Question $6\mathrm{.}11)$ A Carnot heat engine receives heat at $900$ K and rejects the waste heat to the

environment at $300$ K$.$ The entire work output of the heat engine is used to drive a Carnot

refrigerator that removes heat from the cooled space at $-15$oC at a rate of $250$ kJ$/$min and rejects

it to the same environment at $300$ K$.$ Determine

$($a$)$ the rate of heat supplied to the heat engine $($Answer: $61\mathrm{.}1$ kJ$/$min$)$

$($b$)$ the total rate of heat rejection to the environment $($Answer: $311$ kJ$/$min