1. Not finding help here? Sign up for a free 30min 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!

Simple integral of dlnP/dt problem

  1. Aug 31, 2012 #1
    1. The problem statement, all variables and given/known data

    Integrate the Clausius Clapeyron equation to get the saturated partial pressure equation.



    2. Relevant equations

    dln(P)/dT = L/RT2

    Es= Es0 exp(-L/R (1/T - 1/T0))

    3. The attempt at a solution

    P=Es0

    ∫L/RT (limits -> T &T0) = -L/R * (1/T - 1/T0)

    dln(P)/dT = 1/P*dP/dT?



    I've managed to confused myself to the point where these are the only coherent workings I have. I feel that I'm close and missing a trick? My problem is how I get to the exp and the Es0 constant. I know this is to do with dln(P)/dT, but the maths text book and the notes for the course I have don't help at all.
     
  2. jcsd
  3. Aug 31, 2012 #2
    On the left hand side you have a derivative of a function with respect to T. On the right hand side you have a function of T. You can integrate both sides with respect to T. What do you get?
     
  4. Sep 2, 2012 #3
    if you use the dln(P)/dT = 1/P*dP/dT relation

    P= -P (L/R * (1/T - 1/T0))

    I understand you are trying to get me to work through the problem. The problem is my maths are wrong and need to be shown how to do it.
     
    Last edited: Sep 2, 2012
  5. Sep 2, 2012 #4
    You have [tex]\frac {d} {dT} \ln P = \frac L {RT^2}[/tex] You integrate that from [itex]T_0[/itex] to [itex]T[/itex]: [tex]\int_{T_0}^T\frac {d} {dT} \ln P dT = \int_{T_0}^T \frac L {RT^2} dT[/tex] The integral on the left is an integral of a derivative, so integration cancels differentiation: [tex]\int_{T_0}^T\frac {d} {dT} \ln P dT = \left[\ln P\right]_{T_0}^T = \ln P - \ln P_0 = \ln \frac {P}{P_0}[/tex] Can you figure out the rest?
     
    Last edited: Sep 2, 2012
  6. Sep 2, 2012 #5
    Yes, thank you for the help. My brain just seemed to shut down down on this problem.
     
  7. Sep 2, 2012 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    One thing that is confusing is the use of "t" on the left and "T" on the right. I assumed that "t" was "time" and "T" was temperature, which makes the problem very difficult!
     
  8. Sep 2, 2012 #7
    The t vs T thing was my fault, I just wrote the differentiation symbol in the autopilot mode. Sorry about that! I have corrected that.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Simple integral of dlnP/dt problem
  1. Simple integral (Replies: 2)

  2. Simple integral or not? (Replies: 10)

  3. Simple integral (Replies: 1)

Loading...