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!

Work done by gas expansion

  1. Jul 23, 2013 #1
    In my textbook W=∫p.dV is only proved for a syringe with a piston. This is quite easily done but the book never explains how it extrapolates to the general situation for a gas expanding in any deformable container. It seems the point is to prove dV= S.h where S is the surface area of a given container and h is a small displacement alone the direction of the normal to the surface. I tried in this line of thought but things soon get really mathematical and confusing. How can prove this formula in any deformable containers? Thanks in advance!
  2. jcsd
  3. Jul 23, 2013 #2
    Well the mathematical idea is that since for a (n-1) sub-manifold a R^n-1 can be introduced, the orthogonal complement to the hyperplane R^n-1 becomes after a suitable diffeomorphism the normal to the surface in the space, Hence it is possible to write dV=S.h for any n-volume. Then dW=F.h=p.S.h=p.dV...
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook