While running, a 70.0 kg student generates thermal energy at a rate of 1200 W. To maintain a constant body temperature of 37.0 C, this energy must be removed by perspiration or other mechanisms.

Question

If these mechanisms failed and the heat could not flow out of the student's body, for what amount of time could a student run before irreversible body damage occurred? (Protein structures in the body are damaged irreversibly if the body temperature rises to 44.0 C or above. The specific heat capacity of a typical human body is 3480 J/(kg*K) slightly less than that of water. The difference is due to the presence of protein, fat, and minerals, which have lower specific heat capacities.)

t=?? seconds

I believe this is a Quantity of Heat problem, and the equation that I found that I think would work is:

(Delta)Temp/(Delta)time=
(Q/(delta)t)/mc

(44-37)/t=1200/t /(70*3480)

The answer I got using this was incorrect though...

Answer 1

I can't tell from your equation what you did; however,
q = mass x specific heat x delta T.
q = 70 kg x 3480 J/kg*K x 7 = ??
Then q x (1 sec/1200 J) = time in sec.
Check my thinking. 1421 seconds (about 24 minutes)