Question

The amount of heat per second conducted from the blood capillaries beneath the skin to the surface is 280 J/s. The energy is transferred a distance of 1.6 × 10^-3 m through a body whose surface area is 2.0 m². Assuming that the thermal conductivity is that of body fat, determine the temperature difference between the capillaries and the surface of the skin.

Answer 1

given data:
amount of heat per second = 280 J/s
energy is transferred = 1.6*10^-3 m
area = 2 m^2
The equation used to calculate the amount of heat energy that flows during a time t through a medium of cross-sectional area A with a temperature difference between the two ends of ΔT and length L is:

Q =(kAΔT)t/L

k is a constant called the thermal conductivity of the medium, which for body fat is 0.20 J/s-m-°C

Rearranging the equation a little to solve for ΔT:
ΔT = (Q/t)L/(kA)
ΔT = (280 )*(1.6*10-3 ) / ((0.20)(2.0)) = 1.12 °C