Two rods (one semi-circular and other straight) of the same material and of the same cross-sectional area are joined as shown in the figure. The points $A$ and $B$ are maintained at different temperatures. The ratio of the heat transferred through a cross-section of the semi-circular rod to the heat transferred through a cross-section of the straight rod in a given time is

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.

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.

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 $D$?

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