Students will use a NetLogo model to learn about thermal equilibration and develop skills with investigating a complex system as a whole, thinking in levels, and using computational models to understand a concept and test hypotheses.

You will need the following resources to complete this assignment.

• Thermal Equilibration Model

What happens when you leave a hot cup of tea out for a while? In general, what happens when two substances at different temperatures come into contact with each other? What is happening on the microscopic level?

Today’s Purpose
Today we will be answering these questions by using a computer model to analyze the microscopic and macroscopic levels of thermal equilibration (the phenomenon of two substances at different temperatures moving to states of equal temperature).

Thinking in Levels
Computational scientists investigate complex systems on multiple levels using computer models. Without a computer model, it’s not possible to view multiple levels of a system at the same time. In this lesson, we will be considering two levels: the level of individual particles and the level of a group of particles. These are called the individual level and aggregate level.

Predictions
Let’s start by making a couple predictions about what will happen when two substances at different temperatures come into contact with each other.

Start by opening the Thermal Equilibration model in Netlogo:

1. Download the Thermal Equilibration Netlogo model. 
2. Open NetLogo (download link), go to File>Open…, and select the Thermal Equilibration Netlogo model.

WHAT IS THE MODEL?
This model simulates the thermal equilibration of two fluids according to principles of Newtonian mechanics. Each dot represents a particle and its color corresponds to its kinetic energy, with darker reds representing greater kinetic energy. The white strips represent regions of the container over which the average kinetic energy can be measured, with the left side starting with greater kinetic energy (temperature) than the right side.

HOW IT WORKS
Individual particles are randomly distributed throughout a closed box. They are given random directions and a set amount of energy. When the simulation starts, the particles begin to move in straight lines in random directions with a speed proportional to their energy. When they collide with the edge of the box, they reflect without losing energy. When they collide with another particle, they exchange energy with that particle according to the laws of conservation of momentum and energy.

HOW TO USE IT

1. Run simulation and observe the aggregate behavior of the system.
   1. Press the “setup” button to set the initial conditions of the world at the slider values you have chosen. 
   2. Press the “go” button to start the simulation.
   3. Observe what happens to the plots and monitors that read-out average values for the system.
      1. The “total KE of the system” graph records the total energy for the whole system over time.
      2. The “avg-KE” graph records the average kinetic energy over time for the left and right sides of the system, as well as the predicted value for the average kinetic energy of the left side of the system. 
      3. The “time-to-equilibrium” monitor records the first time at which the average kinetic energies of the two sides of the box are approximately equal.
   4. Answer question 3 below based on your observations.
       
2. Run simulation and observe the aggregate behavior of the system.
   1. Press the “setup” button to set the initial conditions of the world at the slider values you have chosen. Set the simulation speed to “normal speed”. 
   2. Right click on a particle in the system and choose “h-particle X” and then “watch h-particle X”. This spotlights a single particle.
      
   3. Press the “go” button to start the simulation.
   4. Observe behavior of an individual particle. Notice what leads to changes in behavior and how its color relates to its speed (kinetic energy). 
   5. Answer question 4 below based on your observations.
       

Today we used a computer model to analyze the individual and aggregate levels of a system of particles undergoing thermal equilibration. 

We observed that on the aggregate level we see uncontrolled systems moving toward states with equal energy distribution. On the individual level, we observed that particles are colliding with other particles and exchanging kinetic energy, either from the higher energy particle to the lower energy particle or from the lower energy particle to the higher energy particle (this is based on laws of conservation of momentum).