An 85 kg yachtsman with a core body temperature of 36 o C falls out of his boat

Question

An 85 kg yachtsman with a core body temperature of 36oC falls out of his boat into the cold ocean waters. His skin rapidly cools to just 5oC and he loses body heat through a layer of body fat. The total surface area of the yachtsman is 2.2 m2

The yachtsman's metabolism continues to produce thermal energy at a rate of 180 W.

If the rate of heat transfer from the yachtsman can be assumed to be approximately constant, by how much will his core body temperature fall in the 30 minutes before he is rescued? (in K)

Heat transfer coefficient of body fat: hfat = 7.47 W m2 K1
Heat capacity of human body: chb = 3.49 kJ kg1 K1

A. 0.51

B. 1.2

C 2.0

D 3.1

E 5.3

Please show working, thank you!!

Explanation / Answer

Q = mcdT

P = Q/t

Q = P*t = 180*30 *60 = 324000 J

324000/85*3.49*10^3 = dT

dT = 1.092 = 1.2 K

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