Problem $1$

Consider a proposed heat engine in contact with a hot reservoir $($Thot $=1200$ K$)$

and cold reservoir $($Tcold $=400$ K$).$ During one cycle of the engine, $1000$ joules

of heat are input from the hot reservoir to the engine.

$($a$)$ Assume the heat engine and the two reservoirs are isolated from the rest of

the universe, and the engine is running at the maximum efficiency. $($In

other words, this is a perfect heat engine.$)$ Determine or calculate the

change in entropy of the universe due to this isolated system during one

cycle of operation. Explain.

$($b$)$ What is the maximum efficiency of this heat engine? Explain.

$($c$)$ What is the maximum amount of work that can be done per cycle? How

much heat must be exhausted to the low temperature reservoir per cycle