Analysis of a Carnot Heat Engine A Carnot heat engine, shown in Fig. 6–48, receives 500 kJ of heat per cycle from a high-temperature source at 652°C and rejects heat to a low-temperature sink at 30°C. Determine (a) the thermal efficiency of this Carnot engine and (b) the amount of heat rejected to

Question

Analysis of a Carnot Heat Engine A Carnot heat engine, shown in Fig. 6–48, receives 500 kJ of heat per cycle from a high-temperature source at 652°C and rejects heat to a low-temperature sink at 30°C. Determine (a) the thermal efficiency of this Carnot engine and (b) the amount of heat rejected to the sink per cycle.

Accepted Answer

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

[latex] \eta_{ th , rev }=1-\frac{T_{L}}{T_{H}} [/latex]

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

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

[latex] \left(\frac{Q_{H}}{Q_{L}}\right)_{ rev }=\frac{T_{H}}{T_{L}} [/latex]

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

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.

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

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