A Carnot heat engine receives heat at 800 K and rejects the waste heat to the surroundings

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A Carnot heat engine receives heat at 800 K and rejects the waste heat to the surroundings at 300 K. The output from the heat engine is used to drive a Carnot refrigerator that removes heat from the cooled space at -20oC at a rate of 400 kJ/min and rejects it to the same surroundings at 300 K. Determine
(a) The rate of heat supplied to the heat engine.
(b) The total rate of heat rejection to the surroundings. What-if Scenario:
(c) What would the rate of heat supplied be if the temperature of the cooled space were 30oC?
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