$A$ body of length $1 \; m$ having a cross-sectional area of $0.75 \; m^2$ has heat flow through it at the rate of $6000 \; J/s$. Find the temperature difference if the thermal conductivity $K = 200 \; J \cdot m^{-1} \cdot s^{-1} \cdot K^{-1}$.

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 $^{\circ}C$.

$A$ rectangular slab consists of two cubes of copper and brass of equal sides having thermal conductivities in the ratio $4: 1$. If the free face of brass is at $0^{\circ} C$ and that of copper is at $100^{\circ} C$,then the temperature of their interface is (in $^{\circ} C$)

Two metal cubes $A$ and $B$ of the same size are arranged as shown in the figure. The extreme ends of the combination are maintained at the indicated temperatures. The arrangement is thermally insulated. The coefficients of thermal conductivity of $A$ and $B$ are $300 \; W/m^{\circ}C$ and $200 \; W/m^{\circ}C$,respectively. After steady state is reached,the temperature of the interface will be ...... $^{\circ}C$.

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 ......

Why do some cooking vessels have a copper coating at the bottom?