The human body must maintain its core temperature inside a rathernarrow range ar
ID: 1664024 • Letter: T
Question
The human body must maintain its core temperature inside a rathernarrow range around 37°C. Metabolic processes, notably muscularexertion, convert chemical energy into internal energy deep in theinterior. From the interior, energy must flow out to the skin orlungs to be expelled to the environment. During moderate exercise,an 80 kg man can metabolize food energy at the rate 300 kcal/h, do60 kcal/h of mechanical work, and put out the remaining 240 kcal/hof energy by heat. Most of the energy is carried from the bodyinterior out to the skin by forced convection (as a plumber wouldsay), whereby blood is warmed in the interior and then cooled atthe skin, which is a few degrees cooler than the body core. Withoutblood flow, living tissue is a good thermal insulator, with thermalconductivity about 0.210 W/m·°C. Show that blood flow isessential to cool the man's body by calculating the rate of energyconduction in kcal/h through the tissue layer under his skin.Assume that its area is 1.20m2, its thickness is 2.50 cm, and it is maintained at37.0°C on one side and at 34.0°C on the other side.1 kcal/h
Explanation / Answer
To find the rate of energy conduction, you take thermalconductivity and multiply by the temperature difference, multiplyby the area (in m2), and then divide by thickness(m). This will result in: [(0.210W/m·°C)(37°C-34°C)(1.2m2)]/(0.025m) =30.24W. 1W = 1J/s. We need to convert this value tokcal/hour. 1J=4.186cal. Therefore: (30.24J/s)/(1 cal/4.186J)= 7.224080268cal/s. To get cal/hr we multiply by 3600s/hr to get26006.68896 cal/hr. Converting units by 1 kcal/1000 cal results inapproximately 26kcal/hour.
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