# Thermodynamic/Carnot efficiency

1. Sep 15, 2010

### contred

1. The problem statement, all variables and given/known data

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 degree celcius wastewater leaves the plant at and is discharged into the ocean at 1,000 gallons PER minute. if the average annual ocean temperature is 10 degree celcius 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 contant at 4,200 J/Kg K.

2. Relevant equations

delta T = Tf - Ti
Q = mc delta T
Carnot n=1-(Tc/Th)
W= total heat times Carnot n
P=W/t

3. The attempt at a solution

1000 Gallons per minute = 63.09 Kg per sec

T1 = 10 +273 = 283K
T2 = 35 +273 = 308K
Delta T = 25 K
Carnot η = 1- 283K/308K = 0.08 = 8%
How can I calculate the maximum power with the rate flow and without the time? I think i am missing an equation.

Last edited: Sep 15, 2010
2. Sep 17, 2010

### p21bass

You can choose a convenient time. Since you calculated the rate in kg/s, you have t and m. You can then determine Q (Total Heat), since you have C (Heat Capacity) as a given, and you calculated m/t and you have T. Once you have Q, you can calculate W and then P, using the same t that you chose earlier.