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: Adiabatic expansion of a monatomic gas

  1. Sep 9, 2007 #1
    1. The problem statement, all variables and given/known data

    The molar energy of a monatomic gas which obeys van der Waals' equation is given by

    E = (3/2)RT - a/V

    V volume, T temperature, a is a constant. Initially you have T1 at V1, and the gas expands adiabatically in a vacuum so that you have V2. What is T2?

    2. Relevant equations

    Van der Waals' equation: P = RT/(V - b) - a/V^2

    3. The attempt at a solution

    Q = 0, so dW = dE. dW = -PdV, and I rewrite P in terms of V and T according to van der Waals' equation, then try to rearrange terms so that I can integrate, but I don't think the terms are separable, and I'm beginning to wonder if there is something wrong in my approach. Any help would be appreciated.
  2. jcsd
  3. Sep 9, 2007 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    You have [itex]dE = (3R/2)dT + (a/V^2)dV [/itex] and you can also write an expression for RdT from the VdW equation. Plug in for RdT from the second into the first, and set dE + PdV = 0. This should leave you with a DE in (P,V). What does it look like? Is this the equation you say is not separable?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook