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If the body's surface temperature is 36 ∘C , what is the net rate of heat loss on a chilly 4 ∘C day? All skin, regardless of color, is effectively black in the infrared where the radiation occurs, so use an emissivity of 0.95. Radiation from the head is a major source of heat loss from the human body. Model a head as a 20-cm-diameter, 20-cm-tall cylinder with a flat top.

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Answer:

27.36516 W

Explanation:

[tex]\sigma[/tex] = Stefan-Boltzmann constant = [tex]5.67\times 10^{-8}\ W/m^2K^4[/tex]

[tex]\epsilon[/tex] = Emissivity = 0.95

[tex]T_h[/tex] = Hot body temperature = 36°C

[tex]T_c[/tex] = Cold body temperature = 4°C

d = Diameter = 20 cm

r = Radius = [tex]\frac{d}{2}=\frac{20}{2}=10\ cm[/tex]

h = Height = 20 cm

Area is given by

[tex]A=\pi r^2+2\pi rh[/tex]

The formula for net radiation heat loss is

[tex]q=\epsilon \sigma (T_h^4-T_c^4)A\\\Rightarrow q=\epsilon \sigma (T_h^4-T_c^4)\times (\pi r^2+2\pi rh)\\\Rightarrow q=0.95\times 5.67\times 10^{-8}\times (309.15^4-277.15^4)\times (\pi 0.1^2+2\pi 0.1\times 0.2)\\\Rightarrow q=27.36516\ W[/tex]

The radiation from the head is a major source of heat loss from the human body is 27.36516 W

Lanuel

The net rate of heat loss on a chilly 4°C day is equal to 27.37 Watts.

Given the following data:

  • Emissivity = 0.95
  • Hot body temperature = 36°C to K = 273.15 + 36 = 309.15 K.
  • Cold body temperature = 4°C to K = 273.15 + 4 = 277.15 K.
  • Height = 20 cm to m = 0.2 m.
  • Diameter = 20 cm
  • Radius = diameter/2 = 20/2 = 10 cm to m = 0.1 m.

Scientific data:

Stefan-Boltzmann constant = 5.67 × 10⁻⁸ W/m²K⁴

How to calculate the net rate of heat loss?

Mathematically, the net rate of heat loss is calculated by using this formula:

q = εσ(Th⁴ - Tc⁴)A = εσ(Th⁴ - Tc⁴)(πr² + 2πrh)

Substituting the given parameters into the formula, we have;

q = 0.95 × 5.67 × 10⁻⁸(309.15⁴ - 277.15⁴)(3.142 × 0.1² + 2 × 3.142 × 0.1 × 0.2)

q = 27.37 Watts.

Read more on rate of heat loss here: https://brainly.com/question/17199050

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