Question

A watt is a measure of power (the rate of energy change) equal to \(1 \mathrm{~J} / \mathrm{s}\). (a) Calculate the number of joules in a kilowatthour. (b) An adult person radiates heat to the surroundings at about the same rate as a 100-watt electric incandescent lightbulb. What is the total amount of energy in kcal radiated to the surroundings by an adult in \(24 \mathrm{~h}\) ?

Short answer

In short, (a) 1 kilowatthour (kWh) is equal to 3600000 Joules, and (b) the total amount of energy in kcal radiated to the surroundings by an adult in 24 hours is approximately 2062.29 kcal.

Step-by-step solution

(a) Calculating Joules in a Kilowatthour (kWh)

: First, we need to find the number of joules in a kilowatthour (kWh). Since we know 1 watt is equal to \(\frac{1 \mathrm{J}}{1 \mathrm{s}}\), we can convert kilowatthour to joules using the following steps: 1 kWh = 1000 Wh (as 1 kilowatt = 1000 watts) Now, we know that 1 Wh = 3600 J, so: 1 kWh = 1000 Wh * 3600 J/Wh = 3600000 J Therefore, 1 kilowatthour (kWh) is equal to 3600000 Joules.

(b) Calculating Energy Radiated by an Adult in 24 hours in kcal

: Given that an adult person radiates heat at the same rate as a 100-watt electric incandescent lightbulb, we first need to find out the total energy radiated in Joules during 24 hours. Energy radiated by the adult per second = 100 J/s Total time = 24 hours = 24 * 3600 seconds Therefore, Energy radiated by an adult person in 24 hours (in Joules) = 100 J/s * 24 * 3600 s = 8640000 J Now, we need to convert the above energy value from Joules to kilocalories (kcal) using the conversion factor: \((1 \mathrm{J} = 0.000239006 \mathrm{kcal})\) Energy radiated by an adult person in 24 hours (in kcal) = 8640000 J * 0.000239006 kcal/J = 2062.29 kcal Hence, the total amount of energy in kcal radiated to the surroundings by an adult in 24 hours is approximately 2062.29 kcal.

Key concepts

Joules to Kilowatt-Hours

When we talk about energy conversion, it's vital to understand how different units relate to each other. One common conversion is from joules to kilowatt-hours (kWh). Joules (J) are the SI unit of energy and measure the work done by a force. Kilowatt-hours, on the other hand, are often used by electrical companies to bill energy usage.
To convert from joules to kilowatt-hours, follow these simple steps:

• Start by knowing that 1 watt equals 1 joule/second.
• Then, remember that a kilowatt is 1000 watts.
  This turns into 1 kWh being 1000 watts over an hour.
• Since one hour is 3600 seconds, 1 kWh equals 1000 watts times 3600 seconds.
• This results in 1 kWh equaling 3,600,000 joules.
  This unit conversion is pivotal in understanding how much energy machines consume or save.

Radiant Energy

Radiant energy refers to energy that travels by waves or particles, particularly electromagnetic radiation like light or heat. Every living being emits some amount of radiant energy, even in complete darkness.
In this case, an adult person radiates energy similar to a 100-watt incandescent light bulb. Here’s a bit more detail:

• The human body constantly transforms chemical energy from food into kinetic energy and thermal energy.
• Through processes such as metabolism, a significant amount of heat is released as radiant energy.
• Taking the example of a 100-watt bulb, the human body emits energy equivalent to 100 joules per second.

This radiant energy is vital for various physical processes and helps maintain our body temperature.

Heat Transfer

Heat transfer is the process of energy moving from a hotter object to a cooler one until they reach equilibrium. This is a natural process that happens in various ways: conduction, convection, and radiation.
Conduction occurs in solids when vibrating atoms transfer their energy to neighboring particles. For example, when you touch a hot surface, heat is conducted to your skin, causing it to feel hot.

• Convection happens in fluids, including air and water, where moving particles carry heat with them.
• Lastly, radiation allows heat transfer through electromagnetic waves, independent of a medium.
  Understanding how heat transfer works helps us comprehend devices like heaters, refrigerators, and even the human body's thermoregulation.
  For instance, an adult's radiated heat is indicative of the radiant heat transfer principle.

Kilocalories

Kilocalories, often seen as kcal, measure energy and are commonly used in contexts involving food and nutrition. A kilocalorie equals 1000 calories and represents the energy needed to raise the temperature of 1 kilogram of water by 1°C.
When considering the energy radiated by a person, converting from joules to kilocalories might be necessary:

• Start by using the conversion factor where 1 joule equals approximately 0.000239 kilocalories.
• For example, if a person radiates 8,640,000 joules in 24 hours, you multiply by the conversion factor to find 2062.29 kilocalories.
  This conversion is crucial for better comparing energy expenditures in terms humans relate to, like dietary energy consumption.

Power Measurement

Power is the rate at which energy is transferred or converted, and it signifies how quickly work is done. The unit of power is the watt, defined as one joule per second. In practical terms, power can be related to tangible actions, like how fast an appliance can heat a room.
When measuring power, keeping these points in mind helps:

• Power displays work fast; for instance, a 100-watt lightbulb uses 100 joules every second.
• In everyday life, devices with higher wattage often perform tasks more quickly.
  For example, a 1500-watt heater warms a room faster than a 500-watt heater because it transforms energy more swiftly.

Ultimately, understanding power measurement allows you to make informed decisions about energy use and efficiency in real-world applications.