Question

Consider a standing person in the center of a large room. Approximate the person as a vertical cylinder of 1.8 m tall and 0.4 m diameter. Average surface temperature of the person is 33°C, and the emissivity of skin surface is 0.96. (a) Calculate the radiative heat transfer from this person. Neglect heat loss from the ends of the cylinder (b) What is the wavelength λmax where the maximum amount of energy will be radiated? (c) What region (primarily) of electromagnetic spectrum is the radiation calculated in b? (d) If a detector is available that can detect only in the wavelength range λmax ± 5 μm, what fraction of the total energy from the human being will this detector be sensitive to?

Answer 1

a)

The radiation heat transfer is given by:

where:

σ = Stefan boltzmann constant = 5.67 X 10-8 W / m2.K4

e = emissivity = 0.96

A = surface area of body

To = surrounding temperature = 298 K (room temperature)

T = body temperature = 33 oC = 306 K

The body is considered to be a cylinder.

Surface Area, A = 0.25 X π X d X d X L

Therefore:

A = 0.25 X π X 0.4 X 0.4 X 1.8 = 0.23 m2

Substituting these values in the equation:

Q = 5.67 X 10-8 X 0.96 X 0.23 X (306^4 - 298^4)

Q = 8.815 W

b)

The wavelength λmax where the maximum amount of energy will be radiated is calculated by Wien's Displacement Law:

λmax = 2.898 X 10-3 / T

λmax = 2.898 X 10-3 / 303

λmax = 9.56 X 10-6 m = 9.56 μm

c)

The radiation belongs to the infrared region of the electromagnetic spectrum.

d)

E = hc / λ

If h and c are constant; the fraction of energy is:

ΔE / E = Δλ / λ

We have

Δλ = 5 μm

λ = 9.56 μm

Substituting this in the above equation:

ΔE / E = 5 / 9.56

ΔE / E = 0.52

Fraction of the total energy from the human being will this detector be sensitive = 0.52