1 kWh = 3.6 × 10^6 J
Explanation
The Kilowatt-hour (kWh) is a commercial unit of electrical energy, commonly used for billing electricity consumption. The Joule (J) is the SI derived unit of energy. Establishing the relationship between these two units requires converting the components of power (kilowatts) and time (hours) into their respective SI base units (Watts and seconds).
Derivation of the Relationship:
- Step 1: Define the units in terms of SI base units.
- 1 Kilowatt (kW) = 1000 Watts (W) = 1000 Joules per second (J/s).
- 1 Hour (h) = 60 minutes × 60 seconds = 3600 seconds (s).
- Step 2: Calculate the total energy.
- Energy = Power × Time
- 1 kWh = 1000 W × 3600 s
- 1 kWh = 1000 J/s × 3600 s
- 1 kWh = 3,600,000 Joules
- Step 3: Express in scientific notation.
- 3,600,000 J = 3.6 × 106 J
Key Takeaway:
One unit of electricity (commercial trade unit) is equal to 1 kWh, which converts to 3.6 × 106 Joules in the SI system. It is crucial to distinguish that kWh is a unit of energy, whereas kW is a unit of power.