- Convert the time duration from hours to seconds: \(1\text{ hour} = 3600\text{ seconds}\).
- Use the relation between power, time, and energy: \(\Delta E_{th} = P \times t\).
- Calculate the total energy: \(120\text{ J/s} \times 3600\text{ s} = 432,000\text{ J}\).
- The final result is \(\boxed{432,000} \text{ Joules}\).
Explanation
- Problem Analysis
The fan consumes power at a rate of \(P = 120\text{ W}\). Since one Watt is defined as one Joule per second (\(1\text{ W} = 1\text{ J/s}\)), the fan adds thermal energy to the air at a rate of \(120\text{ Joules}\) per second. The total energy added over a specific duration is given by the product of the power and the time, expressed as \(\Delta E_{th} = P \times t\).
- Conversion of Time Units
To calculate the total thermal energy, we must first express the duration of one hour in seconds. Since there are \(60\) minutes in an hour and \(60\) seconds in a minute, one hour is equivalent to:
\[t = 1\text{ hour} \times 60\text{ minutes/hour} \times 60\text{ seconds/minute} = 3600\text{ seconds}\]
- Calculation of Thermal Energy
Now, we calculate the total energy added to the air by multiplying the power by the time:
\[\Delta E_{th} = 120\text{ J/s} \times 3600\text{ s} = 432,000\text{ Joules}\]
Thus, the fan adds \(432,000\text{ Joules}\) of thermal energy to the room.
- Final Answer
The total thermal energy added to the air by the fan over the course of one hour is \(\boxed{432,000}\) \(\boxed{\text{Joules}}\).
Examples
Understanding the energy consumption and thermal output of household appliances is fundamental in home energy management. For example, knowing that your devices contribute to the overall temperature of your living space can help you optimize your HVAC usage. If you know that your fan adds a specific amount of energy to the room as heat, you can better estimate how much cooling or ventilation is required during the warmer months, making your home more energy-efficient.