Question

Assume that electricity costs 15 cents per kilowatthour. Calculate the yearly cost of operating each of the following: a. a home computer that consumes \(2.5 \mathrm{kWh}\) per week b. a pool pump that consumes \(300 \mathrm{kWh}\) per week c. a hot tub that consumes \(46 \mathrm{kWh}\) per week d. a clothes dryer that consumes \(20 \mathrm{kWh}\) per week

Short answer

The yearly costs are as follows: a. Home computer: \(19.5. b. Pool pump: \)2340. c. Hot tub: \(358.8. d. Clothes dryer: \)156.

Step-by-step solution

- Compute annual electricity consumption

Calculate the yearly electricity consumption for each device by multiplying the weekly consumption by the number of weeks in a year (52 weeks per year). For the home computer: \(2.5 \mathrm{kWh/week} \times 52 \mathrm{weeks/year} = 130 \mathrm{kWh/year}\).

- Determine cost per device

Calculate the yearly cost for each device by multiplying the annual consumption by the cost per kilowatt-hour (\(0.15/\mathrm{kWh})\). For the home computer: \(130 \mathrm{kWh/year} \times 0.15 \mathrm{\$ / kWh} = 19.5 \mathrm{\$}\).

- Repeat calculations for other devices

Repeat the previous steps for each of the remaining devices: a. Pool pump: \(300 \mathrm{kWh/week} \times 52 \mathrm{weeks/year} = 15600 \mathrm{kWh/year}\). b. Hot tub: \(46 \mathrm{kWh/week} \times 52 \mathrm{weeks/year} = 2392 \mathrm{kWh/year}\). c. Clothes dryer: \(20 \mathrm{kWh/week} \times 52 \mathrm{weeks/year} = 1040 \mathrm{kWh/year}\).

- Compute the yearly cost for all devices

Calculate the yearly operating cost for each device by multiplying the annual consumption by \(0.15/\mathrm{kWh}\). a. Pool pump: \(15600 \mathrm{kWh/year} \times 0.15 \mathrm{\$ / kWh} = 2340 \mathrm{\$}\). b. Hot tub: \(2392 \mathrm{kWh/year} \times 0.15 \mathrm{\$ / kWh} = 358.8 \mathrm{\$}\). c. Clothes dryer: \(1040 \mathrm{kWh/year} \times 0.15 \mathrm{\$ / kWh} = 156 \mathrm{\$}\).

Key concepts

Energy Consumption

Understanding energy consumption is crucial when it comes to managing electricity costs in any household or business. It refers to the amount of electric power used over a certain period by electrical devices or appliances. In the context of the exercise, energy consumption is measured in kilowatt-hours (kWh), which represents the energy usage of appliances over time. For example, a home computer that consumes 2.5 kWh per week uses that amount of energy to operate for the entire week. By tracking the energy consumption of various devices, individuals can better understand their energy habits and look for ways to reduce consumption, which in turn lowers electricity bills.

Energy consumption has both immediate financial implications and long-term environmental impacts, making awareness and conservation important for both individual savings and ecological health.

Kilowatt-Hour

A kilowatt-hour (kWh) is a unit of energy that is commonly used to measure electricity consumption. One kWh is the amount of energy expended by a 1,000-watt appliance running for one hour. For instance, if a 100-watt light bulb is left on for 10 hours, it will consume 1 kWh of energy (100 watts x 10 hours = 1,000 watt-hours = 1 kWh). In the exercise, the pool pump with a weekly consumption of 300 kWh is using a significant amount of energy, equating to a 300,000-watt appliance running for one hour or a 1,000-watt appliance running for 300 hours in a week. By understanding how the kilowatt-hour is quantified, students can better assess their energy use and estimate costs more accurately.

Annual Operating Cost

The annual operating cost of an appliance or an electronic device is the total cost associated with its usage over a one-year period. This includes the costs of energy required to run the device. To calculate the annual operating cost, one must know the device's energy consumption in kWh and the cost per kWh charged by the electricity provider. For example, the exercise demonstrates that multiplying the annual electricity consumption (in kWh) by the cost per kWh gives us the annual operating cost. Hence, the clothes dryer with an annual consumption of 1040 kWh has an annual operating cost of $156 when the electricity cost is 15 cents per kWh. This figure helps individuals budget for their energy expenses and make informed decisions about appliance usage and efficiency upgrades.

Cutting Down Costs

Real-world applications might include investing in energy-efficient appliances or using devices during off-peak hours to take advantage of lower rates.

Household Energy Use

Household energy use encompasses all the electricity consumed by all the devices and appliances within a home. It varies greatly depending on the number and type of appliances, the habits of the residents, and other factors like the size of the home and climate. In our exercise, various appliances from a home computer to a pool pump have been used to demonstrate a range of energy uses. For instance, while a home computer might have relatively low energy consumption compared to that of a pool pump, the cumulative effect of numerous low-consumption devices can still lead to significant overall household energy use. Understanding individual appliance costs can help promote energy-saving strategies such as unplugging devices not in use, performing regular maintenance to ensure devices run efficiently, and replacing old appliances with newer, more energy-efficient models.