Understanding Kilowatt-Hour Conversion to Joules

The question asks us to find the equivalent value of one kilowatt-hour in joules. This involves converting a unit of energy commonly used for billing electricity (kilowatt-hour) into the standard SI unit of energy (joule).

Let's break down the units involved:

• Kilowatt-hour (kWh): This is a unit of energy. It represents the energy consumed by a device operating at a power of one kilowatt for one hour.
• Kilowatt (kW): This is a unit of power. It is equal to 1000 watts (W). Power is the rate at which energy is transferred or used.
• Hour (h): This is a unit of time. The standard SI unit of time is the second (s). There are 3600 seconds in one hour.
• Joule (J): This is the standard SI unit of energy. One joule is defined as the energy transferred or work done when a force of one newton is applied over a distance of one meter. It is also equivalent to one watt-second (W⋅s).

Converting Kilowatt-Hour to Joules Step-by-Step

To convert kilowatt-hour to joules, we need to express kilowatts in watts and hours in seconds, then multiply them, as energy (in watt-seconds or joules) is power (in watts) multiplied by time (in seconds).

We start with 1 kilowatt-hour (kWh).

1. Convert kilowatt to watts:

   \(1 \text{ kW} = 1000 \text{ W}\)

2. Convert hours to seconds:

   \(1 \text{ hour} = 60 \text{ minutes} \times 60 \text{ seconds/minute} = 3600 \text{ s}\)

3. Now, substitute these values into the expression for 1 kilowatt-hour:

   \(1 \text{ kWh} = 1 \text{ kW} \times 1 \text{ hour}\)

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

4. Perform the multiplication:

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

   \(1 \text{ kWh} = 3,600,000 \text{ W⋅s}\)

5. Since one watt-second is equal to one joule (\(1 \text{ W⋅s} = 1 \text{ J}\)), we have:

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

6. Expressing this in scientific notation:

   \(3,600,000 \text{ J} = 3.6 \times 10^{6} \text{ J}\)

   This can also be written as:

   \(3.6 \times 10^{6} \text{ J} = 36 \times 10^{5} \text{ J}\)

So, one kilowatt-hour is equal to \(36 \times 10^{5}\) joules.

Comparing with the Options

Let's look at the given options:

1. \(36 \times 10^{3}\) joules = 36,000 joules
2. \(36 \times 10^{5}\) joules = 3,600,000 joules
3. \(10^{3}\) joules = 1,000 joules
4. \(10^{5}\) joules = 100,000 joules

Our calculated value, 3,600,000 joules, matches the second option, \(36 \times 10^{5}\) joules.

Revision Table: Energy Units

Additional Information on Energy and Power

Energy is the capacity to do work or produce heat. It exists in many forms, such as kinetic energy (energy of motion), potential energy (stored energy), thermal energy, electrical energy, and chemical energy. The joule is the fundamental SI unit for all forms of energy.

Power is the rate at which energy is transferred or converted. It tells us how quickly work is done or energy is used. The SI unit of power is the watt (W), which is equal to one joule per second (J/s). So, if a device has a power rating of 100 W, it uses 100 joules of energy every second.

The kilowatt-hour (kWh) is a practical unit of energy, especially for measuring electrical energy consumption. Billing for household electricity is typically done in kilowatt-hours because the numbers are more manageable than using joules (which would be very large numbers). For example, a 100 W light bulb left on for 10 hours uses energy equal to \(100 \text{ W} \times 10 \text{ hours} = 0.1 \text{ kW} \times 10 \text{ hours} = 1 \text{ kWh}\). In joules, this would be \(1 \text{ kWh} = 3.6 \times 10^6 \text{ J}\).