$($III$)(30$ points$)$ An ideal gas within a piston$-$cylinder assembly executes a Carnot power cycle. The isothermal compression occurs at $300$ K from $90$ kPa to $120$ kPa $.$ If the thermal efficiency is $60\%,$

Determine: $($a$)$ The temperature of the isothermal expansion in $K$ and $($b$)$ the net work developed in kJ per kmol of gas. $($c$)$ Draw the p$-$v diagram, label all processes involved in a power cycle.