A person is standing outdoors in the shade where the temperature is 35 °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 140 cm2 and its emissivity is 0.89.

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 0.65?

(a) Eₐ = 6.36 J/s

(b) Eₐ = 4.64 J/s

Explanation:

Stefan-Boltzmann law: States that the total energy per second radiated or absorbed by a black body is directly proportional to the absolute temperature.

Using, Stefan-Boltzmann equation

Eₐ = eσAT⁴ ... Equation 1

where Eₐ = Radiant energy absorbed per seconds, e = emissivity, σ = stefan - boltzman constant, A = Surface area. and T = temperature in kelvin

(a) Where e = 0.89, σ = 5.67 * 10⁻⁸ watt/m²/K⁴, A = 140 cm² = 140 cm² (m²/10000cm²) = 0.014 m², T = 35 °C = (35 + 273) K = 308 K.

Applying these values in equation 1 above,

Eₐ = 0.89 * 5.67 * 10⁻⁸ * 0.014 * (308) ⁴

Eₐ = 6.36 J/s

(b) when e = 0.65,

∴ Eₐ = 0.65 * 5.67 * 10⁻⁸ * 0.014 * (308) ⁴

Eₐ = 4.64 J/s