A person\'s body is producing energy internally due to metabolic processes. If t

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 1.58 m2, which has a temperature of 34 °C and an emissivity of 0.702. Suppose that metabolic processes are producing energy at a rate of 145 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?

Please show Equations and explain actions if possible. Thank you so much.

Explanation / Answer

given surfae area of body, A = 1.58 m^2
body temperature, Tb = 34 C = 307.16 K
emmisivity, e = 0.702
rate of energy production r = 145 J/s
temperature of the coldest room where the person will not experience temperature drop = T
hence
from thermal equilibrium
heat radiated by body ( from stefan's law) into room of temperature T is sigma*A*e*(Tb^4 - T^4)
hence
sigma*A*e*(Tb^4 - T^4) = 145
5.67*10^-8*1.58*0.702*(307.16^4 - T^4) = 145
T = 284.9813 K = 11.82 C
hence the coldest room temperature at which the body does not experience temperature drop is at 11.82 C

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