a$)($pts $06)$ What is Flue Gas Desulfurization $($FGD$)$ process? Briefly explain and show the basic reactions involved in the process.

b$)($pts $14)$ i$)$ Prove that, the relationship for the rate of change of temperature of a parcel of air as it moves up or down in the atmosphere could be described as:

$[$here$,$ dT $=$ incremental temperature change $($K$)$; dP $=$ incremental pressure change in the parcel $($Pa$)$; Cp $=$ specific heat of air at constant pressure $(1,005$ J$/$Kg$-$K$),$ g $=$ gravitational acceleration $(9\mathrm{.}806$ m$/$s$2)]$

ii$)$ An aircraft flying at an altitude of $16$ km draws in fresh air at $-35\backslash$deg C for cabin ventilation. If that fresh air is compressed to the pressure at sea level, would the air need to be heated or cooled to be delivered to the cabin at $22\backslash$deg C$?$