Chapter 25: Problem 65
A typical cost for electrical power is $0.120 per kilowatthour. (a) Some people leave their porch light on all the time. What is the yearly cost to keep a 75-W bulb burning day and night? (b) Suppose your refrigerator uses 400 W of power when it's running, and it runs 8 hours a day. What is the yearly cost of operating your refrigerator?
Short Answer
Step by step solution
Convert Watts to Kilowatts for the Porch Light
Calculate the Total Kilowatt-hours for the Porch Light
Calculate the Cost for the Porch Light
Convert Watts to Kilowatts for the Refrigerator
Calculate the Daily Kilowatt-hours for the Refrigerator
Calculate the Yearly Kilowatt-hours for the Refrigerator
Calculate the Cost for the Refrigerator
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Kilowatt-Hour
Suppose you have an appliance that's rated at 1000 watts (or 1 kW) and you run it for an hour. The energy used during that time is 1 kWh. That's because a kilowatt-hour is the energy you would use if you kept a 1000-watt appliance running for one hour.
Understanding kilowatt-hours helps you manage your electricity usage and control costs. By knowing how many kilowatt-hours your devices consume, you can compare them and make smarter decisions about their use.
Power Consumption
To convert power consumption from watts to kilowatts, remember this: 1 kilowatt is equal to 1000 watts. For example, if you have a 75-W light bulb and want to calculate its power consumption in kilowatts, divide by 1000, getting 0.075 kW. This conversion allows you to calculate how much energy an appliance uses in kilowatt-hours over time.
Keeping track of power consumption helps you control your electricity bill by knowing which appliances use the most power.
Cost per Kilowatt-Hour
In the example exercise, the cost is $0.120 per kWh. To find out how much money it costs to use an appliance, simply multiply the total kWh used by the cost per kWh.
Calculating costs using the cost per kilowatt-hour allows you to forecast your electricity expenses and budget accordingly. Being aware of this cost helps you use electricity more efficiently and reduces waste.
Electrical Power Usage
For instance, if you run a 400-W refrigerator for 8 hours a day, you consume 3.2 kWh daily. By multiplying this daily usage by 365 days, you discover how much energy the appliance uses yearly, which you can then convert to costs using the cost per kilowatt-hour.
By understanding electrical power usage patterns, you can identify areas where you might save energy, whether by using appliances more efficiently or considering more energy-efficient models.
Mathematical Calculations
Here’s the basic formula:
- Convert power ratings from watts to kilowatts.
- Calculate total energy consumption in kilowatt-hours.
- Multiply by cost per kilowatt-hour to get the cost.
For example, for a 0.4 kW refrigerator used for 8 hours daily, the steps are:
- Calculate daily kWh: 0.4 kW * 8 hours = 3.2 kWh.
- Calculate yearly kWh: 3.2 kWh/day * 365 days = 1168 kWh/year.
- Calculate cost: 1168 kWh * $0.120/kWh = $140.16/year.
Understanding these calculations empowers individuals to make informed decisions about their energy use and costs.