Question 5.2: A central power plant, rated at 800,000 kW, operates using s...
A central power plant, rated at 800,000 kW, operates using steam at 585 K and discards heat to a river at 295 K. If the thermal efficiency of the plant is 70% of the maximum possible value, how much heat is discarded to the river at rated power?
The maximum possible thermal efficiency is given by Eq. (5.7). With T_H as the steam-generation temperature and T_C as the river temperature
\eta_{\text {Carnot }}=1-\frac{T_C}{T_H} (5.7)
\eta_{\text {Carnot }} = 1-\frac{295}{585} = 0.4957 \quad and \quad \eta=(0.7) (0.4957)=0.3470
where η is the actual thermal efficiency. Combining Eq. (5.6) with the first law, written W = −Q_H − Q_C, to eliminate Q_H , yields:
\eta \equiv \frac{-W}{Q_H} (5.6)
Q_C=\left(\frac{1 – \eta}{\eta}\right) W=\left(\frac{1 – 0.347}{0.347}\right) (-800,000)=-1,505,475 kW
This rate of heat transfer to a modest river would cause a temperature rise of several °C.