A heat engine with $0\mathrm{.}500$ molmol of a monatomic ideal gas initially fills a $3000$ cm$3$cm$3$ cylinder at $800$ KK$.$ The gas goes through the following closed cycle:

$-$ Isothermal expansion to $6000$ cm$3$cm$3.$

$-$ Isochoric cooling to $400$ KK$.$

$-$ Isothermal compression to $3000$ cm$3$cm$3.$

$-$ Isochoric heating to $800$ KK$.$

Part A

How much work does this engine do per cycle?

Express your answer with the appropriate units.

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Part B

What is its thermal efficiency?

Express your answer as a percentage.