Consult Multiple-Concept Example 8 to see the concepts that are pertinent here.

Question

Consult Multiple-Concept Example 8 to see the concepts that are pertinent here. 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 1.27 m2, which has a temperature of 34 °C and an emissivity of 0.642. Suppose that metabolic processes are producing energy at a rate of 111 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?

Explanation / Answer

Using Stefan-Boltzmann's law:

Power will be given by:

P = e*sigma*A*(T^4 - T0^4)

Given that

e = emmissivity = 0.642

sigma = Stefan's Coefficient = 5.67*10^-8

A = Surface area = 1.27 m^2

Power = P = 111 J/sec

T = Temperature of radiator = 34 C = 273 + 34 = 307 K

Tc = Temperature of Room = ?

Using these values

111 = 0.642*5.67*10^-8*1.27*(307^4 - Tc^4)

Tc^4 = 307^4 - 111/(0.642*5.67*10^-8*1.27)

Tc = [307^4 - 111/(0.642*5.67*10^-8*1.27)]^(1/4)

Tc = 283.74 K

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