- Homework Statement
A gas with particles of mass m and number density n is in a closed cylinder with a piston of area A. The cylinders initial length is L0. Th probability distribution of velocities in the x direction is p(v).
At time t the piston moves with velocity -u in the x direction. The piston ives much slower than the mean speed of the particles. The volume of the cylinder is reduced according to V= A(L0-ut). Show that the additional momentum from the piston is -2mu and the change in energy of the particles is 2muv. Where v is the velocity of a particle after colliding with the piston. Hint: consider a collision in the piston reference frame.
I am familiar with kinetic theory and know how to derive P = 1/3nmv^2 from a similar set up, but I’m not sure how to work out the momentum in this one.
- Relevant Equations
- p = mv