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 720 C and 460 C, and of the second 435 C and 290 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 990 MW of power? Assume the efficiency of the engines is 65% of the ideal (Carnot) efficiency.

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.

Explanation / Answer

part A)

for the engine 1 ,

efficiency , e1 = 1 - (Tc/Th)

e1 = 1 - ((460 +273)/(720 + 273) )

e1 = 0.262

for the second engine ,

efficiency , e2 = 1 - (290+273)/(435 + 273)

e2 = 0.205

Now, the net efficiency of power plant = 0.65 * 0.205 * 0.262

e = 0.0349

let the amount of coal is m kg

2.8 *10^7 * 0.0349 * m = 990 *10^6

m = 1013.74 Kg/s

the rate of mass of coal burned is 1013.74 Kg/s

part B)

now, let the amount of water is M kg per hour

m * 4186 * (4.5) = 1013.74 * (1 - 0.0349) * 2.8 *10^7 * 3600

m = 5.235 *10^9 Kg/hour

the mass of water passing is 5.235 *10^9 Kg/hour

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