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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 1.38 m2, which has a temperature of 34°C and an emissivity of 0.700. Suppose that metabolic processes are producing energy at a rate of 103 J/s. What is the temperature of the coldest room in which this person could stand and not experience a drop in body temperature?

Answer 1

Heat radiated per second = e σ A T^4

e = emissivity (.700)
σ = Stefan-Boltzmann constant
= 5.67 x 10-8 J/(s m^2 K^4)
A = surface area of object ( 1.38 m^2 )
T = Kelvin temperature

The person will emit radiation at a rate proportional to skin temperature^4, and will absorb radiation at a rate proportional to room temperature^4. Set the net loss equal to the metabolic rate of the person and solve for room temperature.