The emissivity of the human skin is 97.0 percent. Use 35.0 °C for the skin tempe

Question

The emissivity of the human skin is 97.0 percent. Use 35.0 °C for the skin temperature and approximate the human body by a rectangular block with a height of 1.79 m, a width of 34.0 cm and a length of 25.0 cm.

Calculate the power emitted by the human body.

What is the wavelength of the peak in the spectral distribution for this temperature?

Fortunately our environment radiates too. The human body absorbs this radiation with an absorbance of 97.0 percent, so we don't lose our internal energy so quickly. How much power do we absorb when we are in a room where the temperature is 23.5 °C?

How much energy does our body lose in one second?

Explanation / Answer

Given: emmissivity e = asorptivity = 0.97 ; Temperature of body Tb = 35 + 273.15 = 308.15 K

Temperature of surrounding (Ts) = 23.5 + 273.15 = 296.65 K ; dimension of the body: 1.79 m x 0.34 m x 0.25 m

Area of body (A) = 2*(1.79*0.34 + 1.79*0.25 + 0.25*0.34) = 1.1411 m2

(A) Using Stefan-Boltzman Law Power emitted by body (Pe) = *e*A*Tb^4 = 5.6704*10-8*0.97*1.1411*(308.15)4

Hence Pe = 565.92 J/s

(B) By applying Wein's displacement law:

Peak Wavelength (max) = b/Tb = 2.8977*10-3/308.15 = 9403.5 nm

(C) Power absorbed by body (Pa) = *e*A*Ts^4 = 5.6704*10-8*0.97*1.1411*(296.65)4 = 486.05 J/s

(D) Energy lost in one second = (Pe - Pa)*1 = 565.92 - 486.05 = 79.87 J

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