The amount of heat per second conducted from the bloodcapillaries beneath the sk

Question

The amount of heat per second conducted from the bloodcapillaries beneath the skin to the surface is 240 J/s. The energyis transferred a distance of 2.0 x 10^-3 m through a body whosesurface area is 1.6 m^2. Assuming that the thermal conductivity isthat of body fat (k = 0.20 J/(s·m·degrees C)),determine the temperature difference between the capillaries andthe surface of the skin.
a. 9.2 degrees C
b. 5.4 degrees C
c. 1.5 degrees C
d. 6.9 degrees C
e. 3.7 degrees C

The amount of heat per second conducted from the bloodcapillaries beneath the skin to the surface is 240 J/s. The energyis transferred a distance of 2.0 x 10^-3 m through a body whosesurface area is 1.6 m^2. Assuming that the thermal conductivity isthat of body fat (k = 0.20 J/(s·m·degrees C)),determine the temperature difference between the capillaries andthe surface of the skin.
a. 9.2 degrees C
b. 5.4 degrees C
c. 1.5 degrees C
d. 6.9 degrees C
e. 3.7 degrees C

Explanation / Answer

Amount of heat per second Q= 240 J / s

Distance L= 2 * 10 ^ -3 m

Surface area A = 1.6 m^ 2

Thermal conductivity K=0.2 J / [ s m oC ]

Temp difference dt = ?

We know Q = KA dt / L

From this dt = QL / KA

                    = 1.5 oC

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