The steam power plant with a nominal capacity of $300$ MW uses lignite containing $2\mathrm{.}0\%$ sulfur. The thermal efficiency of the unit is $33\mathrm{.}33\%,$ and the sub$-$bituminous coal used has a heating value of $8\mathrm{.}0$ MJ$/$kg$.$ For the desulfurization of flue gases, a Flue Gas Desulfurization $($FGD$)$ unit with calcium oxide $($CaO$)$ is employed, with an efficiency of $90\%.$ It is assumed that only CaSO$3$ is produced, and the lime consists of $95\%$ CaO and $5\%$ inert components, with a feed ratio $($actual to theoretical$)$ of $1\mathrm{.}05.$ The atomic weights are given as follows: calcium $40,$ oxygen $16,$ carbon $12,$ nitrogen $14,$ and sulfur $32.$ Calculate:

$($a$)$ SO$2$ emissions before capture in kmol SO$2/$hr and kg SO$2/$hr$.$

$($b$)$ The actual feed of CaO required in kg$/$hr$.$

$($c$)$ The daily production $($in tonnes$/$day$)$ of sludge with $50\%$ moisture.

$($Note: Overall reaction: CaO$+$SO$2->$CaSO$3)$