Image 1 Caption: A cartoon explicating the Stefan-Boltzmann law in brief. For a more detailed explication, see below.
Features:
The logarithmic Stefan-Boltzmann law is
Table: Blackbody Radiators.
Blackbody Radiator T F Comment
(K) (W/m**2)
CMB-like 2.7260 3.131*10**(-6) The CMB has a blackbody spectrum, but there is
no radiating surface in the modern observable
universe.
Human-body-like 310 5.237*10**2 But the human body does NOT radiate this much
(see the note below).
lose energy at rate F.
Sun-like 5772 6.294*10**7 The Sun does almost radiate like this at the
effective temperature T = 5772 K.
Keywords:
basal metabolic rate (BMR),
basal metabolic rate average ≅ 73 W,
blackbody radiator,
cosmic microwave background (CMB),
effective temperature,
effective temperature of the Sun,
flux,
heat energy,
human body,
human body temperature,
Kelvin temperature scale,
Stefan-Boltzmann constant,
Stefan-Boltzmann law F = σT**4,
Sun,
temperature,
watts.
A human body approximated as a cylinder has surface area ∼ h*2πr ≅ 1.5*6*0.2 ≅ 2 m**2. Thus, according to the above table if it radiated like a blackbody radiator, it should radiate ∼ 1000 W. But the human body is surrounded by an ambient medium at typically ∼ 300 K and the radiation field and heat conduction from the ambient medium is sufficient to transfer heat to the human body to maintain a temperature ∼ 300 K. Upshot is that the human body radiates a DILUTED blackbody radiation field: it has approximately a blackbody spectrum shape for temperature ∼310 K, but has much less radiant flux than a blackbody radiation field of ∼310 K. So the human body does NOT lose heat energy at rate of ∼ 1000 W.
Actually, sunlight we receive on Earth is also a DILUTED blackbody radiation field: it has the shape of a blackbody radiation field of temperature ∼5800 K, but much less radiant flux than a blackbody radiation field of ∼5800 K.
But how much radiant flux does the human body radiate? The basal metabolic rate (BMR) for humans is the minimal rate of energy generation in and therefore the minimal heat energy loss from the human body. The energy generation comes from food energy (i.e., the chemical energy of food). The basal metabolic rate average ≅ 73 W is obviously much less than the flux from the human-body-like blackbody radiator in the above Table: Blackbody Radiators.
For some information from 2019 on the human body metabolic rate, see BBC: Ultimate limit of human endurance found, 2019, Thurber et al. (2019), and references therein.