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 ......... $^oC$.

$A$ hot black body emits energy at the rate of $16 \ J \ m^{-2} \ s^{-1}$ and its most intense radiation corresponds to $20,000 \ \mathring{A}$. When the temperature of this body is further increased and its most intense radiation corresponds to $10,000 \ \mathring{A}$,then the energy radiated in $J \ m^{-2} \ s^{-1}$ will be

Which of the following statements is/are $CORRECT$?
$(i)$ $A$ body with large reflectivity is a poor emitter.
$(ii)$ $A$ brass tumbler feels much colder than a wooden tray on a chilly day.
$(iii)$ The Earth without its atmosphere would be inhospitably cold.
$(iv)$ Heating systems based on the circulation of steam are more efficient in warming a building than those based on the circulation of hot water.

Differentiate clearly between thermal conduction,thermal convection,and thermal radiation.

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 $g$)

On a clear sunny day,an object at temperature $T$ is placed on the top of a high mountain. An identical object at the same temperature is placed at the foot of the mountain. If both the objects are exposed to sun-rays for two hours in an identical manner,the object at the top of the mountain will register a temperature