C$.$ Consider yourself the technical advisor for a Sharktank investor $($SI$).$ An inventor has presented the SI with a new design for a heat engine. The "inventor" states that their design extracts $\backslash (835\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$min$\}\backslash )$ from a thermal reservoir at $1125$ K and rejects $\backslash (395\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$min$\}\backslash )$ to a thermal sink at $305$ K $.$ The SI wants to know whether or not to invest her money. To perform your analysis, you might want to determine:

$8.(05$ pts $)$ In C $,$ what is the design $\backslash (\backslash$eta $\backslash )$ for the proposed heat engine?

$9.(05$ pts $)$ In C$,$ what is the best realizable $\backslash (\backslash$eta$\_\{\backslash$text $\{$best $\}\}\backslash )?$

$10.(05$ pts $)$ In C$,$ what power is produced?

$11.(05$ pts$)$ In C$,$ what do you recommend to the SI$?$