A novel heat engine is being considered for producing work from the thermal ener

Question

A novel heat engine is being considered for producing work from the thermal energy contained in the wastewater discharge from a large food-processing plant. On an average day, 35 ° C wastewater leaves the plant and is discharged into the ocean at 1,000 gallons per minute. If the average annual ocean temperature is 10 ° C at that location, what is the maximum power that could be produced by this heat engine? What would be the thermal cycle efficiency of your maximum power engine? You can assume that the heat capacity of water at constant pressure is constant at 4,200 J/kg K.

Explanation / Answer

1.) max. power = Total heat available for conversion into work:

i.e. Pmax = Qmax = m*Cp*dT

Now, m= 1,000 gpm * (8.32 lbs/gallon)*(kg/2,205 lbs)*(minute/60 seconds) = 0.063 kg/s

hence, Pmax = 0.063 x 4200 x (35 -10) = 6615 J/s

Pmax = 6615 W

2.) Tc = 10 +273 = 283K
Th = 35 +273 = 308K
Carnot ? = 1 - Tc / Th

=1- 283K/308K = 0.081

Carnot ?= 8.1 %

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