1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Expression for volume as a function of pressure

  1. Jan 21, 2014 #1
    1. The problem statement, all variables and given/known data
    When pressure is applied to a liquid, its volume decreases. Assuming that the isothermal compressibility κ=-1/V(δV/δP) is independent of pressure, derive an expression for the volume as a function of pressure.

    2. Relevant equations

    3. The attempt at a solution
    I don't know where to start, but I know the answer should be V2=V1 exp[-κ(P2-P1)].
  2. jcsd
  3. Jan 21, 2014 #2
    Start out by solving your equation for dV/dP.
  4. Jan 22, 2014 #3

    I'm not sure what to do now.
  5. Jan 22, 2014 #4
    Have you learned how to solve a differential equation like this by separation of variables or by integrating factor?
  6. Jan 22, 2014 #5
    No, I haven't taken differential equations.
  7. Jan 22, 2014 #6
    Have you learned how to integrate dV/V?
  8. Jan 22, 2014 #7
    No, I haven't.
  9. Jan 22, 2014 #8
    Do you know what the derivative of ln(x) with respect to x is equal to?
  10. Jan 22, 2014 #9
    It's 1/x
  11. Jan 22, 2014 #10
    OK. This is where we start.
    If [tex]\frac{dln(x)}{dx}=\frac{1}{x}[/tex]
    Is this OK with you so far?
  12. Jan 22, 2014 #11
    Yes, I'm following.
    Does that mean dV/V=dln(V)?
  13. Jan 22, 2014 #12

    I can get this far, but I don't know how to solve it now.
  14. Jan 22, 2014 #13
    Do I just integrate both sides from 1 to 2?
    ∫(from 1 to 2) -κδP=∫(from 1 to 2) δln(V)

    Is this correct?
  15. Jan 22, 2014 #14
    Excellent job!!! Just get rid of that extra equal sign in the last equation.
  16. Jan 22, 2014 #15
    Thanks for the help (and for catching my typo).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted