Question

A typical coal-fired power plant burns 290 metric tons of coal every hour to generate 800 MW of electricity. 1 metric ton= 1000 kg. The density of coal is 1500 kg/m3 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 8.0 m × 11 m room. How tall must the pile be to operate the plant for one day? Part B) What is the power plant's thermal efficiency?

Answer 1

Here ,

mass of coal per hour , m = 290 tonns/hour

part A)

let the height of the pile is h

mass of coal used in a day , M = 24 * 290 ton

M = 24 * 290 * 1000 Kg

Now , as volume = mass/density

8 * 11 * h = 24 * 290 * 1000/1500

h = 52.7 m

the height of the pile must be 52.7 m

part B)

thermal efficiency = energy output/energy input

thermal efficiency = 800 *10^6 W/(290 *1000 * 28 *10^6/3600 W)

thermal efficiency = 0.355

the thermal efficiency is 0.355