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e) The amount of energy the worm needs from its metabolism should be proportional to the worm's volume. What is the ratio of the metabolic needs of the larger warm compared to the smaller worm? Why might the metabolic need limit the increase in thickness of these flatworms?

e) The amount of energy the worm needs from its metabolism should be proportional to the worm's volume. What is the ratio of the metabolic needs of the larger warm compared to the smaller worm? Why might the metabolic need limit the increase in thickness of these flatworms?

Human Anatomy & Physiology (11th Edition)
Human Anatomy & Physiology (11th Edition)
11th Edition
ISBN:9780134580999
Author:Elaine N. Marieb, Katja N. Hoehn
Publisher:Elaine N. Marieb, Katja N. Hoehn
Chapter1: The Human Body: An Orientation
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e) The amount of energy the worm needs from its metabolism should be proportional to the worm's volume. What is the ratio of the metabolic needs of the larger warm compared to the smaller worm? Why might the metabolic need limit the increase in thickness of these flatworms? f) If the oxygen diffusion coefficient in the worm body is 1.4 x 105 cm² /s, how long does it take oxygen to diffuse to the center of the worm if its total thickness is 1mm? g) Diffusion times can be long, as long as there is a steady supply of oxygen for the worm’s metabolic needs. Scientists have measured the oxygen metabolic rate, m, for a number of worms and used that to determine the maximum thickness of a worm. This thickness will also depend on the concentration difference driving oxygen diffusion. The maximum diffusion rate occurs when the concentration inside the worm goes to 0 (all the oxygen is used up). Since the concentration difference driving diffusion is Cocean - Cworm, the maximum concentration difference is just Cocean. Based on all that, the maximum worm thickness is given by max thickness 2DC, m Ocean We'll assume the diffusion coefficient is the same as in part f and the oxygen concentration in the ocean is 2.7 x 104 mol /1. Scientists have measured worm metabolic rates as 100 microliters of oxygen / gram of worm / hr. This is equivalent to 1.2 x 106 moles /1/ sec. What is the maximum worm thickness?
Transcribed Image Text:e) The amount of energy the worm needs from its metabolism should be proportional to the worm's volume. What is the ratio of the metabolic needs of the larger warm compared to the smaller worm? Why might the metabolic need limit the increase in thickness of these flatworms? f) If the oxygen diffusion coefficient in the worm body is 1.4 x 105 cm² /s, how long does it take oxygen to diffuse to the center of the worm if its total thickness is 1mm? g) Diffusion times can be long, as long as there is a steady supply of oxygen for the worm’s metabolic needs. Scientists have measured the oxygen metabolic rate, m, for a number of worms and used that to determine the maximum thickness of a worm. This thickness will also depend on the concentration difference driving oxygen diffusion. The maximum diffusion rate occurs when the concentration inside the worm goes to 0 (all the oxygen is used up). Since the concentration difference driving diffusion is Cocean - Cworm, the maximum concentration difference is just Cocean. Based on all that, the maximum worm thickness is given by max thickness 2DC, m Ocean We'll assume the diffusion coefficient is the same as in part f and the oxygen concentration in the ocean is 2.7 x 104 mol /1. Scientists have measured worm metabolic rates as 100 microliters of oxygen / gram of worm / hr. This is equivalent to 1.2 x 106 moles /1/ sec. What is the maximum worm thickness?
Quantitative: Fick's first law helps us understand the relationship between a molecule's concentration gradient (the difference in its concentration at two locations) and diffusive flux. In organisms without circulatory systems, the delivery of oxygen to their body tissues can be limited by diffusion. Therefore, diffusion can literally determine the allowable thickness of their body. One example of an organism like this is a flatworm. There are over 30,000 species of marine flatworms which are often beautifully colored. Let's think more about what might be happening in a flatworm's body. a) Draw a picture of a slice through a flatworm showing its cross section and the water above and below. We'll let the total worm thickness be 2Ax which will simplify things as we go. b) Write Fick's equation for the flux of oxygen from the water above into the center of the worm. Label your drawing above with the key variables in this equation. c) A typical marine flatworm is about 1 mm thick. If the worm's thickness were to double, what would happen to the oxygen flux to the worm's center? d) Now assume that the worm gets bigger in all three dimensions, doubling in length, width and thickness. We'll also assume that oxygen diffuses into the worm primarily across its large surface area determined by the length and width (essentially ignoring the tiny area from the thin edges around the worm). What is the ratio of the oxygen diffusion rate for the larger worm compared to the smaller worm?
Transcribed Image Text:Quantitative: Fick's first law helps us understand the relationship between a molecule's concentration gradient (the difference in its concentration at two locations) and diffusive flux. In organisms without circulatory systems, the delivery of oxygen to their body tissues can be limited by diffusion. Therefore, diffusion can literally determine the allowable thickness of their body. One example of an organism like this is a flatworm. There are over 30,000 species of marine flatworms which are often beautifully colored. Let's think more about what might be happening in a flatworm's body. a) Draw a picture of a slice through a flatworm showing its cross section and the water above and below. We'll let the total worm thickness be 2Ax which will simplify things as we go. b) Write Fick's equation for the flux of oxygen from the water above into the center of the worm. Label your drawing above with the key variables in this equation. c) A typical marine flatworm is about 1 mm thick. If the worm's thickness were to double, what would happen to the oxygen flux to the worm's center? d) Now assume that the worm gets bigger in all three dimensions, doubling in length, width and thickness. We'll also assume that oxygen diffuses into the worm primarily across its large surface area determined by the length and width (essentially ignoring the tiny area from the thin edges around the worm). What is the ratio of the oxygen diffusion rate for the larger worm compared to the smaller worm?
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Introduction

Note: Since you have provided too many questions and the questions are not interlinked the solution to the first question is provided below as per the guidelines. Please, post the other questions separately. 

 

Relationship between metabolism and body size: 

  • The body size and metabolism are directly proportional to each other. 
  • When the size of the body increases (or body mass), the metabolic rate also increases. 

 

 

 

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