A spherical human has a surface area of 2 m^2 and an emissivity of 0.98. Assuming that the humans surface temp is 37 degrees C, how much heat do they lose by radiation to the environment if the ambient temp is -10 degrees Celsius? If a resting human generates 100W of power, how much more power would a person have to generate to stay warm?
Ok so this problem got me because the question states that the final answer should be between 1 and 10 calories per minute, and i have no idea where i went wrong:
Used Q/t = stefanboltzconstant*0.98*2m^2*(263^4 - 310^4)
(I converted Celsius to K)
Ok so that gave me -494.633 J/s. So, I believe that means that 494.633Joules are lost every second by the human. So since 1 cal = 4.1868J, I then divided 494.633 J by that number to get # of cals lost per second. I got, 118 cals are lost per second.
So I then went to assume that since a resting human generates 100Js, or, 23.98895 cals/s (using same conversion from above), then 394.633 Joules need to be generated on TOP of the 100W to stay warm (I assumed if energy created = energy emitted, then the human would be warm, but wasn't so sure on that). So my final answer was 394.633J/s, or 94cals/s, or 5644cals/min need to be created to keep the human warm
However, this is way out of the 1 to 10 cals/min range our teacher gave us. Where did I go wrong here?
Convert to Cal/min.
5644/1000=5.64Ca/min