Question

How much money will a homeowner owe an electric company if he turns on a 100.00 -W incandescent light bulb and leaves it on for an entire year? (Assume that the cost of electricity is \(\$ 0.12 / \mathrm{kW} \mathrm{h}\) and that the light bulb lasts that long.) The same amount of light can be provided by a 26.000-W compact fluorescent light bulb. What would it cost the homeowner to leave one of those on for a year?

Short answer

Answer: The cost for using the 100 W incandescent light bulb for an entire year would be $105.12, while the cost for using the 26 W compact fluorescent light bulb would be $27.33.

Step-by-step solution

(1) Convert the wattage of the bulbs to kilowatts

To convert wattage to kilowatts, we simply divide the wattage by 1000. 100 W incandescent light bulb: \(\frac{100}{1000} = 0.1\mathrm{kW}\) 26 W compact fluorescent light bulb: \(\frac{26}{1000} = 0.026\mathrm{kW}\)

(2) Calculate the total energy consumption per year

Multiply the wattage in kilowatts by the number of hours in a year (8760 hours). 100 W incandescent light bulb: \(0.1\mathrm{kW} \times 8760\mathrm{h} = 876\mathrm{kW} \mathrm{h}\) 26 W compact fluorescent light bulb: \(0.026\mathrm{kW} \times 8760\mathrm{h} = 227.76\mathrm{kW} \mathrm{h}\)

(3) Calculate the cost for each light bulb per year

Multiply the energy consumption in kilowatt-hours by the cost per kilowatt-hour. 100 W incandescent light bulb cost: \(876\mathrm{kW} \mathrm{h} \times \$0.12 / \mathrm{kW} \mathrm{h} = \$105.12\) 26 W compact fluorescent light bulb cost: \(227.76\mathrm{kW} \mathrm{h} \times \$0.12 / \mathrm{kW} \mathrm{h} = \$27.33\) The homeowner will owe the electric company: - \(\$105.12\) if they use the 100 W incandescent light bulb for an entire year. - \(\$27.33\) if they use the 26 W compact fluorescent light bulb instead for the same period.

Key concepts

Energy Efficiency

Understanding energy efficiency is crucial to both reducing electricity costs and environmental impact. Energy efficiency refers to using less energy to perform the same task.

Take the comparison between the 100 W incandescent light bulb and the 26 W compact fluorescent light bulb from our exercise. The compact fluorescent light bulb provides the same amount of light as the incandescent one but uses significantly less energy, which means it's more energy-efficient.

An easy way to think about energy efficiency in this context is to picture two vehicles traveling the same distance, where one consumes less fuel than the other. In this analogy, the fuel is the electric power, and the less fuel consumed for the same distance (or light output), the more efficient the vehicle (or light bulb) is.

Improving energy efficiency is not only about saving money; it also involves reducing the demand for energy, which can lead to lower greenhouse gas emissions and a reduction in the strain on energy resources. Consequently, energy-efficient devices play a pivotal role in creating sustainable energy consumption.

Kilowatt-Hour Calculation

Calculating energy consumption in kilowatt-hours (kWh) is an essential skill for understanding the relationship between the power usage of an appliance and the length of time it's used. The kilowatt-hour is a unit of energy equal to one kilowatt (1 kW) of power expended for one hour (1 h) of time.

In essence, the steps involve converting the power rating from watts to kilowatts, since household energy is usually billed in kWh. This is done by dividing the wattage by 1,000. For example, a 100 W device converts to 0.1 kW, as 100 divided by 1,000 equals 0.1.

Once the power in kilowatts is established, it's multiplied by the time in hours the device is used, which gives us the energy used in kWh. The exercise presents a real-world application, where a light bulb is left on for an entire year, translating to 8760 hours.

By understanding how to calculate kWh, you can estimate the energy consumption of any electronic device, helping you manage and predict energy costs effectively.

Electricity Cost Analysis

Electricity cost analysis involves calculating the financial cost of energy consumption over time, a vital aspect of managing household finance and energy conservation efforts.

The final step in our exercise is to calculate the expense associated with the energy consumption of the light bulbs. To do this, the energy used (in kWh) is multiplied by the cost per kWh, which is set by the electricity provider. For example, at \(0.12 per kWh, running a 100 W bulb for 876 kWh costs \)105.12 for the year.

By performing an electricity cost analysis, homeowners can assess which appliances or devices are most cost-efficient and make informed decisions about their use. It can highlight potential savings; for instance, switching to the 26 W compact fluorescent bulb saves the homeowner a significant amount per year.

Understanding the cost of electricity not only assists in reducing expenditures but also encourages energy conservation, as consumers become more aware of the financial and environmental impacts of their energy usage.