$A$ 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?

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 ..... $kg/s$.

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.

$A$ 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 $27E$.

If $120 \ J$ of thermal energy is incident on an area of $3 \ m^2$,the amount of heat transmitted is $12 \ J$,and the coefficient of absorption is $0.6$,then the amount of heat reflected is: (in $J$)

Four rods of identical cross-sectional area and made from the same metal form the sides of a square. The temperatures of two diagonally opposite points $A$ and $B$ are $\sqrt{2}T$ and $T$ respectively in the steady state. Assuming that only heat conduction takes place,what will be the temperature difference between the other two points $C$ and $D$?