Question

In 2003 the United States generated 3.88 trillion kWh of electricity, 51% of which came from coal-fired power plants. Assuming an average thermal efficiency of 34% and the heating value of coal as 30 MJ/kg, determine the coal consumption in 2003 in tons.

Answer 1

Electricity from  coal-fired power plants = 0.51 * 3.88 trillion kWh = 1.978 trillion kwh
Heat Value of Coal = 30 * 10^6 J/Kg
Thermal Efficiency = 34%

1 Kw = 3600 kJ/hr

Heat Input required for 1 kw hr of Electricity = 3600 kJ/hr / 34% = 10588 kJ /Kw

For Producing this much , Coal Required = 10588 / 30 *10^3 kJ = 0.353 kG

Coal required to Produce 1.978 trillion kwh = 0.353 * 1.978 * 10^12 Kg
Coal required to Produce 1.978 trillion kwh = 0.353 *1.978 * 10^12 * 1.1 * 10^-3 ton
Coal required to Produce 1.978 trillion kwh = 7.68 * 10^8 tons