$A$ slab consists of two identical plates of copper and brass. The free face of the brass is at $0^{\circ} C$ and that of copper at $100^{\circ} C$. If the thermal conductivities of brass and copper are in the ratio $1: 4$,then the temperature of the interface is (in $^{\circ} C$)

The lengths of two rods made of the same metal and having the same area of cross-section are $0.6 \ m$ and $0.8 \ m$ respectively. The temperatures at the ends of the first rod are $90^{\circ}C$ and $60^{\circ}C$,and those for the second rod are $150^{\circ}C$ and $110^{\circ}C$. For which rod will the rate of heat conduction be greater?

The thickness of a metallic plate is $0.4 \ cm$. The temperature difference between its two surfaces is $20^{\circ}C$. The quantity of heat flowing per second is $50 \ \text{calories}$ through an area of $5 \ cm^2$. In the $CGS$ system,the coefficient of thermal conductivity is:

One end of a copper rod of length $1.0 \; m$ and area of cross-section $10^{-3} \; m^2$ is immersed in boiling water and the other end in ice. If the coefficient of thermal conductivity of copper is $92 \; cal/(m \cdot s \cdot ^\circ C)$ and the latent heat of ice is $8 \times 10^4 \; cal/kg$,then the amount of ice which will melt in one minute is:

Two rods have thermal conductivities $K$ and $3K$ and lengths $1 \ cm$ and $2 \ cm$ respectively. Their cross-sectional areas are equal. They are joined in series as shown in the figure. If the temperatures of the outer ends of this composite rod are $0^{\circ}C$ and $100^{\circ}C$ respectively,find the junction temperature $\phi$ in $^{\circ}C$.

$A$ deep rectangular pond of surface area $A$,containing water (density $=\rho$,specific heat capacity $=s$),is located in a region where the outside air temperature is at a steady value of $-26^{\circ}C$. The thickness of the frozen ice layer in this pond at a certain instant is $x$. Taking the thermal conductivity of ice as $K$ and its specific latent heat of fusion as $L$,the rate of increase of the thickness of the ice layer at this instant would be given by: