6.021/Notes/2006-09-21

• Osmosis is pressure
• [math]\displaystyle{ \pi(x,t)= RTC_\Sigma(x,t) }[/math]
• [math]\displaystyle{ \Phi_V = L_V((p^i-\pi^i)-(p^o-\pi^o)) }[/math]
• Problem: A long pipe with semipermeable membrane at bottom and filled with fresh water is lowered quickly into ocean. How deep does the pipe need to be inserted before the height of the fresh water will rise?
  • The osmotic pressure is about [math]\displaystyle{ 2.5 * 10^6 }[/math], the height of the fresh water in the pipe is negligible pressure. This corresponds to about a depth of around 250m.
  • However, cannot use this method to get fresh water from ocean, because for the oceans on Earth osmolarity increases exponentially with depth.