Question

How much money would you save per hour by replacing a 100-watt incandescent lightbulb with an equally bright 20 -watt fluorescent bulb? Assume the cost of electricity to be 15 cents per kilowatt-hour.

Short answer

You would save 1.2 cents per hour.

Step-by-step solution

Understand the Energy Consumption

A 100-watt incandescent lightbulb consumes 100 watts per hour, and a 20-watt fluorescent bulb consumes 20 watts per hour. The difference in energy consumption would be \( 100 - 20 = 80 \) watts.

Convert Watts to Kilowatts

Electricity costs are usually provided in kilowatt-hours, so we need to convert the watts into kilowatts by dividing by 1,000. Thus, \( 80 \) watts equals \( 0.080 \) kilowatts because \( \frac{80}{1000} = 0.080 \).

Calculate the Cost Savings per Hour

The cost saving per hour is calculated by multiplying the difference in energy consumption by the cost of electricity. Hence, the savings are \( 0.080 \times 0.15 = 0.012 \) dollars per hour or 1.2 cents per hour.

Key concepts

Electricity Cost Calculation

Calculating electricity costs can seem confusing at first, but it's really about understanding a few key concepts. When you use electrical devices, they're consuming energy, and the cost of that energy is usually based on the amount of electricity used, measured in kilowatt-hours (kWh).

• First, identify the power consumption of the device in watts (W).
• Convert this power usage into kilowatts (since 1 kilowatt = 1000 watts).
• Then, multiply this figure by the number of hours you plan to use the device.
• Finally, multiply by the electricity rate (cost per kWh) to get the total cost.

So in the original problem, by comparing two bulbs with different energy usages, we determine the savings in energy (and hence money) by switching to a more efficient bulb.

Kilowatt-hour

The term kilowatt-hour (kWh) is a unit of energy commonly used to measure electricity usage. It is the energy used by a device with a power rate of one kilowatt running for one hour. Understanding kilowatt-hours is crucial because electricity providers bill you based on how much kWh you consume. For example, if you run a device rated at 100 watts for 10 hours:

• First, convert watts to kilowatts: 100 watts = 0.1 kilowatts.
• Then, multiply by the time used: 0.1 kW * 10 hours = 1 kWh.

This shows how much energy the device has consumed, and it's this number that helps in calculating the corresponding cost.

Lighting Energy Consumption

Lighting is one of the most significant areas where we can influence energy consumption. By choosing more energy-efficient lighting, like fluorescent bulbs over incandescent ones, you can significantly reduce energy consumption. Incandescent bulbs are known for using a lot of energy. For instance, a 100-watt incandescent lightbulb consumes 100 watts of power. Fluorescent bulbs:

• Use less power for the same brightness.
• Only consume about 20 watts for the same light output as a 100-watt incandescent bulb.

This switch not only lowers your energy bills but also positively impacts the environment through reduced energy demand. By understanding lighting energy consumption, you can make smart choices that save both money and energy.