2. A. A large muscle is 10 cm in length. The diffusion coefficient for oxygen is
ID: 3477464 • Letter: 2
Question
2. A. A large muscle is 10 cm in length. The diffusion coefficient for oxygen is 1.8x10-5cm2s-1 What time does it take for oxygen to passively diffuse down the length of the muscle? Show calculations. The circulatory flow through this large muscle is 1.5 L/min. Assume The circulation is through a hollow tube in identical length to the large muscle. The radius is 200 microns. The viscosity of the blood is 3x10-3Pa*s. What is the time of oxygen travel down the length of the muscle due to convection? B. C. In part B we made some assumptions. Normally the radius and other parameters vary through the circulatory system. Despite this, flow is constant through the large muscle. Why is this the case?Explanation / Answer
Ans. 2A
Oxygen availability is often a limiting factor for cell survival, and it is generally supplied to a cell by passive diffusion. As oxygen molecules diffuse into the cell, they are consumed, so that there is a progressive fall in oxygen concentration from the surface of the cell to the lowest concentration which occurs at the center of the cell. For a spherical cell with a typical diffusion coefficient for oxygen (105 cm2/s) and an oxygen consumption of resting skeletal muscle (102 ml O2 cm3 min1), the critical size (radius) which is just adequately supplied with oxygen from the surrounding medium is about 1 mm. Thus, we find that diffusion puts an upper limit on the size of cells in regard to their need for oxygen.
Although diffusion is an efficient transport process over short distances as seen by the average time required for a molecule to diffuse a distance x (t x2/2D), so x=10, D = 1.8x10-5 , 100/2(1.8x10-5)= 27.7 x105 Sec.
The diffusion constant for a gas through a substance is defined as the number of c.c. (0Oc, 760 mm.) penetrating through 0.001 mm. (1,u) the thickness and 1 sq. cm. surface per minute when the pressure difference is 1 atmosphere. The diffusion constant for oxygen through animal tissues increases with increasing temperature-about 1 p.c. per degree, taking the rate at 200 as unity.
how can a much larger multicellular organism, such as the human body containing about 100 × 1012 cells, be adequately supplied with oxygen? For mammals, the bathing medium for cells is water and total body water is about 60% of body weight. For a 70-kg person, total body water is distributed among three compartments with the following approximate volumes: intracellular 23 l (33% of body weight); interstitial 16 l (22.5% of body weight); and circulating plasma 3 l (4.5% of body weight). Cells are bathed in interstitial fluid (ISF), but interstitial fluid volume is only a little more than half the intracellular fluid volume. Thus, ISF cannot be considered a large reservoir of fluid, and its composition is directly influenced by cellular metabolism.
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