The ends of two rods of different materials with their thermal conductivities,radii of cross-sections,and lengths all in the ratio $1:2$ are maintained at the same temperature difference. If the rate of flow of heat in the larger rod is $4 \; cal/sec$,the rate of flow of heat in the shorter rod in $cal/sec$ will be:

In the Arctic region,hemispherical houses called Igloos are made of ice. It is possible to maintain a temperature inside an Igloo as high as $20^{\circ} C$ because

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).

Three rods of equal length and cross-sectional area with thermal conductivities $K, 2K$,and $3K$ are joined as shown in the figure. The temperatures of their outer ends are $110\ ^oC, 20\ ^oC$,and $0\ ^oC$ respectively. Find the temperature of the junction in $^oC$.

One end of a $2.35\,m$ long and $2.0\,cm$ radius aluminium rod $(K = 235\,W\cdot m^{-1}K^{-1})$ is held at $20^{\circ}C$. The other end of the rod is in contact with a block of ice at its melting point. The rate in $kg\cdot s^{-1}$ at which ice melts is (Take latent heat of fusion for ice as $\frac{10}{3} \times 10^5\,J\cdot kg^{-1}$)

In the Ingen-Hauz's experiment,the wax melts up to lengths $10 \ cm$ and $25 \ cm$ on two identical rods of different materials. The ratio of thermal conductivities of the two materials is: