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Calculate the Net Heat Transfer of a Person: Heat Transfer by Radiation · Physics Playground

Exercises Heat and thermodynamics

Example 14.9 from College Physics, 14.7 Radiation

Calculate the Net Heat Transfer of a Person: Heat Transfer by Radiation

What is the rate of heat transfer by radiation, with an unclothed person standing in a dark room whose ambient temperature is $22 . 0º C$ . The person has a normal skin temperature of $33 . 0º C$ and a surface area of $1.50 m^{2}$ . The emissivity of skin is 0.97 in the infrared, where the radiation takes place.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
We can solve this by using the equation for the rate of radiative heat transfer.
Solution
Insert the temperatures values $T_{2} = 295 K$ and $T_{1} = 306 K$ , so that
$\frac{Q}{t} = σ eA(T_{2}^{4} - T_{1}^{4})$
14.45

$= (5 . 67 \times 10^{- 8} J/s \cdot m^{2} \cdot K^{4}) (0.97) (1.50 m^{2}) [{(295 K)}^{4} - {(306 K)}^{4}]$
14.46

$= - 99 J/s = - 99 W.$
14.47
Discussion
This value is a significant rate of heat transfer to the environment (note the minus sign), considering that a person at rest may produce energy at the rate of 125 W and that conduction and convection will also be transferring energy to the environment. Indeed, we would probably expect this person to feel cold. Clothing significantly reduces heat transfer to the environment by many methods, because clothing slows down both conduction and convection, and has a lower emissivity (especially if it is white) than skin.

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From College Physics (1st edition) by OpenStax (Rice University), section 14.7, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.

Strategy

Solution

Discussion