Question

How much coal is burned in a day by a coal-fired power plant producing 500 MW of electrical power with an efficiency of 34%? The heating value of coal is 25,000,000 (25x10⁶) Btu/ton. Give your answer in tons.

Answer 1

Time, t= 1 day = 1 x 24 x 60 x 60 seconds = 86400s

Power, P = 500 MW = 500 x 10^6 W

Energy output, Eo = P x t = (500 x 10^6 W) x (86400s) = 432 x 10^11 Joules = 432 x 10^11 x 0.000948 Btu = 4.09457 x 10^10 Btu

Efficiency = output energy / input energy

Therefore, input energy = outpit energy / efficiency

Ei = Eo/34% = (4.09457 x 10^10 Btu)/(34/100) = 1.20428 x 10^11 Btu

Mass of coal required = Ei/energy per ton of coal = (1.20428 x 10^11 Btu) / (25 x 10^6 Btu/ton) = 4.81712 x 10^3 tons