Question

Typical household electricity use in the U.S. is about 30 kilowatthours (kWh) per day. If the electricity is produced by a natural gas plant operating at \(40 \%\) efficiency, each household requires \(75 \mathrm{kWh}\) of energy from natural gas each day. Converting this to Joules, and using the intensity of \(49 \mathrm{~g} / \mathrm{MJ}\) from Table \(9.1\), how \(\mathrm{much} \mathrm{CO}_{2}\) is produced daily to supply a house with electricity from a natural gas source?

Short answer

Answer: 13.23 kg of CO2 is produced daily.

Step-by-step solution

Converting power usage to energy consumption in Joules

First, find the energy consumption in Joules by converting the household daily electricity usage from kWh to Joules by using the conversion factor 1 kWh = \(3.6*10^6\, \mathrm{J}\). The energy from natural gas each day is \(75 \mathrm{kWh}\). So, \(E_{natural\,gas} = 75 \mathrm{kWh} * 3.6 * 10^6\, \mathrm{J/kWh} = 2.7 * 10^8\, \mathrm{J}\).

Calculate the mass of CO2 produced

We can now use the intensity of \(49 \mathrm{g}/\mathrm{MJ}\) to calculate the mass of CO2 produced daily. First, convert the intensity to \(\mathrm{g/J}\): \(49 \mathrm{g/MJ} = 49 \mathrm{g}/(10^6\, \mathrm{J})= 49 * 10^{-6}\, \mathrm{g/J}\). Now, multiply the energy consumption in Joules by the intensity of \(\mathrm{CO}_{2}\) emissions: \(Mass_{\mathrm{CO}_{2}} = 2.7 * 10^8\, \mathrm{J} * 49 * 10^{-6}\, \mathrm{g/J} = 13230\, \mathrm{g}\).

Convert the mass of CO2 to the required units

We have found that a household produces 13230 grams of \(\mathrm{CO}_{2}\) daily to supply electricity from a natural gas source. The mass can be converted to any required units, such as kilograms or pounds as needed. For example, to convert to kilograms, divide by 1000: \(Mass_{\mathrm{CO}_{2}} = 13230\, \mathrm{g} * \dfrac{1 \, \mathrm{kg}}{1000\, \mathrm{g}} = 13.23\, \mathrm{kg}\). So, the daily \(\mathrm{CO}_{2}\) production to supply a house with electricity from a natural gas source is 13.23 kg.

Key concepts

Electricity Use Calculation

Understanding how much electricity we consume at home is the first step toward energy conservation and efficiency. To calculate your household's electricity use, start by looking at the appliances and devices you use daily. Each item will have a power rating, typically in watts (W) or kilowatts (kW), which indicates how much power it uses when in operation.

For example, suppose a household typically uses around 30 kilowatt-hours (kWh) of electricity each day. This number represents the energy consumption over time. The kilowatt-hour is a unit of energy equal to one kilowatt (1 kW) of power expended for one hour (1 h) of time. Hence, a 40-watt bulb running for 25 hours would use one kWh of energy (40 watts * 25 hours = 1000 watt-hours = 1 kWh).

Calculating your total electricity use requires you to sum up the energy use of all your appliances, which usually appears on your electricity bill. But remember that factors like usage patterns and efficiency ratings also affect the actual energy consumption.

Energy Conversion

Energy conversion is about changing one form of energy into another. In the context of household energy use, electrical energy often comes from burning fossil fuels like natural gas, which releases chemical energy. This process is not 100% efficient; some energy is lost, usually as heat.

Take a natural gas power plant operating at a 40% efficiency rate. This means that for every 100 units of energy from natural gas, only 40 are converted into usable electricity. The rest is dissipated. To supply the required 75 kWh of energy to a house, we would need to burn enough natural gas to initially produce 187.5 kWh (75 kWh / 0.40), highlighting the inefficiencies in energy conversion.

Understanding these conversions is vital, as they have direct implications on how much natural resource is used and the quantity of emissions produced. Hence, improving energy conversion efficiency is key to reducing our resource footprint and managing environmental impact.

CO2 Emissions

The link between energy use and CO2 emissions is crucial, especially when considering environmental impacts. CO2, or carbon dioxide, is a greenhouse gas that contributes to global warming. The amount of CO2 emissions from electricity production largely depends on the source of the energy and the efficiency of the generation process.

In our natural gas plant example, efficiency plays a significant role in determining CO2 emissions. Lower efficiency means more fuel burned and higher emissions. Mathematically, converting 75 kWh of energy from natural gas (with 40% efficiency) to Joules and then using the CO2 emission intensity, we can calculate the resultant daily emissions from providing electricity to a household.

Calculating the carbon footprint involves working with emission factors, which are averages that estimate the amount of CO2 released per unit of energy produced. In this calculation, the emission intensity of natural gas from the plant is 49 g/MJ. By converting the energy used to Joules and applying the emission factor, one can deduce the amount of CO2 emitted, which can then be expressed in various units (grams, kilograms, etc.), illustrating the environmental impact of our energy choices.