rods respectively such that $\frac{K_{2}}{K_{1}}=9, \frac{A_{1}}{A_{2}}=2, \frac{L_{1}}{L_{2}}=2$.

Then, for the arrangement as shown in the figure. The value of temperature $T$ of the steel - copper junction in the steady state will be ........... $^{\circ} C$

The temperature drop through each layer of a two layer furnace wall is shown in figure. Assume that the external temperature $T_1$ and $T_3$ are maintained constant and $T_1 > T_3$. If the thickness of the layers $x_1$ and $x_2$ are the same, which of the following statements are correct.