Consider a naked human body, with a surface area of 1.5 m^2 and an average temperature of 30° C (skin temperature), that stands at the middle of an empty breezy room whose surfaces have a temperature of 10° C.
Assuming the human body as a blackbody (5% error), compute the net rate of heat loss of this person by radiation in watts.
(i) P = dE/dt = ε σ A T^4
(ii) P = dE/dt = ε σ A ( T^4 - (T_(surrounding environment)^4 )
The Attempt at a Solution
To actually answer the question of the problem, I'm pretty sure that it just wants me to do as follows.:
P = dE/dt = ε σ A ( T^4 - (T_(surrounding environment)^4 )
P = (1) (5.67E-8) (1.5) (303.15^4 - 283.15^4)
P = 171.6086089452735 W.
Having said that, since the surrounding environment is a non-vacuum (meaning that it is a set of stuff that can and do emit radiation), should the equation instead be
P = ε_human σ A_human (T_human)^4 - ε_human σ A_human (T_walls)^4
(the double A_human is not a typo)
P = ε_human σ A_human (T_human)^4 - ε_walls σ A_human (T_walls)^4
P = σ A_human [ε_human (T_human)^4 - ε_walls (T_walls)^4], such that
P = σ A_human [ε_human (T_human)^4 - ε_walls (T_walls)^4] = σ A_human ε [(T_human)^4 - (T_walls)^4] only if ε_human = ε_walls?
Any input would be GREATLY appreciated!