If the surface temperature of the skin is taken to be T body=30C , how much ther

Question

If the surface temperature of the skin is taken to be Tbody=30C , 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.

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 =5.67×108W/m2/K4

Explanation / Answer

P=eA(T^4)
Where e and are as you stated
P is the power in watts
T is the temperature in Kelvin (add 273 to the 30 to convert to Kelvin.)
A is the surface area in metres. If the circumference of the cyclinder is 0.8m and C=(2pi*radius), then radius=(0.8/2pi)=0.1274m. The equation for the surface area of a cylinder is A=2pi*r^2+2pi*r*L(where r is the radius and h is the height (i.e. 2m))=2*3.14*0.1274^2 +2*3.14*0.1274*2 = 1.7021 m^2
P=eA(T^4)=0.6*5.67×108*1.7021*303^4=488.08 W

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