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 27 C and 7 C, respectively.

Part A

What is the maximum theoretical efficiency of this power plant?

Express your answer using two significant figures.

e = ______

Part B

If the power plant is to produce a power of 190 kW , at what rate must heat be extracted from the warm water? Assume the maximum theoretical efficiency.

Express your answer using two significant figures.

_______ W

Part C

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

Express your answer using two significant figures.

______ W

Part D

The cold water that enters the plant leaves it at a temperature of 11 C. What must be the flow rate of cold water through the system? Give your answer in kg/s and L/s.

Express your answer using two significant figures.

dm/dt = ______  kg/s

Part E

Express your answer using two significant figures.

dm/dt = ___ L/s

Explanation / Answer

Here,

Tc = 7 degree C = 280 K

Th = 27 degree C = 300 K

part A)

for the maximum theoretical efficiency of this power plant

maximum theoretical efficiency of this power plant = 1 - Tc/Th

maximum theoretical efficiency of this power plant = 1- 280/300

maximum theoretical efficiency of this power plant= 0.0667

the maximum theoretical efficiency of this power plant is 6.67 %

part B)

as W/Qh = 0.0667

190/Qh = 0.0667

Qh = 2850 kW

the rate of heat extracted from the warm water is 2850 kW

part C)

rate must heat be absorbed by the cold water = Qh - W

rate must heat be absorbed by the cold water = 2850 - 190

rate must heat be absorbed by the cold water = 2660 kW

part D)

let the flow rate is V

V * 4186 * (11 - 7) = 2660 * 10^3

V = 158.9 Kg/s

the flow rate of cold water is 158.9 Kg/s

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