Question 6.5: Analysis of a Carnot Heat Engine A Carnot heat engine, shown...

The heat supplied to a Carnot heat engine is given. The thermal efficiency and the heat rejected are to be determined.
Analysis (a) The Carnot heat engine is a reversible heat engine, and so its efficiency can be determined from Eq. 6–18 to be

\eta_{ th , rev }=1-\frac{T_{L}}{T_{H}}

\eta_{ th , C}=\eta_{ th , rev }=1-\frac{T_{L}}{T_{H}}=1-\frac{(30+273) K }{(652+273) K }= 0 . 6 7 2

That is, this Carnot heat engine converts 67.2 percent of the heat it receives to work.
(b) The amount of heat rejected Q_{L} by this reversible heat engine is easily determined from Eq. 6–16 to be

\left(\frac{Q_{H}}{Q_{L}}\right)_{ rev }=\frac{T_{H}}{T_{L}}

Q_{L, rev }=\frac{T_{L}}{T_{H}} Q_{H, rev }=\frac{(30+273) K }{(652+273) K }(500 kJ )=164 kJ

Discussion Note that this Carnot heat engine rejects to a low-temperature sink 164 kJ of the 500 kJ of heat it receives during each cycle.