In this problem you will consider the balance of thermal energy radiated and absorbed by a person.

Assume that the person is wearing only a skimpy bathing suit of negligible area. As a rough approximation, the area of a human body may be considered to be that of the sides of a cylinder of length L=2.0m and circumference C=0.8m.

For the Stefan-Boltzmann constant use σ=5.67×10−8W/m2/K4.

Part A

If the surface temperature of the skin is taken to be Tbody=30∘C, how much thermal power Prb does the body described in the introduction radiate?

Take the emissivity to be e=0.6.

Express the power radiated into the room by the body numerically, rounded to the nearest 10 W.

Prb =
460

W

Part B

The basal metabolism of a human adult is the total rate of energy production when a person is not performing significant physical activity. It has a value around 125 W, most of which is lost by heat conduction to the surrounding air and especially to the exhaled air that was warmed while inside the lungs. Given this energy production rate, it would seem impossible for a human body to radiate 460 W as you calculated in the previous part.

Which of the following alternatives seems to best explain this conundrum?

The human body is quite reflective in the infrared part of the spectrum (where it radiates) so e is in fact less than 0.1.
The surrounding room is near the temperature of the body and radiates nearly the same power into the body.
Part C

Now calculate Pbr, the thermal power absorbed by the person from the thermal radiation field in the room, which is assumed to be at Troom=20∘C. If you do not understand the role played by the emissivities of room and person, be sure to open the hint on that topic.

Express the thermal power numerically, giving your answer to the nearest 10 W.

Part D

Find Pnet, the net power radiated by the person when in a room with temperature Troom=20∘C.

Express the net radiated power numerically, to the nearest 10 W.