The average daytime temperature at the surface of the Moon is \(380 \mathrm{~K}\), and the temperature of the lunar core is estimated at \(1000 \mathrm{~K}\). Suppose you want to run a heat engine that operates on a Carnot cycle to use this temperature difference to run a \(2.50-\mathrm{MW}\) power station at some future lunar colony.

(a) At what rate does this engine extract thermal energy from the lunar core?

(b) At what rate does the process change the entropy of the core system?

(c) What is the thermal efficiency of this engine?