Question

In the conduction equation Q = (kA T)t/L, the combination of factors kA/L is called the conductance. The human body has the ability to vary the conductance of the tissue beneath the skin by means of vasoconstriction and vasodilation, in which the flow of blood to the veins and capillaries underlying the skin is decreased and increased, respectively. The conductance can be adjusted over a range such that the tissue beneath the skin is equivalent to a thickness of 0.080 mm of Styrofoam or 3.5 mm of air. By what factor can the body adjust the conductance? Express your answer as a number greater than one with no units.

Answer 1

17.08984375

Step-by-step explanation:

A = Area

L = Thickness of material

`k_a` = Electrical conductivity of air = 0.0256

`k_s` = Electrical conductivity of Styrofoam = 0.01

Conductance is given by

`G=(k A)/(l)`

For Styrofoam

`G_s=(k_sA)/(l)\\\Rightarrow G_s=(0.01* A)/(0.08)`

For air

`G_a=(k_aA)/(l)\\\Rightarrow G_a=(0.0256* A)/(0.0035)`

Dividing the two equations

`(G_s)/(G_a)=((0.01* A)/(0.08))/((0.0256* A)/(3.5))\\\Rightarrow (G_s)/(G_a)=17.08984375`

The body can adjust up to a factor of 17.08984375