At a steam power plant, steam engines work in pairs, the heat output of the firs

Question

At a steam power plant, steam engines work in pairs, the heat output of the first one being the approximate heat input of the second. The operating temperatures of the first are 740C and 440 C, and of the second 415 C and 270 C.

Part A

If the heat of combustion of coal is 2.8×107J/kg, at what rate must coal be burned if the plant is to put out 950 MW of power? Assume the efficiency of the engines is 65% of the ideal (Carnot) efficiency.

Express your answer using two significant figures.

Part B

Water is used to cool the power plant. If the water temperature is allowed to increase by no more than 4.5C, estimate how much water must pass through the plant per hour.

Express your answer using two significant figures.

Explanation / Answer

Part A

1 = 0.65 of [1013- 713] / 1013 = 0.65 of 300 / 1013 = 0.192
2 = 0.65 of [688- 543] / 688 = 0.65 of 145/ 688 = 0.1369

Out put of first engine = input of the second engine
= 0.192 of input in the first engine

Out put of second engine =
0.1369 of 0.192 of input in the first engine
= 0.026284 of input in the first engine

950 MW = 0.026284 of input in the first engine

Input in the first engine = 950 MW/ 0.026284
= 36143.66 *106 J / s

Heat combustion of coal is 2.8* 107 J/kg
36143.66 *106 J / s / 2.8e^7 =1290.84 kg/s

The rate is 1290.84 kg/s

Part B)

q = mc(deltaT) where

m= q/c(deltaT),

Specific heat of water (c)=4,184 Joules

Delta T= 4.5 c

Q= 36143.66 *106- 950 MW

Q= 35193 J/s

M= 35193* 106 /4184*4.5
M= 1869184 Kg

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