$A$ 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

Determine whether the following statements are True or False:
$(a)$ "Conduction stops once a rod achieves thermal steady state."
$(b)$ $A$ surface that is a good emitter is also a good absorber.
$(c)$ $A$ perfect black body must be black in color.
$(d)$ The value of heat capacity is the same under different conditions for a given matter.

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.

$A$ 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?

$A$ 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 $27E$.

Three rods of Copper,Brass,and Steel are welded together to form a $Y$ shaped structure. The area of cross-section of each rod is $4 \ cm^2$. The end of the copper rod is maintained at $100^\circ C$,whereas the ends of the brass and steel rods are kept at $0^\circ C$. The lengths of the copper,brass,and steel rods are $46 \ cm$,$13 \ cm$,and $12 \ cm$ respectively. The rods are thermally insulated from the surroundings except at the ends. The thermal conductivities of copper,brass,and steel are $0.92$,$0.26$,and $0.12 \ CGS$ units respectively. The rate of heat flow through the copper rod is ....... $cal \ s^{-1}$.