A typical coal-fired power plant burns 340 metric tons of coal every hour to gen

Question

A typical coal-fired power plant burns 340 metric tons of coal every hour to generate 710 MW of electricity. 1 metric ton 1000 kg. The density of coal is 1500 Kg/m^3and its heat of combustion is 28 MJ/Kg . Assume that all heat is transferred from the fuel to the boiler and that all the work done in spinning the turbine is transformed into electrical energy.
a) Suppose the coal is piled up in a 8.0m* 15m room. How tall must the pile be to operate the plant for one day?
b) What is the power plant's thermal efficiency?

Explanation / Answer

If it burns 340 tons/hr, it burns 24*340 tons/day. That much coal occupies volume of:
(24*340 tons)/(1.5 tons/m3) = 5440 m3

So we have (8 m)(15 m)(height) = 5440 m3

Solving for height I get 45.33 m

There is a problem with the second part: 340 tons/hr = 0.094 tons/second which assuming your 28 MJ/Kg is only 2.64 MW, nowhere near 710 MW. Is it possible that the 710 number is supposed to be MW-hours instead of MW? In other words, a quantity of energy instead of power?

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