Question

The amount of heat per second conducted from the blood capillaries beneath the skin to the surface is 240 J/s. The energy is transferred a distance of 2.0 x 10^-3 m through a body whose surface area is 1.6 m^2. Assuming that the thermal conductivity is that of body fat (k = 0.20 J/(s•m•degrees C)). Determine the temperature difference between the capillaries and the 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

Answer 1

c. 1.5 degrees C

Step-by-step explanation:

Given that

Q= 240 J/s ( we know that J.s=W)

Q= 240 W

L= 2 x 10⁻3 m

A= 1.6 m²

K=0.20 J/(s•m•degrees C))

Lets take temperature difference is ΔT

We know that from Fourier law

`Q=KA(\Delta T)/(L)`

Now by putting the all values

`Q=KA(\Delta T)/(L)`

`240=0.2* 1.6* (\Delta T)/(2* 10^(-3))`

ΔT = 1.5 degrees C

c. 1.5 degrees C