Question $7$

$(10$ points$)$

A company claims that it developed a state$-$of$-$the$-$art heat engine with the best thermal performance in the market. The engine would take in $325$ kJ of heat from a source at $1000$ K and reject $125$ kJ of heat to a sink at $400$ K $.$ During this process, the heat engine can extract $200$ kJ of work done.

a$)$ Analyze the company's claim on the thermal performance of the heat engine.

$(5$ points$)$

b$)$ Assume that the thermal efficiency of the heat engine is only $\backslash (50\backslash \%\backslash )$ of that of a Carnot engine running between the same temperature limits$.$ Find $\backslash ($ Q$\_\{\backslash$text $\{$out $\}\}\backslash )$ and $\backslash ($ W$\_\{\backslash$text $\{$out $\}\}\backslash )$ of the heat engine if it is taking in the same amount of heat from the heat source.

$(5$ points$)$