Question

n experimental power plant at the Natural Energy Laboratory of Hawaii generates electricity from the temperature gradient of the ocean. The surface and deep-water temperatures are 28°C and 6°C, respectively.

(a) What is the maximum theoretical efficiency of this power plant?
%

(b) If the power plant is to produce 200 kW of power, at what rate must heat be extracted from the warm water? Assume the maximum theoretical efficiency.
MW
At what rate must heat be absorbed by the cold water?
MW

(c) The cold water that enters the plant leaves it at a temperature of 10°C. What must be the flow rate of cold water through the system? Give you answer in kg/h and L/h.
kg/h
L/h

Answer 1

maximum theoretical efficiency of this power plant= 1-lower temperature/higher temperature= 1- (273+6)/(273+28) = 7.3%

the rate at which heat be extracted from the warm water= power plant is to produce/ efficiency= 200 kW /0.073 = 2736.36 kW = 2.736 MW

rate at which heat must be absorbed by the cold water= rate at which heat be extracted from the warm water -power plant is to produce =2736.36 kW- 200 kW=  2536.36 kW = 2.536 MW

Now, cold water that enters the plant at 6°C leaves it at a temperature of 10°C, and absorbs 2536.36 kW.

So, the flow rate of cold water through the system * specific heat * temperature change = rate at which heat must be absorbed by the cold water

So, m kg/s * 4.186 kJ/kgC * (10-6)C = 2536.36 kW= 2536.36 kJ/s

So, m= 151.48 kg/s, and in kg/h, 151.48*3600 = 545328 kg/h and in L/h,545328 L/h