Question

You are studying for the first physics exam and forget to watch the time. The next morning you ignore your alarm clock until you realize you will not reach the bus unless you run as fast as you can to the bus station in 15min. Carrying your school books during the 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 body temperature rise during the 15min if you had no way of getting rid of your excess thermal energy?

b. Assume that the only way that your body cools itself is evaporation of sweat. To keep your body temperature the same, how much 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 heat of vaporization of sweat from skin is slightly higher than the value for water. Use the value given value in your text book. (Heat of 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 in so you would radiate away the excess energy assuming that you would lose all extra heat through radiation, and your body temperature would be kept constant at 37ºC. Is this reasonable?

d. At what body temperature would you radiate away the excess energy assuming that you would lose all the extra heat through radiation.

Answer 1

A)

Efficiency of human body is about 25%. So 75% of the total internal 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.

B)

Total amount of water evaporated =

This much water is needed to be drank to keep the body hydrated.

C)

Most of our body heat radiates through our head which has an average area of 0.4m² and average coefficient of heat transfer = 7W/m²K

based on these values Newton's law of cooling is applicable in this situation, which is,

So the temperature difference must be 562.6^oC below 37^oC
-273^oC is the lowest possible temperature in this universe. Clearly Radiation is not the possible way to make things possible.

D)

The minimum possible temperature difference is 562.6^oC 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 ~ 290^oC ( ! ) should be the body temperature.