Three rods of the same dimension have thermal conductivities $3K$ , $2K$ and $K$ . They are arranged as shown in fig. Given below, with their ends at $100^oC, 50^oC $and $20^oC$. The temperature of their junction is ......... $^oC$

In a steady state, the temperature at the end $A$ and $B$ of $20\,cm$ long rod $AB$ are $100\,^oC$ and $0\,^oC$ respectively. The temperature of a point $9\,cm$ from $A$ is....... $^oC$

Which of the following statements is/are $CORRECT$ Correct option are

$(i)$ 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 circulation of steam are more efficient in warming a building than those based on circulation of hot water

Three rods $AB, BC$ and $AC$ having thermal resistances of $10\, units, \,10 \,units$ and $20 \,units,$ respectively, are connected as shown in the figure. Ends $A$ and $C$ are maintained at constant temperatures of $100^o C$ and $0^o C,$ respectively. The rate at which the heat is crossing junction $B$ is   ........ $ \mathrm{units}$

Four rods of same material and having the same cross section and length have been joined, as shown. The temperature of junction of four rods will be........ $^oC$

Which of the following factors affect the thermal conductivity of a rod?