A heat engine with a thermal efficiency of $45\%$ produces $880$ kJ of work. Heat transfer to the engine is from a reservoir at a temperature of $600$ K$,$ and the heat transfer from the engine to the surrounding air is at $250$ K$.$

i$.$ Sketch a schematic diagram to represent the heat engine system.

ii$.$ Determine the heat transfer to and from the heat engine.

iii. If the heat engine is replaced by a Carnot heat engine producing the same work output,determine the heat transfer to and from the Carnot heat engine.