A $1,000MW$ coal$-$burning power plant is burning West Virginia bituminous coal with $8\%$ ash content. The power plant is $33\%$ efficient, with $35\%$ of the ash settling out in the firing chamber as bottom ash. A simplified schematic diagram is shown below. Assume $3\mathrm{.}5kWh$ per pound of coal.

$($a$)$ Determine the input energy using the efficient and output energy

$($b$)$ Determine the rate of coal input to the furnace $(kg$ coal$/$ day$)$

$($c$)$ Calculate the rate of fly ah settled in the firing chamber as bottom ash $($kg$/$day$).($using that coal consists of $8\%$ ash$)$

$($d$)$ Assuming that the electrostatic precipitator $($ESP$)$ is $99\%$ efficient, calculate the rate of fly ash emitted to the atmosphere in $k\frac{g}{?}$ day

$($e$)$ Draw an energy diagram for the facility and calculate the rate of heat emitted to the environment in $k\frac{J}{s}$;