Two identical long bars $A$ and $B$ made of different materials are coated with wax and have one end immersed in a hot oil bath. When the steady state is reached, the lengths for which the wax melts are $l_A$ and $l_B$. If $k_A$ and $k_B$ are the thermal conductivities of the materials, then:

An ice box is used to keep food cool,having a surface area of $1 \, m^2$ and a thickness of $5.0 \, cm$. The thermal conductivity of the ice box material is $K = 0.01 \, J/(m \cdot s \cdot ^\circ C)$. The inside temperature is maintained at $0 \, ^\circ C$ and the outside temperature is $30 \, ^\circ C$. If the latent heat of fusion of ice is $334 \times 10^3 \, J/kg$,calculate the mass of ice that melts in one day.

Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity $K_{1}, K_{2},$ and $K_{3}$,respectively. They are joined together at their ends to make a long rod. One end of the long rod is maintained at $100^{\circ} C$ and the other at $0^{\circ} C$. If the joints of the rod are at $70^{\circ} C$ and $20^{\circ} C$ in steady state and there is no loss of energy from the surface of the rod,the correct relationship between $K_{1}, K_{2}$ and $K_{3}$ is:

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:

Two slabs have thicknesses $d_{1}$ and $d_{2}$. Their thermal conductivities are $K_{1}$ and $K_{2}$ respectively. They are in series. The free ends of the combination of these two slabs are kept at temperatures $\theta_{1}$ and $\theta_{2}$. Assume $\theta_{1} > \theta_{2}$. The temperature $\theta$ of their common junction is

The temperature drop through each layer of a two-layer furnace wall is shown in the figure. Assume that the external temperatures $T_1$ and $T_3$ are maintained constant and $T_1 > T_3$. If the thicknesses of the layers $x_1$ and $x_2$ are the same,which of the following statements is correct?