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 25 degree C and 6 degree C, respectively. (a) What is the maximum theoretical efficiency of this power plant? (b) If the power plant is to produce 230 kW of power, at what rate must heat be extracted from the warm water? Assume the maximum theoretical efficiency At what rate must heat be absorbed by the cold water? (c) The cold water that enters the plant leaves it at a temperature of 10 degree C. What must be the flow rate of cold water through the system? Give you answer in kg/h and L/h.

Explanation / Answer

(a) The maximum efficiency is realized by a Carnot engine
E=1-(279/298)K
= 6%

b) Pout/E = 230kW/0.060 =3.0 MW(warm)
3.0 MW-230 kW=(1/E)(230kW) =2.9 MW(cold)

(c) specific heat of water is c=4190 J/(kg K)]

dm/dt = dQ/dt/cT = (2.9 x 106W)(3600s/h)/(4190j/(Kg.K)(10K- 6K)
=6x105 Kg/h

= 600 000.00 Liters per hour (L/h)

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