AP Physics 2

## Gas pressure from atomic collisions A gas is a very large number of atoms or molecules moving in random directions, colliding with one another and with the walls of their container. The pressure a gas exerts has no mysterious source: it is the net effect of those atoms striking a surface. A single collision with a wall lasts only an instant and exerts a tiny force, but billions of them arrive every microsecond, and the average of their forces is steady. Each collision can be analysed with conservation of momentum. Take a wall that is fixed in place. An atom of mass $m$ arrives with a velocity component $v_x$ perpendicular to the wall and leaves with $-v_x$ if the collision is elastic, so its momentum component changes by $2mv_x$. The wall must have supplied that impulse, and by Newton's third law the atom gave the wall the same impulse in the opposite direction. The components of velocity parallel to the wall do not change in a smooth wall collision and contribute no force. Collisions between two atoms, or between an atom and a moving piston, are handled the same way, in one or two dimensions, using the vector conservation of momentum and, for elastic collisions, conservation of kinetic energy. **Pressure** is the magnitude of the force perpendicular to a surface divided by the area of the surface: $$ P = \frac{F_\perp}{A} $$ The unit is the pascal, $1\ \mathrm{Pa} = 1\ \mathrm{N/m^2}$. Here $F_\perp$ is the sum of the perpendicular components of the forces that all the…