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 30°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

Explanation / Answer

a. maximum theoritical efficiency or carnot efficiency = (Tw - Tc) / Tw [in Kelvin]

= (303.16 - 279.16) / 303.16 = 0.079

hence efficiency = 0.079 or 7.9%

b. heat required = output heat / efficiency = 200 / 0.079 = 2531.64 kW = 2.531 MW

heat going into cold water = input heat - output heat = 2531.64 - 200 = 2331.64 kW = 2.331 MW

c. specific heat of water = 4186 J/kg.C

water enters at 6 degreeC and leaves at 10 degC, difference delta T = 4 degC

Q = m.C. delta T

m = Q / C.delta T = 2331..64 x1000 / (4186 x 4)

= 139.25 kg/sec = 501,300kg/h

density of water = 1 .i.e 1 L = 1kg of water

hence, m = 501,300 L/h

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