Two closed containers of same dimensions made of different materials are completely filled with ice. The ice in the first container takes $20 \ min$ and that in the second container takes $10 \ min$,respectively,for complete melting. The ratio of the thermal conductivities of the materials of the two containers is . . . . . . .

The length of a metal rod is $20 \ cm$ and its area of cross-section is $4 \ cm^2$. If one end of the rod is kept at a temperature of $100^{\circ} C$ and the other end is kept in ice at $0^{\circ} C$, then the mass of the ice melted in $7 \ minutes$ is (Thermal conductivity of the metal $= 90 \ W \ m^{-1} \ K^{-1}$ and latent heat of fusion of ice $= 336 \times 10^3 \ J \ kg^{-1}$) (in $g$)

One end of a thermally insulated rod is kept at a temperature $T_1$ and the other at $T_2$. The rod is composed of two sections of lengths $l_1$ and $l_2$ and thermal conductivities $K_1$ and $K_2$ respectively. The temperature at the interface of the two sections is

The area of a glass window is $10 \ m^2$ and its thickness is $2 \ mm$. The outside and inside temperatures are $40^{\circ}C$ and $20^{\circ}C$ respectively. The thermal conductivity in $MKS$ units is $0.2$. The heat conducted per second into the room 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 $.......... \, ^{\circ} C$.

$A$ conducting rod of length $1 \,m$ has an area of cross-section $10^{-3} \,m^2$. One end is immersed in boiling water $(100^{\circ} C)$ and the other end in ice $(0^{\circ} C)$. If the coefficient of thermal conductivity of the rod is $96 \,cal/(s \cdot m \cdot ^{\circ}C)$ and the latent heat of fusion for ice is $8 \times 10^4 \,cal/kg$,then the amount of ice that will melt in one minute is: