A certain coal$-$fired power plant has a rated power capacity of P $=950$ MW$.$ The output of this plant is W $=0\mathrm{.}33$QH$,$ where QH is the energy input as heat from the hot reservoir. $$ Part $($a$)$

Write an equation for the efficiency of a heat engine in terms of QH and the heat QC exhausted to a low temperature reservoir. Part $($b$)$

Which would increase the efficiency more, doubling QH or reducing QC by half?

$$ Part $($c$)$

Calculate the maximum thermal efficiency of the power plant.

$$ Part $($d$)$

Calculate the absolute value of the exhausted heat $($QC$)$ each second in MJ for the power plant.

$$ Part $($e$)$

If the power plant operates for a full day at its rated capacity, how much energy QH in MJ is needed?

$$ Part $($f$)$

If$,$ on average, one ton of coal contains Q $=25$ GJ of energy, how many tons nH of coal would the plant need to operate for a day at its rated capacity?

$$ Part $($g$)$

How many tons nC of this coal is exhausted as wasted heat to QC in a single day?