During heavy exercise 2.0 liters of blood are pumped to the surface of a person

Question

During heavy exercise 2.0 liters of blood are pumped to the surface of a person per minute to carry away core heat. If the blood is cooled by 2.0°C at the surface, what is the rate of heat transfer in watts due to blood flow (force convection) .

You may assume that the specific heat of blood is the same as that for water and that the density of blood is 1.05g/cm3.

Note that although the core and skin normally differ in temperature by 3°-4°C, the blood will not be cooled by that much . Skin temperature will rise during exercise and the blood must have a greater temperature than the skin in order to transfer heat to it through vessel walls (conduction). Please provide formulas used and step by step solution.

Explanation / Answer

Q/t = mcdT/t

m = v*rho

v = 2liters = 2000 cm^3

m = 2000 cm^3 * 1.05 g/cm^3 = 2100 gm

c = 4.186 J/g

Q/t = 2100 g * 4.186 * 2 /1s

Q/t = 17581.2 J/s = 17581.2 W ( W = J/s)

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