The rate of heat flow through the cross-section of the rod shown in the figure is ($T_2 > T_1$ and the thermal conductivity of the material of the rod is $K$).

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

$A$ thermocol box has a total wall area (including the lid) of $1.0 \,m^2$ and wall thickness of $3 \,cm$. It is filled with ice at $0^{\circ} C$. If the average temperature outside the box is $30^{\circ} C$ throughout the day, the amount of ice that melts in one day is (Given: $K_{\text{thermocol}} = 0.03 \,W/mK$, $L_{\text{fusion(ice)}} = 3.00 \times 10^5 \,J/kg$) (in $\,kg$)

Which of the following material is most suitable for cooking utensils?

Two bars of thermal conductivities $K$ and $3K$ and lengths $1\, cm$ and $2\, cm$ respectively have equal cross-sectional area. They are joined length-wise as shown in the figure. If the temperatures at the ends of this composite bar are $0\,^{\circ}C$ and $100\,^{\circ}C$ respectively,then the temperature $\varphi$ of the interface is......... $^oC$.

Two metal rods $1$ and $2$ of same lengths have same temperature difference between their ends. Their thermal conductivities are $K_1$ and $K_2$ and cross-sectional areas are $A_1$ and $A_2$,respectively. If the rate of heat conduction in rod $1$ is four times that in rod $2$,then: