An experimental power plant at the Natural Energy Laboratory of Hawaii generates

Question

An 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 26 C and 7 C, respectively.

Part A

What is the maximum theoretical efficiency of this power plant?

Part B

If the power plant is to produce a power of 200 kW , at what rate must heat be extracted from the warm water? Assume the maximum theoretical efficiency.

Part C

At what rate must heat be absorbed by the cold water? Assume the maximum theoretical efficiency.

Part D

The cold water that enters the plant leaves it at a temperature of 12 C. What must be the flow rate of cold water through the system? Give your answer in kg/s and L/s.

Explanation / Answer

(a) %eff =100( Th - Tc)/Th
26C = 299K
7C = 280K

%eff = 100 (299-280)/299

%eff= 6.35%

(b) heat required for 200kw
heat required = ouput/ eff

200/.0635 = 3150 kw or 3150kJ/s

(c) heat into cold water = input heat - kw output
= 3150 -200
= 2950 kw or 2950kJ/s

(d)specific heat of water = 4186J/Kg-C degree
water comes in at 7 degrees and leaves at 12 for a 5 degree difference

(2950 x10^3 watts / 4186 watt-sec/ kg-C) / 5 degrees= 141 kg/sec

1kg water = I liter
141 Liters/sec

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