(a) A 70-kg person at rest has an oxygen consumption rate Qhum = 14.5 liter/h, 2% of which is supplied by diffusion through the skin. Assuming that the skin surface area of this person is Ahum = 1.7 m2 , calculate the diffusion rate for oxygen through the skin in units of liters/(h cm2 ).

(b) What is the maximum diameter of a spherical animal, whose oxygen consumption at rest can be supplied entirely by diffusion through its skin? Make the following assumptions:
i. The density of animal tissue is rho = 1 g/cm3 .
ii. At rest, all animals require the same amount of oxygen per unit volume.
iii. The diffusion rate for oxygen through the skin is the same for all animals.

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creamydhaka creamydhaka · Answer 1 · 2019-12-06T12:55:17+01:00

Answer:

(a) [tex]fd=1.7058\times 10^{-5}\ L.hr^{-1}.cm

(b) [tex]r=26.008\ cm[/tex]

Explanation:

(a)

area of human skin, [tex]A_h=1.7\ m^2[/tex]

[tex]d=0.29\ L.hr^{-1}[/tex]

Flux of diffusion rate,

[tex]fd=\frac{d}{A}[/tex]

[tex]fd=\frac{0.29}{17000}[/tex]

[tex]fd=1.7058\times 10^{-5}\ L.hr^{-1}.cm

(b)

Surface area for a spherical animal:

[tex]A=4.\pi.r^2[/tex]

Diffusion flux rate for animal:

[tex]fd=\frac{14.5}{A}[/tex]

[tex]1.7058\times 10^{-5}=\frac{14.5}{4.\pi.r^2}[/tex]

[tex]r=26.008\ cm[/tex]