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

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.

Explain why:
$(a)$ a body with large reflectivity is a poor emitter.
$(b)$ a brass tumbler feels much colder than a wooden tray on a chilly day.
$(c)$ an optical pyrometer (for measuring high temperatures) calibrated for an ideal black body radiation gives too low a value for the temperature of a red hot iron piece in the open,but gives a correct value for the temperature when the same piece is in the furnace.
$(d)$ the earth without its atmosphere would be inhospitably cold.
$(e)$ heating systems based on circulation of steam are more efficient in warming a building than those based on circulation of hot water.

The sun,acting as a black body,emits maximum radiation at a wavelength of $0.48 \ \mu m$. The average radius of the sun is $6.96 \times 10^{8} \ m$. The Stefan-Boltzmann constant is $5.67 \times 10^{-8} \ W/m^2K^4$ and Wien's constant is $0.293 \ cm \cdot K$. The decrease in the mass of the sun per second due to radiation is ..... $kg/s$.

In a closed room,heat transfer takes place by

Fill in the blanks:
$(a)$ $0.49 \frac{\text{cal}}{\text{cm} \cdot \text{K} \cdot \text{s}} = \dots \frac{\text{J}}{\text{m} \cdot \text{K} \cdot \text{s}}$
$(b)$ If the rate of emission of heat of a substance is less than its rate of absorption,then its temperature $\dots$.
$(c)$ The rate of emission of heat of a substance is directly proportional to $\dots$ of temperature of it and surroundings.