A student is trying to decide what to wear. His bedroom is at 20.0°C. His skin temperature is 30.0°C. The area of his exposed skin is 1.45 m2. People all over the world have skin that is dark in the infrared, with emissivity about 0.915. Find the net energy loss from his body by radiation in 14.3 min.

Question

Physics

Ellen Meyer

2 February, 10:28

A student is trying to decide what to wear. His bedroom is at 20.0°C. His skin temperature is 30.0°C. The area of his exposed skin is 1.45 m2. People all over the world have skin that is dark in the infrared, with emissivity about 0.915. Find the net energy loss from his body by radiation in 14.3 min.

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Maddison · Answer 1

Stefan's Boltzman Law gives the value of radiation from a black body at a particular temperature. The relation is

E = eσ (T₂⁴ - T₁⁴)

e is emmisivity, σ is a constant = 5.67 x 10⁻⁸, E is energy emitted per unit time per unit area

E =.915 x 5.67 x 10⁻⁸ x (303⁴ - 293⁴)

=.915 x 5.67 x 10⁻⁸ x (84.28 - 73.70) x 10⁸

= 55 W / m²s

Area A = 1.45 m²

time t = 14.3 min

= 858 s

Total radiation

= 55 x 858 x 1.45 W

= 68425 J