4. (15 points) Consider a spherical organism of radius ro within which respiration occurs at a uniform volumetric rate of That is, oxygen (species A) consumption is governed by a first- order reaction, homogeneous chemical reaction. a. If a molar concentration of CA(ro) = CA,o is maintained at the surface of the organism, obtain an expression for the radial distribution of oxygen, CA(r), within the organism. Hint: To simplify solution of the species diffusion equation, invoke the transformation y = rCA. b. Obtain an expression for the rate of oxygen consumption within the organism. c. Consider an organism of radius ro = 0.10 mm and a diffusion coefficient of DAB = 108 m2/s. If CA, o = 5 x105 kmol/m3 and k1 20 s1, estimate the corresponding value of the molar concentration at the center of the organism. What is the rate of oxygen consumption by the organism?
4. (15 points) Consider a spherical organism of radius ro within which respiration occurs at a uniform volumetric rate of That is, oxygen (species A) consumption is governed by a first- order reaction, homogeneous chemical reaction. a. If a molar concentration of CA(ro) = CA,o is maintained at the surface of the organism, obtain an expression for the radial distribution of oxygen, CA(r), within the organism. Hint: To simplify solution of the species diffusion equation, invoke the transformation y = rCA. b. Obtain an expression for the rate of oxygen consumption within the organism. c. Consider an organism of radius ro = 0.10 mm and a diffusion coefficient of DAB = 108 m2/s. If CA, o = 5 x105 kmol/m3 and k1 20 s1, estimate the corresponding value of the molar concentration at the center of the organism. What is the rate of oxygen consumption by the organism?
Human Physiology: From Cells to Systems (MindTap Course List)
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Chapter11: The Blood
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Question

Transcribed Image Text:4. (15 points) Consider a spherical organism of radius ro within
which respiration occurs at a uniform volumetric rate of That is,
oxygen (species A) consumption is governed by a first- order
reaction, homogeneous chemical reaction.
a. If a molar concentration of CA(ro) = CA,o is maintained at
the surface of the organism, obtain an expression for the
radial distribution of oxygen, CA(r), within the organism.
Hint: To simplify solution of the species diffusion equation,
invoke the transformation y = rCA.
b. Obtain an expression for the rate of oxygen consumption
within the organism.
c. Consider an organism of radius ro = 0.10 mm and a
diffusion coefficient of DAB = 108 m2/s. If CA, o = 5 x105
kmol/m3 and k1 20 s1, estimate the corresponding value
of the molar concentration at the center of the organism.
What is the rate of oxygen consumption by the organism?
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