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

(a)
`fd=1.7058* 10^(-5)\ L.hr^(-1).cm</p><p>(b) [tex]r=26.008\ cm`

Step-by-step 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=(2)/(100) * 14.5`

`d=0.29\ L.hr^(-1)`

Flux of diffusion rate,

`fd=(d)/(A)`

`fd=(0.29)/(17000)`

Diffusion flux rate for animal:

`fd=(14.5)/(A)`

`1.7058* 10^(-5)=(14.5)/(4.\pi.r^2)`

`r=26.008\ cm`