At a steam power plant, steam engines work in pairs, the heat output of the firs
ID: 1480577 • Letter: A
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 740 C and 460 C, and of the second 435 C and 270 C.
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 860 MW of power? Assume the efficiency of the engines is 65% of the ideal (Carnot) efficiency.
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
A) rate of work output, PW = 860 MW
we know effiecency, n = rate of workdone/rate of input
n = PW/Pin
==> PIn = PW/n
= PW/0.65
= 860/0.65
= 1323 MW
the rate at which the coal must be burned = 1323*10^6/(2.8*10^7)
= 47.25 kg/s
B) Pout = Pin - PW
= 1323 - 860
= 463 MW
= 463*10^6 J/s
Energy givn out in 1 one hour, Q = 60*60*463*10^6
= 1.6668*10^12 J
let m is the mass of the water to be send.
m = Q/(c*dT)
= 1.6668*10^12/(4186*4.5)
= 8.85*10^7 kg
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