Four rods of identical cross-sectional area and made from the same metal form the sides of square. The temperature of two diagonally opposite points and $T$ and $\sqrt 2 $ $T$ respective in the steady state. Assuming that only heat conduction takes place, what will be the temperature difference between other two points

Consider two insulating sheets with thermal resistances $R_1$ and $R_2$ as shown. The temperatures $\theta $ is

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 $..........\,{ }^{\circ} C$.

A hollow sphere of inner radius $R$ and outer radius $2R$ is made of a material of thermal conductivity $K$. It is surrounded by another hollow sphere of inner radius $2R$ and outer radius $3R$ made of same material of thermal conductivity $K$. The inside of smaller sphere is maintained at $0^o C$ and the outside of bigger sphere at $100^o C$. The system is in steady state. The temperature of the interface will be ........ $^oC$

If the radius and length of a copper rod are both doubled, the rate of flow of heat along the rod increases ....... times

$A$ wall has two layers $A$ and $B$ made of different materials. The thickness of both the layers is the same. The thermal conductivity of $A$ and $B$ are $K_A$ and $K_B$ such that $K_A = 3K_B$. The temperature across the wall is $20°C$ . In thermal equilibrium