Question 6.1: Net Power Production of a Heat Engine Heat is transferred to...

The rates of heat transfer to and from a heat engine are given.
The net power output and the thermal efficiency are to be determined.
Assumptions Heat losses through the pipes and other components are negligible.
Analysis A schematic of the heat engine is given in Fig. 6–16. The furnace serves as the high-temperature reservoir for this heat engine and the river as the low-temperature reservoir. The given quantities can be expressed as

\dot{Q}_{H}=80 MW \text { and } \dot{Q}_{L}=50 MW

The net power output of this heat engine is

\dot{W}_{\text {net,out }}=\dot{Q}_{H}-\dot{Q}_{L}=(80-50) MW =30 MW

Then the thermal efficiency is easily determined to be

\eta_{ th }=\frac{\dot{W}_{ net , out }}{\dot{Q}_{H}}=\frac{30 MW }{80 MW }=0.375(\text { or } 37.5 \%)

Discussion Note that the heat engine converts 37.5 percent of the heat it receives to work.