A plant to generate electricity exploits a temperature difference in the ocean n

Question

A plant to generate electricity exploits a temperature difference in the ocean nearby. At the surface the temperature is 27 C and in a colder, deeper region it is 7 C.

Part B

Assuming that the plant were able to achieve the maximum efficiency, determine the rate at which heat would have to be absorbed from the surface water to generate 200 kW  of power.

Express your answer using two significant figures.

Part C

At what rate would heat be rejected into the colder water?

Express your answer using two significant figures.

Part D

Assume that the cold water that enters the plant from the deeper region leaves the plant at a temperature of 12 C. Determine the rate, in L/s, at which cold water must flow through the system.

Express your answer using two significant figures.

Explanation / Answer

Here ,

hot temperature , Th = 27 degree C

Th = 300 K

cold temperature , Tc= 7 degree C

Tc = 280 K

part B)

Maximum efficiency = 1- Tc/Th

Maximum efficiency = 1 - 280/300

Maximum efficiency = 0.0667

Now , Work done/heat absorbed = efficiency

0.0667 = 200 kW/heat absorbed

heat absorbed = 3000 kW

the rate of heat absorbed is 3000 kW

part C)

rate of heat rejection = heat absorbed - work done

rate of heat rejection = 3000 - 200

rate of heat rejection = 2800 kW

part D)

let the rate of flow is V L/s

heat rejected = V * density * specific hea t * change in temperature

2800 * 10^3 = V * 1 Kg/L * 4186 * (12 - 7)

solving

V = 133.8 L/s

the rate of flow of cold water is 133.8 L/s

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