A solid copper sphere (density $\mathrm{\rho }$ and specific heat $c$) of radius $\mathrm{r}$ at an initial temperature $200 \mathrm{K}$ is suspended inside a chamber whose walls are at almost $0 \mathrm{K}$. Calculate the time required for the temperature of the sphere to drop to $100 \mathrm{K}$. (Assume sphere as a black body)

A wall consists of alternating blocks with length $d$ and coefficient of thermal conductivity $K_1$ and $K_2$. The cross-sectional area of the blocks is the same. The equivalent coefficient of thermal conductivity of the wall between left and right is: 

A metallic sphere having radius $0.08 \mathrm{m}$ and mass $m=10 \mathrm{kg}$ is heated to a temperature of $227°\mathrm{C}$ and suspended inside a box whose walls are at a temperature of $27°\mathrm{C}$. The maximum rate at which its temperature will fall is :

(Take $e= 1$, Stefan’s constant $\mathrm{\sigma }= 5.8 \mathrm{x} {10}^{-8} \mathrm{W} {\mathrm{m}}^{-2} {\mathrm{K}}^{-4}$and specific heat of the metal $s= 90 \mathrm{cal} {\mathrm{kg}}^{-1}{\mathrm{deg}}^{-1},\mathit{ }\mathrm{J} = 4.2 \mathrm{Joules} {\mathrm{Calorie}}^{-1}$)