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Jessica’s parents are always telling her to turn off the lights when she leaves a room. A light bulb requires 75 watts to run when it is turned on. The fi xture in Jessica’s room requires four of these bulbs. a. Jessica’s parents estimate that she leaves the lights on unnecessarily for 2.5 hours per day. How many watt-hours of electricity are used by these bulbs during 2.5 hours? b. Approximately how many kilowatt-hours of electricity are used in a year to keep these bulbs lit for 2.5 hours per day? c. At a cost of \(\$ 0.09\) per kilowatt-hour, how much money is wasted per year by keeping these lights on unnecessarily? Round to the nearest dollar. d. If five million teenagers keep lights on as Jessica does, how much is wasted in unnecessary electric expenses?

Step by step solution

01

Calculate watt-hours

Firstly, calculate the total power of the bulbs by multiplying the wattage per bulb (75 watts) by the number of bulbs (4). This gives 300 watts. Then, multiply this by the number of hours the lights are left on (2.5 hours) to get the watt-hours. Therefore, the lights use \(300 \times 2.5 = 750\) watt-hours

02

Convert watt-hours to kilowatt-hours for a day

To convert watt-hours to kilowatt-hours, divide the number of watt-hours by 1000, because 1kWh = 1000Wh. Therefore, \(750 \div 1000 = 0.75\) kWh.

03

Convert daily kilowatt-hours to annual

Assuming there are approximately 365 days in a year, multiply the daily kWh by 365 to calculate annual kWh. Therefore, \(0.75 \times 365 = 273.75\) kWh.

04

Calculate cost of electricity used per year

Now, multiply the annual kWh by the cost per kWh (\$0.09). Therefore, \(273.75 \times 0.09 = \$ 24.64 \). Round this to the nearest dollar to get \$25 per year.

05

Calculate total cost for five million teenagers

Finally, multiply the cost per teenager (\$25) by the number of teenagers (5 million). Therefore, \$25 \times 5,000,000 = \$125,000,000.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electricity Usage

When you switch on an electrical device, it begins to draw power, measured in watts, from the electrical supply. In Jessica's case, each light bulb uses 75 watts. Since she has four bulbs in her fixture, the total power usage is four times 75 watts, which equals 300 watts. It's important to be aware of this power usage because it directly affects the amount of electricity you consume and, consequently, your energy bill.
Understanding electricity usage helps in maintaining energy efficiency, which can reduce both electricity wastage and costs. The more watts a device uses, the more electricity it consumes, and, naturally, the higher the expense.

Watt-Hours

Watt-hours are a measure of energy consumption over time. It's calculated by multiplying the power in watts by the time the appliance runs in hours. In the exercise, Jessica leaves her lights on for 2.5 hours each day. Thus, her bulbs use 300 watts of power per hour, and over 2.5 hours, they consume:\
\[ 300 \text{ watts} \times 2.5 \text{ hours} = 750 \text{ watt-hours} \]
This demonstrates how energy is not just about the power a device uses but how long it uses it. By multiplying the wattage by time, we precisely measure the total 'work' done by the electricity.

Kilowatt-Hours

Kilowatt-hours (kWh) are a larger unit of energy commonly used by utility companies to measure and bill electricity usage. Since one kilowatt-hour is equivalent to 1,000 watt-hours, converting watt-hours to kilowatt-hours involves dividing by 1,000. Jessica's bulbs use 750 watt-hours each day, which converts to:\
\[ \frac{750 \text{ watt-hours}}{1000} = 0.75 \text{ kWh} \]
To find out the yearly usage, multiply the daily kilowatt-hour usage by the number of days in a year (365), giving us:\
\[ 0.75 \text{ kWh/day} \times 365 \text{ days/year} = 273.75 \text{ kWh/year} \]
This conversion helps in understanding how daily energy usage contributes to annual consumption.

Annual Energy Cost

The annual energy cost calculates how much money is spent on electricity over a year. With a rate of \(0.09 per kilowatt-hour, the cost can be figured by multiplying the annual kWh usage by this rate. In Jessica's scenario, with a yearly consumption of 273.75 kWh, the annual cost is calculated as follows:\
\[ 273.75 \text{ kWh} \times 0.09 \text{ dollars/kWh} = 24.64 \text{ dollars} \]
Rounding this figure gives us approximately \)25. If multiplied by five million teenagers doing the same, the total wasted expenditure is astronomically high, demonstrating how small actions scale up dramatically when widespread. This underlines the importance of switching off lights when not in use to save money and energy.