A typical coal-fired power plant burns 280 metric tons of coal every hour to gen

Question

A typical coal-fired power plant burns 280 metric tons of coal every hour to generate 770 MW of electricity. 1 metric ton=1000 kg. The density of coal is 1500 kg/m^3 and 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.

Part A
Suppose the coal is piled up in a 15m X 10m room. How tall must the pile be to operate the plant for one day?___________m


Part B
What is the power plant's thermal efficiency?

Explanation / Answer

(a) Mass of coal needed for one day = 280 x 1000 x 24 = 6720000 kg

Volume of coal = mass/density = 6720000/1500 = 4480 m3

Volume of coal = length x width x height = 15 x 10 x height = 4480

Height of pile = 4480/150 = 29.9 m

(b) Thermal energy released by combustion of coal per hour = mass x heat of combustion

= 280 x 1000 x 28 = 7840000 J

Thermal power released by combustion of coal = energy/time

= 7840000/3600 = 2178 MW

Thermal efficiency = electrical power/thermal power x 100

= 770/2178 x 100 = 35.4 %

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