What is the approximate energy emitted as blackbody radiation by a human being each second? What is the blackbody energy absorbed by a person in 1 s in a room? Why are the answers different?
To calculate the approximate energy emitted as blackbody radiation by a human being each second, we can use the Stefan-Boltzmann law. This law states that the total power (energy per unit time) radiated by a blackbody is proportional to the fourth power of its temperature (in Kelvin). The formula is:
P = σ * A * T^4
Where:
P is the power (energy per unit time) radiated,
σ is the Stefan-Boltzmann constant (approximately 5.67 x 10^-8 W m^-2 K^-4),
A is the surface area of the blackbody, and
T is the temperature in Kelvin.
For a human being, let's assume a typical body temperature of 37°C, which is approximately 310 K. The surface area of an average human body can be estimated to 1.8 m^2.
Plugging these values into the formula, we get:
P = 5.67 x 10^-8 * 1.8 * 310^4
≈ 399.6 watts (W)
Therefore, the approximate energy emitted as blackbody radiation by a human being each second is approximately 400 watts.
Now let's consider the blackbody energy absorbed by a person in 1 second in a room. This depends on various factors such as the temperature of the room and the emissivity of the person's skin.
In a typical room, the temperature is usually around 20-25°C, which can be converted to Kelvin (293-298 K). Assuming the person's skin has an emissivity of 0.98 (since human skin is a good emitter and absorber of thermal radiation), we can use the following formula to calculate the energy absorbed:
P_absorbed = ε * σ * A * T_room^4
Where ε is the emissivity (0.98), σ is the Stefan-Boltzmann constant, A is the surface area of the person, and T_room is the room temperature.
Using the same surface area as before (1.8 m^2), plugging in the values, and considering the average room temperature of 298 K, we get:
P_absorbed = 0.98 * 5.67 x 10^-8 * 1.8 * 298^4
≈ 370.5 watts (W)
Therefore, the blackbody energy absorbed by a person in 1 second in a room is approximately 370.5 watts.
The reason these two values (energy emitted and energy absorbed) are different is because they are based on different temperatures and calculations. The energy emitted is based on the body temperature of the human being, whereas the energy absorbed takes into account the temperature of the room and the emissivity of the person's skin. The absorption and emission of blackbody radiation depend on the temperature difference between the object and its surroundings, as well as the properties of the object's surface.