You are studying for the first
You are studying for the first physics exam and forget to watchthe time. The next morning you ignore your alarm clock until yourealize you will not reach the bus unless you run as fast as youcan to the bus station in 15min. Carrying your school books duringthe run results in a total energy use of 1200W. You start sweating,which is the way your body keeps you cool.
a. Assume a typical efficiency how much would your bodytemperature rise during the 15min if you had no way of getting ridof your excess thermal energy?
b. Assume that the only way that your body cools itself isevaporation of sweat. To keep your body temperature the same, howmuch water do you have to evaporate during the 15 min of running?How much water do you need to drink not to get dehydrated? The heatof vaporization of sweat from skin is slightly higher than thevalue for water. Use the value given value in your text book. (Heatof vaporization given in the text book is 22.6 x10^5 J/Kg)
c. What would be the outside temperature that you need to run inso you would radiate away the excess energy assuming that you wouldlose all extra heat through radiation, and your body temperaturewould be kept constant at 37ºC. Is this reasonable?
d. At what body temperature would you radiate away the excessenergy assuming that you would lose all the extra heat throughradiation.
Efficiency of human body is about 25%. So 75% of the totalinternal energy goes away as heat.
In 15 minutes total energy expenditure = 15*60s*1500W =1.35*106 J.
So thermal energy = 1.35*0.75*106 J =1.012*106 J. This comes off as heat.
Total amount of water evaporated =
This much water is needed to be drank to keep the bodyhydrated.
Most of our body heat radiates through our head which has anaverage area of 0.4m2 and average coefficient of heattransfer = 7W/m2K
based on these values Newton’s law of cooling is applicable inthis situation, which is,
So the temperature difference must be 562.6oC below37oC-273oC is the lowest possible temperature in thisuniverse. Clearly Radiation is not the possible way to make thingspossible.
The minimum possible temperature difference is562.6oC or Kelvin
So if the body is at 562.6 K and the environment gets to 0K(Entirely impossible) then all heat should be radiated.
562.6K ~ 290oC ( ! ) should be the bodytemperature.