A heat engine is operating on a Carnot cycle and has a thermal efficiency of $55$ percent. The waste heat from this engine is rejected to a nearby lake at $15$C at a rate of $800$ kJ$/$min$.$

Determine $($a$)$ the power output of the engine and $($b$)$ the temperature of the source.

Answers: $($a$)16\mathrm{.}3$ kW$,($b$)640$ K