The kilowatt-hour (kWh) and the joule (J) are both units of energy or work. The kWh is commonly used for electrical energy billing, while the joule is the SI derived unit for energy.
Kilowatt-hour (kWh)
A kilowatt-hour represents the energy consumed by a device with a power rating of one kilowatt operating for one hour. For example, a 1 kW heater running for 1 hour uses 1 kWh. Practical applications include household electricity bills, where consumption is measured in kWh.
Joule (J)
The joule is defined as the energy transferred when a force of one newton acts through a distance of one meter. It is part of the International System of Units (SI). One joule is a relatively small amount of energy; for context, lifting a small apple one meter requires about 1 J.
Step 1: Write the conversion factor: 1 kWh = 3,600,000 J.
Step 2: Multiply the given value by the factor: $$10 \\text{ kWh} \\times 3{,}600{,}000 \\frac{\\text{J}}{\\text{kWh}} = 36{,}000{,}000 \\text{ J}$$
Therefore, 10 kWh = 36,000,000 J (36 million joules).
The exact conversion factor is 1 kWh = 3,600,000 J. This is derived from the definitions: 1 kilowatt = 1000 watts, 1 hour = 3600 seconds, and 1 watt = 1 joule per second. Therefore, the energy in joules is the product of power (in kW) and time (in hours) multiplied by 3.6 million.
The kilowatt-hour is more convenient for large amounts of energy consumed in homes. One kWh is equivalent to 3.6 million joules, so using joules would result in very large numbers. For example, a typical household uses several hundred kWh per month, which would be hundreds of millions of joules. Additionally, kWh aligns with typical power ratings (kW) and usage time (hours), making calculations intuitive.
"On fait la science avec des faits, comme on fait une maison avec des pierres ; mais une accumulation de faits n'est pas plus une science qu'un tas de pierres n'est une maison." "Science is built up of facts, as a house is built of stones; but an accumulation of facts is no more a science than a heap of stones is a house." — Henri Poincaré (French Mathematician, Theoretical Physicist & Mining Engineer)