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 $g$)

The only possibility of heat flow in a thermos flask is through its cork,which is $75 \ cm^2$ in area and $5 \ cm$ thick. Its thermal conductivity is $0.0075 \ cal/(cm \cdot s \cdot ^\circ C)$. The outside temperature is $40^\circ C$ and the latent heat of fusion of ice is $80 \ cal/g$. The time taken by $500 \ g$ of ice at $0^\circ C$ in the flask to melt into water at $0^\circ C$ is ....... $hr$.

Statement $A$: Convection involves flow of matter within a fluid due to unequal temperatures of its parts.
Statement $B$: $A$ hot bar placed under a running tap water loses heat due to the effect of convection within water.
Statement $C$: Heat transfer always involves a temperature difference between two systems.

Two bodies $A$ and $B$ have thermal emissivities of $0.01$ and $0.81$ respectively. The outer surface areas of the two bodies are the same. The two bodies emit total radiant power at the same rate. The wavelength ${\lambda _B}$ corresponding to maximum spectral radiancy in the radiation from $B$ is shifted from the wavelength corresponding to maximum spectral radiancy in the radiation from $A$ by $1.00\;\mu m$. If the temperature of $A$ is $5802\;K$,then:

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: