The coefficient of thermal conductivity of copper is $9$ times that of steel. In the composite cylindrical bar shown in the figure,what will be the temperature at the junction of copper and steel (in $^{\circ} C$)?

$A$ copper rod of length $10 \ cm$ and cross-sectional area $100 \ cm^2$ is to conduct $4000 \ J/s$ of heat. The thermal conductivity of copper is $400 \ W/m \cdot ^\circ C$. The temperature difference between the two ends of the rod must be maintained at ............. $^\circ C$.

The figure shows a system of two concentric spheres of radii $r_1$ and $r_2$ kept at temperatures $T_1$ and $T_2$,respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to

Two plates of equal area are placed in contact. Their thicknesses are $2$ and $3$ units respectively. The temperature of the outer surface of the first plate is $-25^{\circ}C$ and the temperature of the outer surface of the second plate is $25^{\circ}C$. Find the temperature of the contact surface if: $(a)$ they are made of the same material,$(b)$ their thermal conductivities are in the ratio $2:3$.

If $6000 \ J/s$ of heat flows through a conductor of length $1 \ m$ and cross-sectional area $0.75 \ m^2$,then the temperature difference between its ends is ...... $^\circ C$. $[K = 200 \ J/(m \cdot K)]$

Two identical rods of copper and iron are coated with wax uniformly. When one end of each is kept at the temperature of boiling water,the lengths up to which wax melts are $8.4 \ cm$ and $4.2 \ cm$ respectively. If the thermal conductivity of copper is $0.92$,then the thermal conductivity of iron is: