Two sheets of thickness $d$ and $3d$ are touching each other. The temperature just outside the thinner sheet side is $A$,and on the side of the thicker sheet is $C$. The interface temperature is $B$. If $A, B$,and $C$ are in arithmetic progression,the ratio of the thermal conductivity of the thinner sheet to the thicker sheet is:

Two plates $A$ and $B$ have thermal conductivities $84 \, W m^{-1} K^{-1}$ and $126 \, W m^{-1} K^{-1}$ respectively. They have the same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of $A$ and $B$ are kept at $100^{\circ} C$ and $0^{\circ} C$ respectively,then the temperature of the surface of contact in steady state is $.......... \, ^{\circ} C$.

Two ends of rods of length $L$ and radius $r$ of the same material are kept at the same temperature difference. Which of the following rods conducts the most heat?

Copper and iron rods of identical dimensions are coated with wax. The ratio of thermal conductivity of copper to iron is $10:9$. If one end of each rod is placed in hot water,the wax melts. Find the ratio of the lengths of the rods for which the wax melts at the same rate.

$A$ cylindrical rod with one end in a steam chamber and the other end in ice results in melting of $0.1 \ gm$ of ice per second. If the rod is replaced by another with half the length and double the radius of the first,and if the thermal conductivity of the material of the second rod is $\frac{1}{4}$ that of the first,the rate at which ice melts in $gm/sec$ will be:

$A$ rectangular ice box of total surface area of $1000 \,cm^2$ initially contains $1.5 \,kg$ of ice at $0^{\circ}C$. If the thickness of the walls of the box is $2 \,mm$ and the temperature outside the box is $42^{\circ}C$, then the mass of the ice remaining in the box after $160 \,minutes$ is (Thermal conductivity of the material of the box $= 10^{-2} \,W m^{-1} K^{-1}$ and latent heat of the fusion of ice $= 336 \times 10^3 \,J kg^{-1}$) (in $kg$)