What is the net amount of heat this person could radiate per second into a room at 18.0 ∘C (about 64.4 ∘F) if his skin's surface temperature is 30.0 ∘C? (At such temperatures, nearly all the heat is infrared radiation, for which the body's emissivity is 1.0, regardless of the amount of pigment.)

Question

Chemistry

Alexander Salas

17 March, 16:25

What is the net amount of heat this person could radiate per second into a room at 18.0 ∘C (about 64.4 ∘F) if his skin's surface temperature is 30.0 ∘C? (At such temperatures, nearly all the heat is infrared radiation, for which the body's emissivity is 1.0, regardless of the amount of pigment.)

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Wallace · Answer 1

142.6 joules is the amount of heat that a person could radiate per second

Explanation:

To solve this, we have to apply Stephan-Boltzmann's law:

Q/ΔT = σ. ε. A. (Te⁴ - Ta⁴) where

σ = Boltzmann's constant → 5.67*10⁻⁸ W/m². K⁴

ε = Body's emissivity, in this case = 1

Α = Surface, we assume a value of 2m²

Te = Temperature of the body's surface, in this case 30°C

Ta = Temperature of the room, where the body is. In this case, 18°C

Notice that T° must be Absolute T° → T°C + 273

18°C + 273 = 291K

30°C + 273 = 303K. Let's replace dа ta:

Q/s = 5.67*10⁻⁸ W/m². K⁴. 1. 2m² (303⁴K - 291⁴K)

Q/s = 5.67*10⁻⁸ W/m². K⁴. 1. 2m². 1.26*10⁻⁹K⁴

Q/s = 142.6 W

1 W = Joules/s