One kilowatt hour (1 kWh) of electrical energy is equal to how many joules (J)?

Introduction / Context:
In electricity and power consumption, the kilowatt hour (kWh) is a commonly used unit of energy on electricity bills and in practical applications. However, in physics, the standard SI unit of energy is the joule (J). Being able to convert between kilowatt hours and joules is important for solving numerical problems related to electrical energy, power ratings of appliances, and cost of electricity usage. This question directly tests the standard conversion factor between 1 kWh and joules.

Given Data / Assumptions:
• We are given the energy unit 1 kWh. • We know that 1 kilowatt (kW) = 1000 watts (W). • We know that 1 hour = 3600 seconds. • We recall that 1 watt is equal to 1 joule per second.

Concept / Approach:
A kilowatt hour represents the energy consumed when a device with a power rating of 1 kilowatt operates for 1 hour. Power is defined as rate of doing work or rate of energy consumption, P = E / t, which means that E = P * t. To convert 1 kWh to joules, we convert kilowatts to watts and hours to seconds, then multiply power in watts by time in seconds. Because 1 W = 1 J/s, the product of watts and seconds directly gives energy in joules.

Step-by-Step Solution:
Step 1: Start from the definition: 1 kWh = 1 kilowatt of power used for 1 hour. Step 2: Convert kilowatts to watts: 1 kW = 1000 W. Step 3: Convert hours to seconds: 1 hour = 3600 s. Step 4: Use the relation E = P * t, where P = 1000 W and t = 3600 s. Step 5: Calculate E = 1000 * 3600 = 3 600 000 J. Step 6: Express this in scientific notation: 3 600 000 J = 3.6 * 10^6 J.

Verification / Alternative check:
We can double check by estimating. 1000 is 10^3 and 3600 is approximately 3.6 * 10^3. Multiplying 10^3 by 3.6 * 10^3 gives 3.6 * 10^6, which matches the earlier calculation. This confirms that the conversion factor is consistent and widely used in textbooks, energy calculators, and electricity billing. Therefore, 1 kWh is equal to 3.6 * 10^6 joules.

Why Other Options Are Wrong:
Option a (3.6 * 10^-8 J): This is extremely small and completely inconsistent with the energy consumed by a 1 kW device running for an hour. Option b (3.6 * 10^-6 J): This is also a very tiny amount of energy and does not match the unit conversions. Option c (3.6 * 10^8 J): This would be 100 times larger than the correct value and does not follow from the correct multiplication. Option e (3.6 * 10^4 J): This is only 36 000 J, which is far less than the energy for 1 kW over 3600 seconds.

Common Pitfalls:
The most common mistake is to forget either the factor of 1000 when converting kilowatts to watts or the factor of 3600 when converting hours to seconds. Another error is mishandling powers of ten when expressing the final answer in scientific notation. Students sometimes write 3.6 * 10^5 or 3.6 * 10^7 by mistake. To avoid errors, always break the conversion into clear steps, multiply 1000 by 3600 explicitly, and then convert the final number into proper scientific notation.

Final Answer:
One kilowatt hour is equal to 3.6 * 10^6 J.