Question

You have probably seen people jogging in extremely hot weather and wondered "Why?" As we shall see, there are good reasons not to do this! When jogging strenuously, an average runner of mass 68.0 kg and surface area 1.85 m2 produces energy at a rate of up to 1330 W , 80.0 % of which is converted to heat. The jogger radiates heat, but actually absorbs more from the hot air than he radiates away. At such high levels of activity, the skin's temperature can be elevated to around 33.0 ∘C instead of the usual 30.0 ∘C. (We shall neglect conduction, which would bring even more heat into his body.) The only way for the body to get rid of this extra heat is by evaporating water (sweating).

A: How much heat per second is produced just by the act of jogging? (J/s)

B: How much net heat per second does the runner gain just from radiation if the air temperature is 40.0 ∘C (104 ∘F)? (Remember that he radiates out, but the environment radiates back in.) (W)

C: What is the total amount of excess heat this runner's body must get rid of per second? (J/s)

D: How much water must the jogger's body evaporate every minute due to his activity? The heat of vaporization of water at body temperature is 2.42×10⁶ J/kg . (g)

E: How many 750 mL bottles of water must he drink after (or preferably before!) jogging for a half hour? Recall that a liter of water has a mass of 1.00 kg .

Answer 1

A: How much heat per second is produced just by the act of jogging? (J/s)

The energy emitted by the broker is

80 percent of the energy produced is converted into heat

remember that

ie.

heat per second is produced just by the act of jogging

B: How much net heat per second does the runner gain just from radiation if the air temperature is 40.0 ∘C (104 ∘F)? (Remember that he radiates out, but the environment radiates back in.) (W)

Stefan's law is used

where:

   Area
It is a constant
temperature of the person
Ambient air temperature
  Let's consider 1 emisivilidad

evaluated numerically

C: What is the total amount of excess heat this runner's body must get rid of per second? (J/s)

Energia issued

energy absorbed

Net energy emitted

D: How much water must the jogger's body evaporate every minute due to his activity? The heat of vaporization of water at body temperature is 2.42×106 J/kg . (g)

remember

energy released in a minute

The evaporated mass is

The heat of vaporization of water at body temperature

E: How many 750 mL bottles of water must he drink after (or preferably before!) jogging for a half hour? Recall that a liter of water has a mass of 1.00 kg .

the mass of water evaporated per 30minutes is:

if remember

Transforming in milliliters

You should to drink about a bottle of water