The Overheated Jogger While jogging, a 70.0-kg student generates thermal energy

Question

The Overheated Jogger While jogging, a 70.0-kg student generates thermal energy at a rate of 1200 W. To maintain a constant body temperature of 37.0 degree C, this energy must be removed by perspiration or other mechanisms. If these mechanisms failed and the heat could not flow out of the student's body, irreversible body damage could occur. Protein structures in the body are irreversibly damaged if body temperature rises to 44.00 degree C or above. The specific heat of a typical human body is 3480 J/(kg middot K), slightly less than that of water. e difference is due to the presence of protein, fat, and minerals, which have lower specific heat capacities.) For how long a time t could a student jog before irreversible body damage occurs? Express your answer in minutes. t = ______ minutes

Explanation / Answer

m = 70 kg, T2 = 44 oC, T1 = 37 oC , Cp = 3480 J/kg.K

P = 1200 W

P = Q/t

Q = P*t

Q = m*Cp*(T2 -T1)

P*t = m*Cp*(T2 -T1)

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

t =1421 s

t = 1421/60

t = 23.68 min

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