74. (a) At a steam power plant, steam engines work in pairs, 76 the heat output

Question

74. (a) At a steam power plant, steam engines work in pairs, 76 the heat output of the first one being the approximate heat input of the second. The operating temperatures of the first are 750°C and 440°C, and of the second 415°C and 270°C. If the heat of combustion of coal is 2.8 × 107 J/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. (b) Water is used to cool the power plant. If the water temperature is allowed to increase by no more than 4.5 Co, estimate how much water must pass through the plant per hour. 77. is ea 75. Suppose a heat pump has a stationary bicycle attachment a ra that allows vou to provide the vork instead of usino an

Explanation / Answer

(a) the coal rate:

Note that the sum of the work of each engine equals 950 MW, so:
W1 + W2 = 950000 kW -- eq 1

& thermal efficiency of heat engines is work output divided by heat input:
e = W/Qa

so we can rewrite equation 1:
e1*Qa1 + e2*Qa2 = 950000 kW

since, Qa1-Qr1 = Qa2 ("output of heat from one being the approximate input of the second") and Qa1-Qr1 = eff1*Qa1, so:

e1*Qa1 + e2*eff1*Qa1 = 950000 kW -- eq 2

the thermal effficiency of heat engine 1 is:
e1 = 0.65*eff1 carnot
e1 = 0.65*[(750-440)/(750+273)] = 0.196

likewise, the thermal efficiency of heat engine 2 is:
e2 = 0.65*[(415-270)/(415+273)] = 0.136

substituting values to eq 2:
(0.196 + 0.136*0.244)*mf*28,000 = 950000
mf = 148.15 kg/sec

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