Consider a leaf of surface area $10c{m}^2$ parallel to the ground. The leaf absorbs all incident radiation and its emissivity is $1.$ The top surface of the leaf radiate to the clear night sky$,$ and the effective radiation temperature of the sky is assumed to be $140$ K $.$ The bottom surface of the leaf radiates to the ground and the ground temperature is $7C.$ Both the top and bottom surfaces are also exchanging heat with air through convection. The air temperature is $5C.$ Consider the leaf is very thin so the entire leaf is at one temperature.

$($i$).$ Write an energy balance involving convective and radiative heat transfer

$($ii$).$ For a convective heat transfer coefficient of $25\frac{W}{m^2}K$ prove that the leaf temperature is $272\mathrm{.}8$ K $.$