The average daytime temperature at the surface of the Moon is 380 K, and the tem

Question

The average daytime temperature at the surface of the Moon is 380 K, and the temperature of the lunar core is estimated at 1000 K. Suppose you want to run a heat engine that operates on a Carnot cycle to use this temperature difference to run a 1.90-MW power station at some future lunar colony.

Part A:

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

Part B:

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

Part C:

What is the thermal efficiency of this engine?

Explanation / Answer

cold temperature=380 K

hot temperature=1000 K

then carnot efficiency=1-(cold temperature/hot temperature)

=1-(380/1000)=0.62

hence output/heat input=0.62

as output required=1.9 MW,

input=output/0.62=3.0645 MW

part A:

energy to be extracted=heat input to the engine=3.0645 MW

part B:

rate of change of entrop=rate of energy input/temperature of the core

=3.0645*10^6 W/1000 K

=3.0645*10^3 W/K

part C:

efficieny of the engine is 0.62 or 62%

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