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

Three rods $AB, BC$ and $AC$ having thermal resistances of $10\, units, \,10 \,units$ and $20 \,units,$ respectively, are connected as shown in the figure. Ends $A$ and $C$ are maintained at constant temperatures of $100^o C$ and $0^o C,$ respectively. The rate at which the heat is crossing junction $B$ is   ........ $ \mathrm{units}$

A piece of glass is heated to a high temperature and then allowed to cool. If it cracks, a probable reason for this is the following property of glass

The heat is flowing through two cylindrical rods of same material. The diameters of the rods are in the ratio $1 : 2$ and their lengths are in the ratio $2 : 1$ . If the temperature difference between their ends is the same, the ratio of rate of flow of heat through them will be

A metallic prong consists of $4$ rods made of the same material, cross-sections and same lengths as shown below. The three forked ends are kept at $100^{\circ} C$ and the handle end is at $0^{\circ} C$. The temperature of the junction is ............. $^{\circ} C$

Give definition, unit and dimensional formula of thermal conductivity.