Question

(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.

Answer 1

Answer:

(a) $fd=1.7058\times 10^{-5}\ L.hr^{-1}.cm(b) [tex]r=26.008\ cm$

Explanation:

(a)

• Oxygen consumption rate of humans, $Q_h=14.5\ L.hr^{-1}$

area of human skin, $A_h=1.7\ m^2$

• diffusion rate through skin of humans, $d=2\%\ of\ Q_h$

• ∴$d=\frac{2}{100} \times 14.5$

$d=0.29\ L.hr^{-1}$

Flux of diffusion rate,

$fd=\frac{d}{A}$

$fd=\frac{0.29}{17000}$

$fd=1.7058\times 10^{-5}\ L.hr^{-1}.cm(b)Surface area for a spherical animal:[tex]A=4.\pi.r^2$

Diffusion flux rate for animal:

$fd=\frac{14.5}{A}$

$1.7058\times 10^{-5}=\frac{14.5}{4.\pi.r^2}$

$r=26.008\ cm$