One kilowatt hour (kWh) is the amount of work or energy generated when one kilowatt of power is supplied for a time of one hour. A kilowatt hour is the unit of energy used by power companies when figuring your electric bill. Determine the number of joules of energy in one kilowatt hour.
The correct answer and explanation is:
Correct Answer:
1 kilowatt-hour (kWh) = 3,600,000 joules (J)
Explanation:
To convert kilowatt-hours (kWh) to joules (J), we need to understand the relationship between power, time, and energy.
1. Understanding Units:
- Watt (W) is a unit of power, and it is defined as 1 joule per second (J/s).
- Kilowatt (kW) is 1,000 watts.
- 1 hour = 3,600 seconds (since 1 hour = 60 minutes and 1 minute = 60 seconds)
2. Formula for Energy:
Energy (in joules) = Power (in watts) × Time (in seconds)
So:
- 1 kilowatt = 1,000 watts
- 1 hour = 3,600 seconds
Substitute into the formula: Energy=1,000 W×3,600 s=3,600,000 J\text{Energy} = 1{,}000 \, \text{W} \times 3{,}600 \, \text{s} = 3{,}600{,}000 \, \text{J}
3. Why Is This Important?
Power companies bill consumers based on the energy consumed, which is usually measured in kilowatt-hours rather than joules because joules are small and impractical for household billing. For example, running a 1,000-watt appliance for one hour uses 1 kWh, which is 3.6 million joules.
This conversion is useful not just for understanding your electric bill, but also for comparing energy use and cost across different systems—such as gas vs. electric heating, or understanding battery capacity in electric vehicles (often given in kWh).
In Summary:
- 1 kilowatt-hour = 1,000 watts × 3,600 seconds = 3,600,000 joules
- This value represents the energy used when running a 1,000-watt device for one hour.