Three rods of the same dimension have thermal conductivities $3K$,$2K$,and $K$. They are arranged as shown in the figure,with their ends at $100^oC$,$50^oC$,and $20^oC$. The temperature of their junction is ......... $^oC$.

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 $g$)

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.

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 ....... $hr$.

$A$ long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $\theta$ along the length $x$ of the bar from its hot end is best described by which of the following figures?

$A$ heated body emits radiation which has maximum intensity at frequency $f_m$. If the temperature of the body is doubled,then: