Which consumes more energy, a \(1.2-\mathrm{kW}\) hair dryer used for 10 min or a \(7-\) W night-light left on for 24 h?

Understanding how to calculate energy consumption is crucial for determining which devices use more power and can help manage electricity costs. The formula for calculating energy consumption is actually quite simple, yet it forms the basis of our understanding of energy usage. Energy (\textbf{E}), measured in joules (J), kilowatt-hours (kWh), or other energy units, is equal to Power (\textbf{P}), measured in watts (W) or kilowatts (kW), multiplied by Time (\textbf{t}), usually in hours (h). Mathematically, it is expressed as: \[E = P \times t\]For example, to calculate the energy consumption of a device, you need to know the device's power rating and how long it has been in operation. With this information, you can easily compute how much energy the device consumes over a certain period.

To better grasp power to energy conversion, imagine power as the rate at which energy is used or produced. The watt is the unit of power in the International System of Units and one watt is equivalent to one joule per second. When converting power to energy, you're essentially determining how much energy is used over a period of time at a certain rate of consumption or production. To carry out this conversion, you multiply the power rating of an appliance (in watts) by the time (in hours) it has been operating. If the power is given in kilowatts, remember to convert it to watts by multiplying by 1,000 before using it in your calculations. \
\For instance, in the exercise provided, the hair dryer's power is noted as 1.2 kW, or 1,200 W, and it is used for \(\frac{10}{60}\) hours, equating to 0.2 hours. Finding the energy consumption then involves multiplying 1,200 W by 0.2 hours, revealing the total energy consumed by the hair dryer over that duration.

When comparing energy usage between devices, it's essential to convert both to the same units of energy for an accurate comparison. Once you have the energy consumed by each device, you can directly compare the figures. In contexts like our exercise, this allows us to make informed decisions about our energy consumption habits, potentially leading to energy conservation.
Let's take the detailed step-by-step solution as an example. After calculating the energy consumption for each device using the energy consumption formula, we compare the two results. The hair dryer, though used for a shorter period, has a much higher power rating, resulting in higher total energy used compared to the night-light left on for 24 hours. Summarizing the calculations provides a clear understanding of which device consumes more energy, empowering students and individuals to analyze and optimize their energy usage effectively.