(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A solar-thermal power plant is to be built in a desert location where the only source of cooling water is a small creek with average flow rate of 100kg/s and an average temperature of 30 degrees C. The plant is to cool itself by boiling away the entire creek. If the maximum temperature achieved in the plant is 500K, what is the maximum electric power output it can sustain without running out of cooling water?

2. Relevant equations

[tex]Q=mcdT[/tex]

[tex]\frac{dQ}{dt}=\frac{dm}{dt}cdT[/tex]

[tex]\epsilon=1-\frac{T_{c}}{T_{h}}=1-\frac{Q_{c}}{Q_{h}}=\frac{W}{Q_{h}}[/tex]

[tex]W=Q_{h}-Q_{c}[/tex]

[tex]\frac{dW}{dt}=\frac{Q_{h}}{dt}-\frac{Q_{c}}{dt}[/tex]

3. The attempt at a solution

Not sure which numbers to substitute where so here goes

[tex]\frac{dm}{dt}=100[/tex]

[tex]\frac{dQ_{c}}{dt}=100\times 4184 \times 70 = 29288000[/tex]

[tex]\epsilon_{max}=1-303/500 = 0.394[/tex]

[tex]Q_{h}= \frac{Q_{c}}{1-\epsilon} = 29288000/0.606 = 48330033[/tex]

[tex]W= 48330033 - 29288000 = 19042033[/tex]

Which gives my answer as the max power output as 19MW.

The answer in the book is 166MW.

I'm not sure of many other reasonable combinations to stick these numbers in to pop out 166MW.

Thanks

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# Maximum power output

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