One kWh is equal to

Options

A. `3.6 xx 10 ^(6) J`
B. `3.6 xx 10 ^(5)J`
C. `3.6 xx 10 ^(4)J`
D. `3.6 xx 10 ^(3)J`

Answer

To find out how many joules are in one kilowatt-hour (kWh), we can follow these steps:

### Step 1: Understand the definition of kilowatt-hour
1 kilowatt-hour (kWh) is the amount of energy consumed when 1 kilowatt (kW) of power is used for 1 hour.

### Step 2: Convert kilowatts to watts
1 kilowatt is equal to 1000 watts (or \(10^3\) watts).

### Step 3: Calculate energy in joules
Energy in joules can be calculated using the formula:
\[ \text{Energy (in joules)} = \text{Power (in watts)} \times \text{Time (in seconds)} \]

### Step 4: Convert hours to seconds
1 hour is equal to 3600 seconds (since 1 hour = 60 minutes and 1 minute = 60 seconds):
\[ 1 \text{ hour} = 60 \text{ minutes} \times 60 \text{ seconds/minute} = 3600 \text{ seconds} \]

### Step 5: Substitute values into the formula
Now we can substitute the values into the energy formula:
\[ \text{Energy} = 1000 \text{ watts} \times 3600 \text{ seconds} \]

### Step 6: Calculate the result
Now, calculate the multiplication:
\[ \text{Energy} = 1000 \times 3600 = 3,600,000 \text{ joules} \]
This can also be expressed in scientific notation:
\[ 3,600,000 \text{ joules} = 3.6 \times 10^6 \text{ joules} \]

### Conclusion
Thus, 1 kWh is equal to \(3.6 \times 10^6\) joules.