Question

A person is standing outdoors in the shade where the temperature is 17 degree C. (a) What is the radiant energy absorbed per second by his head when it is covered with hair? The surface area of the hair (assumed to be flat) is 200 cm^2 and its emissivity is 0.83. (b) What would be the radiant energy absorbed per second by the same person if he were bald and the emissivity of his head were 0.53?

Answer 1

The emissivity equals the absorptivity. If this is not clear, think of a perfectly matt black surface, emissivity =1. When it is in equilibrium with its surroundings the amount of energy radiated per second must equal the amount of energy absorbed per second. A black surface is good emitter AND a good absorber. Absorptivity is NOT (1- emissivity), emissivity = absorptivity.

200cm² = 200x10⁻⁴m²
17⁰C = 290K
____________________
a)
P = εAσT⁴ = 0.83 x 200x10⁻⁴ x 5.67x10⁻⁸ x 290⁴ = 6.66 J/s (watts is a better unit though).

b) Repeat the above calculation or save some work by multiplying the above answer by 0.53/0.83
P = 6.66 x (0.53/0.83) = 4.25 J/s