Question

A person's body is producing energy internally due to metabolic processes. If the body loses more energy than metabolic processes are generating, its temperature will drop. If the drop is severe, it can be life-threatening. Suppose a person is unclothed and energy is being lost via radiation from a body surface area of 1.24 m2, which has a temperature of 34 °C and an emissivity of 0.582. Suppose that metabolic processes are producing energy at a rate of 105 J/s. What is the temperature in kelvins of the coldest room in which this person could stand and not experience a drop in body temperature?

Answer 1

Use this equation called the Stefan-Boltzmann Law:

P = eA(stefan's constant)(T^4 - Tc^4)

in which...

P = power in units of joules per second

e = emissivity

A = surface area

stefan's constant = 5.6703 x 10^-8 in units of watts/(meters^2 x Kelvins^4)

T = temperature of radiator in Kelvin

Tc = temperature of surroundings in Kelvin

The power generated by the body must be equal to the energy lost due to the heat of the surroundings if the temperature of the body is to remain constant. Therefore...

105 W = (0.582)(1.24 m^2)(5.6703 x 10^-8 W/(m^2 x K^4))(307 K^4-Tc^4)

Tc = 281.92 K = 8.92 °C