Activity 2: BoxGas

Newton’s Laws

Students explore the dynamics of collisions and Newton’s Laws for simple particles feeling only contact forces in Activity 1.  

This leads to the following qualitative formulation of Newton’s Laws
 

1. 1. Unless something pushes (or pulls) you, the way you are moving will not change
   2.  If you push something, the bigger it is the less it changes how it moves.
   3. If you push something, it pushes back – just as hard.
 
6. We then explain that the simulator below implements Newtonian collisions and allow students to explore their consequences. This demo is designed to be “standalone” and will run in the browser. 

Three kinds of particles…

The simulator supports three species of particle — Blue with a mass of 1 unit, Orange with a  mass of 16 units, and Green with a radius of 100 units.

Temperature 

The speeds of the particles in a simple gas obey a statistical pattern known as the Maxwell-Boltzmann distribution.  This pattern develops solely as a result of the many simple collisions experienced by the particles, each of which is governed by Newton’s laws.  

The heat stored in a gas reflects the kinetic energy of the individual particles within it.  Click the “Hist.” button (or press T on your keyboard) to display a floating chart with the speed distributions of the Blue and Orange particles; the temperature of the gas is proportional to the most common speed of the particles. 

• Watch as the initial velocity distribution takes on the Maxwell-Boltzmann form.
• How does the smoothness of the distribution depends on the number of particles?
• What happens to the temperature (which is fixed by the location of the peak) of the Blue particles as more massive particles are added?
• How does the distribution of speeds for the Blue and Brown particles differ?  

Brownian Motion

Add many Blue particles and a few heavy particles. You can track their motion with the “Trail” button (or press R).  Use the “Hide” button (or press H) to make the Blue particles invisible.  Compare the result to videos of Brownian motion. 

• Can you explain the different behaviours of the Brown and Green particles? 
• How does the motion of the Brown and Green particles depend on the number of Blue particles in the box?

Gravity Controls

Click the “g” button (or press G) to enable gravity so that a vertical weight force acts on each particle. The background shading is now striped, and the color saturation is proportional to the relative density of small blue particles 

• How does gravity change the dynamics?
• Are there any aspects of this simulation that resemble the properties of an atmosphere? [Note that real atmospheres also absorb and emit radiation, so this model is very simple indeed]

Keyboard Shortcuts

• Spacebar – Pause/play
• A / Z – increase/decrease simulation speed 
• H – toggle visibility of Blue particles
• T – toggle histogram overlay
• R – toggle heavy particle trails 
• G – toggle gravity 
• P/O – increase/decrease vertical density binning

Feedback 

We welcome feedback, comments and suggestions for extensions.