Question

The US annual consumption of electricity is 3 ⇥ 1012 kWh. If all the electricity were produced by bituminous coal, with an energy content of 2.81 ⇥ 1010 J/ton, at an efficiency of 40%, the amount of coal burned per second would be:

(a) 1828 tons / second. (b) 30.4 tons / second. (c) 12.2 tons / second.

1 kWh of electricity from coal, assuming a plant with 40% efficiency, energy content of coal of 2.81⇥1010 J/ton, and coal made of pure C, produces:

(a) 1.17 kg of CO2 (b) 1.17 tons of CO2. (c) 0.47 kg of CO2.

Answer 1

Ans 1

Electricity consumption = 3 x 10^12 kWh / year

= (3 x 10^12 kWh / year) x (1 year / 8760 h)

= 3.425 x 10^8 kW x 1000W/kW

= 3.425 x 10^11 W

C = 3.425 x 10^11 J/s

Energy content in coal E = 2.81 x 10^10 J/ton

Efficiency = 40%

amount of coal burned per second if efficiency is 100%

= C/E

= (3.425 x 10^11 J/s) / (2.81 x 10^10 J/ton)

= 12.2 ton/s

amount of coal burned per second if efficiency is 40%

= 12.2/0.4 = 30.4 tons/second

Option B is the correct answer

Ans 2

Energy produced by coal P = 1 kWh = 3.6 x 10^6 J

Energy content in coal E = 2.81 x 10^10 J/ton

Coal required = P/E

= (3.6 x 10^6 J) / (2.81 x 10^10 J/ton)

= 0.00012811 ton x 1000kg/ton

= 0.12811 kg

12 kg coal produces = 44 kg CO2

CO2 produced = 44 x 0.12811 / 12 = 0.4697 kg

Efficiency of plant = 40%

CO2 produced = 0.4697/0.4 = 1.17 kg

Option A is the correct answer