If all the solid waste of 230 million tonnes were burned in waste-to-energy power plants that are 20% efficient,
a) how many kilowatt-hours of electrical energy could be produced in a year? Compare this quantity with the total U.S. electrical energy production of approximately 3.8 trillion kWh annually.
b) what would be the equivalent average electric power output from all these waste burning power plants? how many 1-GW coal-fired plants could they displace
To calculate the answers, we'll follow these steps:
Step 1: Calculate the electrical energy that can be produced from 230 million tonnes of solid waste.
First, we need to convert tonnes to kilograms by multiplying by 1000:
230 million tonnes * 1000 = 230 billion kilograms.
Since the waste-to-energy power plants are 20% efficient, we multiply the weight of the waste by the efficiency factor:
230 billion kg * 0.20 = 46 billion kg.
To calculate the energy produced, we need to use the energy content of waste in kilojoules per kilogram (kJ/kg). This value can vary based on the composition of the waste, but for our calculation, let's assume an average value of 10,000 kJ/kg.
Multiply the weight of the waste by its energy content:
46 billion kg * 10,000 kJ/kg = 460 trillion kJ.
Step 2: Convert kilojoules to kilowatt-hours.
To convert kJ to kWh, divide the energy in kilojoules by the conversion factor of 3,600 (1 kilowatt-hour = 3,600 kilojoules):
460 trillion kJ / 3,600 = 127.8 trillion kilowatt-hours (kWh).
a) The waste would generate approximately 127.8 trillion kWh of electrical energy in a year.
Step 3: Compare with U.S. electrical energy production.
The total U.S. electrical energy production is approximately 3.8 trillion kWh annually.
To compare, we divide the waste energy production by the U.S. electrical energy production:
127.8 trillion kWh / 3.8 trillion kWh = 33.6.
a) The electrical energy production from burning the solid waste would be approximately 33.6 times the total U.S. electrical energy production in a year.
b) To find the equivalent average electric power output, we divide the energy production (in kWh) by the time (in hours). If we assume a year has 8,760 hours:
127.8 trillion kWh / 8,760 hours = 14.6 billion kilowatts (kW).
To compare this with coal-fired plants, we convert 1 GW (gigawatt) to kW by multiplying by 1,000:
1 GW * 1,000 = 1 billion kW.
b) The waste burning power plants would have an equivalent average electric power output of approximately 14.6 billion kW, meaning they could displace around 14.6 coal-fired power plants with a capacity of 1 GW each.