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

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 $g$)

$A$ 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

In Column-$I$,system surroundings and in Column-$II$ modes of heat transfer are given below. Match the following:

Column-$I$	Column-$II$
$(a)$ Cup of hot tea in room	$(i)$ Forced convection
$(b)$ Substance kept near fire	$(ii)$ Natural convection
	$(iii)$ Conduction
	$(iv)$ Radiation

$A$ heated body maintained at $T \ K$ emits thermal radiation of total energy $E$ with a maximum intensity at frequency $v$. The emissivity of the material is $0.5$. If the temperature of the body is increased and maintained at temperature $3T \ K$,then:
$(i)$ The maximum intensity of the emitted radiation will occur at frequency $v/3$.
$(ii)$ The maximum intensity of the emitted radiation will occur at frequency $3v$.
$(iii)$ The total energy of emitted radiation will become $81E$.
$(iv)$ The total energy of emitted radiation will become $27E$.

In a closed room,heat transfer takes place by