In SI units, 1 kilowatt hour (1 kWh) of electrical energy is equal to how many joules?

Introduction / Context:

This numerical question is about converting a practical energy unit used by electricity companies into the standard SI unit, the joule. Electricity bills often show energy consumption in kilowatt hours (kWh), but physics equations typically use joules (J). Knowing the exact conversion between these units is essential for solving power and energy problems correctly.

Given Data / Assumptions:

• 1 watt (W) = 1 joule per second (1 J/s).
• 1 kilowatt (kW) = 1000 W.
• 1 hour (h) = 3600 seconds.
• We want to find the energy in joules corresponding to 1 kWh.

Concept / Approach:

Energy is related to power and time by the relation Energy = Power * Time. A kilowatt hour means that a device with a power of 1 kilowatt operates for one hour. To convert to joules, we convert kilowatts to watts and hours to seconds, then multiply. Careful handling of powers of 10 is needed to avoid errors in the final exponent.

Step-by-Step Solution:

Verification / Alternative check:

You can think of a 1000 W heater running for one hour. Each second it uses 1000 J of energy. In 3600 seconds, it uses 1000 * 3600 J, which is 3.6 million joules. Many textbooks and electricity company references confirm the standard conversion 1 kWh = 3.6 x 10^6 J, so the result matches widely accepted data.

Why Other Options Are Wrong:

• 3.6 x 10^5 J: This is smaller by a factor of 10 and results from missing a zero in the calculation.
• 3.6 x 10^-5 J and 3.6 x 10^-6 J: These represent extremely tiny amounts of energy and clearly cannot correspond to one kilowatt hour, which is a large everyday energy unit.

Common Pitfalls:

Typical mistakes include forgetting that 1 kilowatt is 1000 watts, miscalculating the number of seconds in an hour, or misplacing the decimal when writing the final answer in scientific notation. Some students also confuse kilowatt hours with kilojoules. Carefully doing the unit conversions step by step and then rewriting the final number with the correct power of 10 helps avoid these errors.

Final Answer:

1 kilowatt hour is equal to 3.6 x 10^6 joules.