An average sleeping person metabolizes at a rate of about 80 W by digesting food or burning fat. Typically, 20% of this energy goes into bodily functions, such as cell repair, pumping blood, and other uses of mechanical energy, while the rest goes to heat. Most people get rid of all this excess heat by transferring it (by conduction and the flow of blood) to the surface of the body, where it is radiated away. The normal internal temperature of the body (where the metabolism takes place) is 37∘C37 ∘ C, and the skin is typically 7C∘7C ∘ cooler. By how much does the person’s entropy change per second due to this heat transfer?

-4.7 x 10^-3 J/K-s

Explanation:

The Power generated by metabolizing food = 80 W

The watt W is equivalent to the Joules per sec J/s

therefor power = 80 J/s

20% of this energy is not used for heating, amount available for heating is

==> H = 80% of 80 = 0.8 x 80 = 64 J/s

The inner body temperature = 37 °C = 273 + 37 = 310 K

The entropy of this inner body ΔS = ΔH/T

ΔS = 64/310 = 0.2065 J/K-s

The skin temperature is cooler than the inner body by 7 °C

Temperature of the skin =  37 - 7 = 30 °C = 273 + 30 = 303 K

The entropy of the skin = ΔS = ΔH/T

ΔS = 64/303 = 0.2112 J/K-s

change in entropy of the person's body = (entropy of hot region: inner body) - (entropy of cooler region: skin)

==> 0.2065 - 0.2112 = -4.7 x 10^-3 J/K-s

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