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!

Van der Waals gas

  1. Oct 11, 2015 #1
    1. For a van der Waals gas πT=a/Vm2. Calculate ΔUm for the isothermal expansion of nitrogen gas from an initial volume of 1.00 dm3 to 24.8 dm3at 298K. What are values for q and w?


    2. Relevant equations
    I looked up a for N2 gas to be 1.352 atm*dm6/mol2
    dU(V,T)=(∂U/∂V)TdV+(∂U/∂T)VdT
    (∂U/∂V)TT
    (∂U/∂T)V=Cv

    3. The attempt at a solution

    I start with (∂U/∂V)TT and substitute in πT and Cv
    which gives dU(V,T)=πTdV+CvdT

    Since this is isothermal dt=0 so dU(V,T)=πTdV

    I integrate both sides ∫dU=∫πTdV. πT= a/Vm2.
    a is a constant so it comes out of the integral leaving
    ΔU=a∫dV/Vm2.= a*n2 ∫ dV/V2

    Evaluating the integral
    ΔU= -((a*n2)/2)*V-3.
    After plugging in values for a, Vi, and Vf I get:
    ΔU=-((1.352 *n2)/2)*[(1/24.83)-(1/13)]

    I get 0.676 *n 2 J/mol2. I just don't know what to do with the moles.

    I know how to get work which is just w=-nrt∫dV/V and the solution is -7.95 kJ of work
    but without ΔU I cannot calculate q.
     
  2. jcsd
  3. Oct 11, 2015 #2
    I actually solved my own problem. I apparently don't know how to integrate.
     
  4. Oct 11, 2015 #3
    Could you post the solution, please? I'm having trouble with this one myself.
     
  5. Oct 12, 2015 #4
    Everything is right up until I pulled out the n^2 from the integral, just keep it as Vm. I also integrated wrong so if you get the proper solution of the integral, which is -1/Vm then you can just plug everything in. With unit conversion you get U then you can calculate q.
     
  6. Oct 12, 2015 #5
    Thank you!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Van der Waals gas
  1. Van der waals gas (Replies: 0)

  2. Van der Waals gas (Replies: 0)

Loading...