Question

Problem 3 (a) Assuming the human body (skin temperature 34◦C) to behave like an ideal thermal radiator, find the wavelength where the intensity from the body is a maximum. In what region of the electromagnetic spectrum is radiation with this wavelength? (b) Making whatever (reasonable) assumptions you may need, estimate the power radiated by a typical person isolated from the surroundings. (c) Estimate the radiation power absorbed by a person in a room in which the temperature is 20◦C.

Answer 1

Step-by-step explanation:

a )

We shall apply Wein's displacement law

λm x T = b where λm is wavelength of radiation having maximum intensity

T is absolute temperature of body , and b is a constant

b = 2898 μm-K

T = 273 + 34 = 307 K

λm x 307 = 2898

λm = 9.44 μm

= 9440 nm

It is infrared radiation .

b )

We shall apply Stefan's law of radiation.

E = σA T⁴

E is emitted radiation by body acting as black body , A is surface area , T is absolute temperature of body

σ = 5.67 x 10⁻⁸ J / m²T⁴

Surface area of a typical man's body A = 1.9 m²

T = 273 + 34 = 307 K

Assuming human body as black body

E = 5.67 x 10⁻⁸ x 1.9 x 307⁴ J/s

= 9.57 x 10² J/s

= 957 W .

c )

Radiation absorbed

E = 5.67 x 10⁻⁸ x 1.9 x ( 273 + 20 )⁴ J/s

= 794 W .