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A nuclear power plant operates at 75\% of its maximum theoretical (Carnot) efficiency between temperatures \SI{625}{\degreeCelsius} and \SI{350}{\degreeCelsius}. If the plant produces electric energy at the rate of $\SI{1.3}{GW}$, how much exhaust heat is discharged per hour?
$\SI{1.57e13}{J}$
The ideal efficiency of this nuclear power plant, working between the two mentioned temperatures, is \begin{align} \eta_C &= 1\frac{T_L}{T_H}\\ &= 30.6\%. \end{align} The real efficiency is 75\% of the ideal, i.e. \begin{align} \eta &= 0.75 \cdot 0.306\\ &= 23\%. \end{align} If the plant produces $\SI{1.3}{GW}$ electrical power (equals 23\%), it produces \begin{align} P_h &= \frac{\SI{1.3}{GW}}{0.23}\cdot 0.77\\ &= \SI{4.36}{GW} \end{align} exhaust heat power. In one hour, this is \begin{align} E_h &= P_h \cdot t\\ &= \SI{1.57e13}{J}. \end{align}
19:25, 12. June 2017  si  Urs Zellweger (urs)  Current Version 