Question

As a rough approximation, the human body may be considered to be a cylinder of length l=2.0m and circumference c=0.8m . (to simplify things, ignore the circular top and bottom of the cylinder, and just consider the cylindrical sides.) if the emissivity of skin is taken to be e=0.6 , and the surface temperature is taken to be t= 30 ∘ c , how much thermal power p does the human body radiate?

Answer 1

458.826 watts

Step-by-step explanation:

According to Stefan-Boltzmann's Law, thermal energy emitted by a black body per second per unit area is directly proportional to the fourth power of the absolute temperature and is given by;

`(P)/(A)` = σ
`eT^(4)`

P = ?

A = l x c = 2 x 0.8 =
`1.6m^(2)`

(Please ignore Armstrong symbol, I don't know how it appeared using the equation tool)

σ =
`5.6703 X 10^(-8)  watt/m^(2) K^(4)`

e = 0.6

T =
`30^(o) C` = 303 K

P = σeTA

P =
`5.6703 X 10^(-8)` x 0.6 x
`303^(4)` x 1.6

P = 458.826 watts

Answer 2

e= 0.6
Constant sigma is 5.6704004× 10∧ (-8)
The area is LC = 2× .8 = 1.6m∧2
to convert degrees celcious to Kelvin =303K
The equation is
P = e ? AT∧4.
Then the answer is 460 watts.