A watt is a measure of power (the rate of energy change) equal to 1 J/s. (b) An adult person radiates heat to the surroundings at about the same rate as a 100-watt electric incandescent light bulb. What is the total amount of energy in kcal radiated to the surroundings by an adult over a 24 h period?

Verified step by step guidance

1. Understand that power is the rate of energy transfer, and 1 watt is equal to 1 joule per second (1 W = 1 J/s).
2. Calculate the total energy in joules radiated by the person over 24 hours. Since the person radiates energy at a rate of 100 watts, multiply 100 J/s by the total number of seconds in 24 hours (24 hours * 60 minutes/hour * 60 seconds/minute).
3. Convert the total energy from joules to kilocalories. Use the conversion factor: 1 kcal = 4184 J.
4. Perform the conversion by dividing the total energy in joules by 4184 J/kcal to find the energy in kilocalories.
5. Summarize the process: You have calculated the total energy radiated by an adult over 24 hours in kilocalories by first finding the energy in joules and then converting it to kilocalories.

Key Concepts

Power and Energy Conversion

Power is defined as the rate at which energy is transferred or converted, measured in watts (W), where 1 W equals 1 joule per second (J/s). To find the total energy produced over time, one can multiply power by time. In this case, the energy radiated by the adult can be calculated by converting the power output (100 W) into energy over a 24-hour period.

Time Conversion

To calculate energy over a specific time frame, it is essential to convert the time into seconds, as power is measured in joules per second. For 24 hours, this conversion involves multiplying 24 hours by 3600 seconds per hour, resulting in a total of 86,400 seconds. This total time will be used in the energy calculation.

Energy Units and Conversion to kcal

Energy can be expressed in various units, including joules (J) and kilocalories (kcal). To convert joules to kilocalories, one must use the conversion factor where 1 kcal equals 4184 J. After calculating the total energy in joules, dividing by 4184 will yield the equivalent energy in kilocalories, which is a more common unit for measuring energy in biological contexts.