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An inventor claims to have designed and build an engine that produces $\SI{1.50}{MW}$ of usable work while taking in $\SI{3.00}{MW}$ of thermal energy at $\SI{150}{\degreeCelsius}$, and rejecting $\SI{1.50}{MW}$ of thermal energy at $\SI{58}{\degreeCelsius}$. Is there anything fishy about his claim? Explain.
fishy
The inventor claims an efficiency of \begin{align} \eta &= \frac{P_o}{P_i}\\ &= \frac{\SI{1.50e6}{W}}{\SI{3.00e6}{W}}\\ &= 0.50 = 50\% \end{align} while the maximum possible efficency of performance for a machine, working between these to temperatures is \begin{align} \eta_C &= 1\frac{T_L}{T_H}\\ &= 1\frac{\SI{215}{K}}{\SI{425}{K}}\\ &= 49\%. \end{align} This means, that this machine is better than ideal. Even ideal is not possible, sind real machines have an efficiency of performance which lies significantly below the ideal one.
10:05, 19. June 2018  lsg improved  Urs Zellweger (urs)  Current Version 
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