Analysis of a Carnot Heat Engine
A Carnot heat engine, shown in Fig. 6–47, 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.
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_{\text {th,rev }}=1-\frac{T_{L}}{T_{H}} ( 6–18)
\eta_{\text {th,rev }}=1-\frac{T_{L}}{T_{H}}=1-\frac{(30+273) \mathrm{K}}{(652+273) \mathrm{K}}=\mathbf{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)_{\mathrm{rev}}=\frac{T_{H}}{T_{L}} (6-16)
Q_{L, \text { rev }}=\frac{T_{L}}{T_{H}} Q_{H, \mathrm{rev}}=\frac{(30+273) \mathrm{K}}{(652+273) \mathrm{K}}(500 \mathrm{~kJ})=164 \mathrm{~kJ}
Discussion Note that this Carnot heat engine rejects to a low-temperature sink 164 \mathrm{~kJ} of the 500 \mathrm{~kJ} of heat it receives during each cycle.