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 730 C and 440 C, and of the second 415 C and 280 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 960 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 4.5

C, estimate how much water must pass through the plant per hour.

Express your answer using two significant figures.

Explanation / Answer

PART A

w1 = e*Q

e = n*(1-(Tl/TM)

For first engine

e = 0.65*(1-(440 + 273)/(730+273)) = 0.187

For second engine

e' =  0.65*(1-(280 + 273)/(415+273)) = 0.1275

Q*( 0.187+0.1275*0.813) = 960*106

Rate = Q/H = 4.57*109/2.8*107 = 163

PART B

Q = (4.57*109 - 960*106)*3600 = 1.3*1013

m = Q/c*deltat = 1.3*1013/(4186*4.5) = 6.9*108

V = m/deltra

V =6.9*108 /1000 *1/0.0038 = 18.16*107 gal/h

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