The outer faces of a rectangular slab made of equal thickness of iron and brass are maintained at $100^{\circ} C$ and $0^{\circ} C$ respectively. The temperature at the interface is ........... $^{\circ} C$ (Thermal conductivity of iron and brass are $0.2$ and $0.3$ respectively.)

Five rods of same dimensions are arranged as shown in the figure. They have thermal conductivities $K_1, K_2, K_3, K_4$ and $K_5$. When points $A$ and $B$ are maintained at different temperatures,no heat flows through the central rod if

$A$ cylindrical metallic rod in thermal contact with two heat reservoirs at its two ends conducts an amount of heat '$Q_1$' in time '$t$'. The metallic rod is melted and the material is formed into a rod of length four times the length of the original rod. The amount of heat conducted by the new rod when placed in thermal contact with the same two reservoirs in time '$t$' is '$Q_2$'. Then $\frac{Q_1}{Q_2}$ is:

$Assertion :$ $A$ brass tumbler feels much colder than a wooden tray on a chilly day.
$Reason :$ The thermal conductivity of brass is more than the thermal conductivity of wood.

Two rods,one made of copper and the other of steel,having the same length and cross-sectional area,are joined together. The thermal conductivity of copper is $385 \, J s^{-1} m^{-1} K^{-1}$ and that of steel is $50 \, J s^{-1} m^{-1} K^{-1}$. If the copper end is held at $100^{\circ} C$ and the steel end is held at $0^{\circ} C$,the junction temperature is ........... $^{\circ} C$ (Assuming no other heat losses).

The ratio of the diameters of two metallic rods of the same material is $2 : 1$ and their lengths are in the ratio $1 : 4$. If the temperature difference between their ends is equal,the rate of flow of heat in them will be in the ratio: (in $:1$)