Explain using particles of mass m moving a cubic box with sides length l that the particle velocity is proportional to pressure.

The faster the particle, the larger its momentum, so the larger the force on the wall. The particle will also take less time to travel across the box and back again, and so will hit the walls more often. Since pressure = force/area if the force increases due to more collisions then the pressure will increase. ( Particles will become faster as their temperature increases.)

Explain using particles of mass m moving a cubic box with sides length l that the number of particles, N, is proportional to pressure.

Instead of just one particle, imagine you have a whole stream of them hitting the wall A. Each particle exerts a force on the wall as it hits it, so the total force on the wall will be proportional to the number of particles. Since pressure = force/ area if force increases then so does pressure.

Explain using particles of mass m moving a cubic box with sides length l that the volume of the box is inversely proportional to pressure.

If you shrink the box, The particles have less distance to travel before they hit a wall, so you've increased the number of times the particles hit the walls of the box per second, which increases the total force on the wall. Because the box is now smaller, the area of the walls is smaller. So there's a greater force on a smaller area, meaning the pressure is greater.

Explain what /c^{2} means?

/c^{2} is the mean square speed and has units m^{2}s^{-2}. /c^{2} is the square of the speed of an average particle, so the square roof of it gives you the typical speed.

How do you calculate /c^{2}?

You take the average of the squares of the velocities, called the mean square speed.

What is the root mean square speed?

r.m.s speed = (mean square speed)^{1/2} = (/c^{2})^{1/2}

State the 7 assumptions made about gases when using the ideal gas equations.

1) The gas contains a large number of particles.

2) The particles move rapidly and randomly.

3) The motion of the particles follows Newton's laws.

4) Collisions between particles themselves or at the walls of a container are perfectly elastic.

5) There are no attractive forces between particles.

6) Any forces that act during collisions are instantaneous

7) Particles have a negligeable volume compared with the volume of the container.

When do real gases behave like ideal gases?

Real gases behave like ideal gases a long as the pressure isn't too big and the temperature is reasonably high ( compared with their boiling points. ).

What is the random walk?

How can it be used to estimate the distance moved by the particle?

A random walk assumes that each paticles starts in one palce, moves N steps in radnom directions, and ends up somewhere else.

What

What's really useful is that the average distance moved in those N steps is proportional to (N)^{1/2 }.

What is the distance a particle can travel between collisions?

The distance the particle can travel between collisions is usually around 10^{-7m }.