Understanding Kilowatt-Hour Energy Conversion

The question asks us to determine the equivalent energy of one kilowatt-hour in Joules. A kilowatt-hour (kWh) is a common unit of energy, especially for measuring electrical energy consumption. The Joule (J) is the standard SI unit of energy.

To convert kilowatt-hour to Joules, we need to understand the definitions of the units involved:

• Power: The rate at which energy is transferred or used. The standard unit is the Watt (W), where 1 Watt = 1 Joule per second (J/s).
• Kilowatt (kW): A larger unit of power, where 1 kilowatt = 1000 Watts.
• Time: Measured in seconds (s) in the SI system. Hours (h) are also commonly used. 1 hour = 60 minutes = 60 × 60 seconds = 3600 seconds.
• Energy: The capacity to do work. It is often calculated as Power × Time. The standard SI unit is the Joule (J).

The unit kilowatt-hour (kWh) represents the energy consumed when power is one kilowatt for a period of one hour. Using the relationship Energy = Power × Time, we can perform the conversion:

First, convert kilowatt to Watts:

$$ 1 \text{ kW} = 1000 \text{ W} $$

Next, convert hours to seconds:

$$ 1 \text{ h} = 3600 \text{ s} $$

Now, substitute these values into the Energy = Power × Time formula for one kilowatt-hour:

$$ 1 \text{ kWh} = (1 \text{ kW}) \times (1 \text{ h}) $$

Substitute the equivalent values in Watts and seconds:

$$ 1 \text{ kWh} = (1000 \text{ W}) \times (3600 \text{ s}) $$

Since 1 Watt = 1 Joule per second (1 W = 1 J/s), we can write:

$$ 1 \text{ kWh} = (1000 \frac{\text{J}}{\text{s}}) \times (3600 \text{ s}) $$

Multiply the numbers:

$$ 1 \text{ kWh} = 1000 \times 3600 \text{ J} $$

$$ 1 \text{ kWh} = 3,600,000 \text{ J} $$

So, one kilowatt-hour of energy is equal to 3,600,000 Joules.

Let's compare this result with the given options:

• Option 1: 3600000 Joules
• Option 2: 360 Joules
• Option 3: 36000 Joules
• Option 4: 360000 Joules

Our calculated value of 3,600,000 Joules matches Option 1.

Revision Table: Energy Conversion Units

Additional Information: Power and Energy

Power is the rate at which energy is used or produced. Energy is the total amount of work done or energy transferred over a period of time. Think of power like speed (how fast you are doing something) and energy like distance (how much you have done in total). A higher power means you are using or producing energy faster.

The Joule is a fundamental unit for energy in science, but the kilowatt-hour is often used in everyday life, especially for electricity billing, because it deals with larger amounts of energy that are more convenient to measure for typical household consumption.

Understanding this conversion is important for calculating energy costs. If your electricity rate is, for example, $0.15 per kWh, you can calculate the cost of using a 100 W light bulb for 10 hours:

Energy used = Power × Time

Power = 100 W = 0.1 kW

Time = 10 hours

Energy used = 0.1 kW × 10 h = 1 kWh

Cost = Energy used × Rate = 1 kWh × $0.15/kWh = $0.15

This example shows how the kilowatt-hour unit is practical for energy calculations in daily life, while the Joule is the standard unit used in physics and other scientific contexts.