A metallic rod of cross-sectional area $9.0\,\,cm^2$ and length $0.54 \,\,m$, with the surface insulated to prevent heat loss, has one end immersed in boiling water and the other in ice-water mixture. The heat conducted through the rod melts the ice at the rate of $1 \,\,gm$ for every $33 \,\,sec$. The thermal conductivity of the rod is ……. $ Wm^{-1} K^{-1}$

The ratio of thermal conductivity of two rods of different material is $5 : 4$ . The two rods of same area of cross-section and same thermal resistance will have the lengths in the ratio

A heat source at $T = 10^3\, K$ is connected to another heat reservoir at $T = 10^2\, K$ by a copper slab which is $1\, m$ thick. Given that the thermal conductivity of copper is $0.1\, WK^{-1}\, m^{-1}$, the energy flux through it in the steady state is ……….. $Wm^{-2}$

Heat is flowing through two cylindrical rods of the 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, then the ratio of the amounts of heat conducted through per unit time will be

Three rods of Copper, Brass and Steel are welded together to form a $Y$ shaped structure. Area of cross – section of each rod $= 4\ cm^2$ . End of copper rod is maintained at $100^o C $ where as ends ofbrass and steel are kept at $0^o C$. Lengths of the copper, brass and steel rods are $46, 13$ and $12\ cms$ respectively. The rods are thermally insulated from surroundings excepts at ends. Thermal conductivities of copper, brass and steel are $0.92, 0.26$ and $0.12\ CGS$ units respectively. Rate ofheat flow through copper rod is ……. $cal\, s^{-1}$