An electrical power plant has an overall efficiency of 17%. The plant is to deli

Question

An electrical power plant has an overall efficiency of 17%. The plant is to deliver 147 MW of electrical power to a city, and its turbines use coal as fuel. The burning coal produces steam at 190°C, which drives the turbines. This steam is then condensed into water at 28°C by passing through coils in contact with river water.

(a) How many metric tons of coal does the plant consume each day (1 metric ton = 1 103 kg)? Incorrect: Your answer is incorrect. Your response differs from the correct answer by more than 10%. Double check your calculations. metric tons

(b) What is the total cost of the fuel per year if the delivered price is $6 per metric ton? $

(c) If the river water is delivered at 19°C, at what minimum rate must it flow over the cooling coils in order that its temperature not exceed 28°C? (Note: The heat of combustion of coal is 7.8 103 cal/g.) kg/s

Explanation / Answer

Here ,

a) efficiency , e = 17 % = 0.17

Power delivered , Po = 147 MW

a) let the amount of coal needed is m

Po = e * input energy

Po = e * m * (heat produced per Kg)

147 * 10^6 * (365 * 24 * 3600) = 0.17 * m * (7.8 *10^3 * 4186 1/Kg)

solving for m

m = 8.35 *10^8 Kg

m = 8.35 *10^5 ton

the mass of coal used daily is 8.35 *10^5 ton

b)

for the total cost of fuel per year

total cost of fuel per year = m * rate * 365

total cost of fuel per year = 8.35 * 10^5 * 6 * 365

total cost of fuel per year = 1829048866 $

c)

let the rate of flow of water is M

Now , heat lost to water = (1 - e)* Po/(e)

m * 4186 * (28 - 19) = (1 - 0.17) * 147 *10^6/(0.17)

solving for m

m = 19.1 Kg/s

the rate of water flow must be 19.1 Kg/s

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