# How much heat per second does a runner gain just from radiation?

1. Oct 10, 2011

### JustinLiang

1. The problem statement, all variables and given/known data
When jogging strenuously, an average runner of mass 68kg and surface area 1.85m^2 produces energy at a rate of up to 1300 W, 80% 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 33C instead of the usual 30C. (We shall neglect conduction) 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? (b) How much net heat per second does the runner gain just from radiation if the air temperature is 40C? (Remember that he radiates out, but the environment radiates back in.)

2. Relevant equations
P=σeAT^4

3. The attempt at a solution
(a) This one is easy, just multiply 1300W by 0.8 which gets me 1040W.
(b) Given P=σeAT^4, I solved for the heat per second radiated into the body by the air (I am pretty sure emissivity is 1, it didn't specify...):
P=(5.6704x10^-8)(1)(1.85m^2)(273.15K+40K)^4
=1008.777W

Clearly this is wrong because 1008.777-1040 gives you a loss of heat? The answer suggests there is a gain of 87.1W.

What am I doing wrong?

Thanks.

2. Oct 10, 2011

### BruceW

1040W is the total power output from the person, so this includes power output via sweating. Part b requires only the power output due to radiation, so you need to calculate this.

3. Oct 10, 2011

### JustinLiang

In that case I get 1008W, but the answer is 87.1W?

4. Oct 10, 2011

bump...