Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Related questions
Question
![Suppose a cell is suspended in a solution containing a solute of constant concentration \( C_s \). Suppose further that the cell has constant volume \( V \) and that the area of its permeable membrane is the constant \( A \). By Fick's law, the rate of change of its mass \( m \) is directly proportional to the area \( A \) and the difference \( C_s - C(t) \), where \( C(t) \) is the concentration of the solute inside the cell at time \( t \). Find \( C(t) \) if \( m = V \cdot C(t) \) and \( C(0) = C_0 \). See the figure below. (Use \( k > 0 \) as the proportionality constant.)
\[ C(t) = \]
---
**Diagram Explanation:**
The diagram illustrates a cell in a solution.
- The cell is represented as a circle with arrows pointing inwards, indicating the movement of solute molecules through the cell membrane.
- Inside the cell, the concentration is labeled as \( C(t) \).
- The external solution has a constant concentration labeled as \( C_s \).
- The diagram emphasizes the diffusion process, where solute molecules move from areas of higher concentration to lower concentration through the semi-permeable membrane of the cell.
This helps in understanding the application of Fick’s law in biological systems, particularly in how substances like nutrients or waste products move across cellular membranes.](https://content.bartleby.com/qna-images/question/d608d232-a827-4526-b5b4-a763d0855f8e/b9a4ac91-d34b-486f-8a92-ff5c38a6189b/6p3wnrh_processed.png)
Transcribed Image Text:Suppose a cell is suspended in a solution containing a solute of constant concentration \( C_s \). Suppose further that the cell has constant volume \( V \) and that the area of its permeable membrane is the constant \( A \). By Fick's law, the rate of change of its mass \( m \) is directly proportional to the area \( A \) and the difference \( C_s - C(t) \), where \( C(t) \) is the concentration of the solute inside the cell at time \( t \). Find \( C(t) \) if \( m = V \cdot C(t) \) and \( C(0) = C_0 \). See the figure below. (Use \( k > 0 \) as the proportionality constant.)
\[ C(t) = \]
---
**Diagram Explanation:**
The diagram illustrates a cell in a solution.
- The cell is represented as a circle with arrows pointing inwards, indicating the movement of solute molecules through the cell membrane.
- Inside the cell, the concentration is labeled as \( C(t) \).
- The external solution has a constant concentration labeled as \( C_s \).
- The diagram emphasizes the diffusion process, where solute molecules move from areas of higher concentration to lower concentration through the semi-permeable membrane of the cell.
This helps in understanding the application of Fick’s law in biological systems, particularly in how substances like nutrients or waste products move across cellular membranes.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 3 steps
Knowledge Booster
Similar questions
Recommended textbooks for you
- Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
Numerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill Education
Introductory Mathematics for Engineering Applicat...Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEY 
Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
Advanced Engineering Mathematics
Advanced Math
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:9780073397924
Author:Steven C. Chapra Dr., Raymond P. Canale
Publisher:McGraw-Hill Education
Introductory Mathematics for Engineering Applicat...
Advanced Math
ISBN:9781118141809
Author:Nathan Klingbeil
Publisher:WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,