The ends of a metal bar of constant cross-sectional area are maintained at temperatures $T_1$ and $T_2$ which are both higher than the temperature of the surroundings. If the bar is unlagged,which one of the following sketches best represents the variation of temperature with distance along the bar?

$A$ rod of length $L$ and uniform cross-sectional area has varying thermal conductivity which changes linearly from $2K$ at end $A$ to $K$ at the other end $B$. The ends $A$ and $B$ of the rod are maintained at constant temperatures $100^oC$ and $0^oC$, respectively. At steady state, the graph of temperature $T = T(x)$, where $x$ is the distance from end $A$, will be:

What are the modes of heat transfer due to a temperature difference?

$A$ wall with a cavity consists of two layers of brick separated by a layer of air. All three layers have the same thickness,and the thermal conductivity of the brick is much greater than that of air. The left layer is at a higher temperature than the right layer,and a steady-state condition exists. Which of the following graphs correctly predicts the variation of temperature $T$ with distance $d$ inside the cavity?

The dimensions of $\sigma b^4$,where $\sigma$ is Stefan's constant and $b$ is Wien's constant,are:

One end of a uniform metal rod of length $100 \, cm$ is placed in ice and the other end is placed in boiling water. A point of the rod which is at a distance of $60 \, cm$ from the ice end is maintained at a constant temperature of $325^{\circ} C$. If $2 \, g$ of water is converted into steam per second, the mass of ice melted per second in steady state is (Latent heat of steam $= 6.75$ times latent heat of fusion of ice). (in $g$)