If $6000 \ J/s$ of heat flows through a conductor of length $1 \ m$ and cross-sectional area $0.75 \ m^2$,then the temperature difference between its ends is ...... $^\circ C$. $[K = 200 \ J/(m \cdot K)]$

$A$ brass rod of length $2 \ m$ and radius $1 \ cm$ has one end maintained at $250 \ ^oC$. When steady state is reached, the rate of heat flow through any cross-section is $0.5 \ cal \ s^{-1}$. Find the temperature of the other end in $^oC$. (Thermal conductivity of brass $K = 0.26 \text{ cal s}^{-1} \text{ cm}^{-1} \text{ } ^\circ\text{C}^{-1}$)

$A$ wall is made of equally thick layers $P$ and $Q$ of different materials. The thermal conductivity of $Q$ is half of that of $P$. In the steady state,if the temperature difference across the wall is $24^{\circ} C$,then the temperature difference across the layer $P$ is ............... . (in $^{\circ} C$)

Four rods of the same material with different radii $r$ and length $l$ are used to connect two reservoirs of heat at different temperatures. Which one will conduct the most heat?

Two concentric spheres of radii $r_1$ and $r_2$ are maintained at temperatures $T_1$ and $T_2$ respectively. The rate of radial heat flow between the two concentric spheres is proportional to:

Ice formed over lakes has