In the previous two lessons, we qualitatively explored:

• the behavior of gas particles inside fixed volume containers
• and how the simultaneous behavior of many gas particles at micro-level result in a macro-level property, pressure.

In this lesson, we are going to start developing quantitative relationships between the macro-level properties of gasses. To do so, we will use a slightly different version of the bike tire model from the lesson 2 and a quantitative data analysis application called CODAP.

The goals of this lesson are:

• What is the relationship between the number of particles in a gas container and gas pressure?
• How can we design experiments within computational models to collect quantitative data?
• How can we analyze quantitative data using CODAP to determine a mathematical relationship between our two variables?

Before starting our computational experiments, let us familiarize ourselves with our experimental setup. The first component of our experimental setup is a slightly modified version of the Bike Tire model from the previous lesson.

1. There is no "add particles" button anymore. We will decide the number of particles inside the bike tire before running each experiment. 
2. There is a new   slider. This slider will help us run experiments until the system stabilizes (e.g., the model will stop).

Now let's begin with running three simple experiments:

1. Set the "number-of-particles" parameter to 100 and the "ticks-to-run" parameter to 15.
   1. Click the   button to set-up the experiment.
   2. Then  button to run the experiment.
       
2. Once the experiment is completed, move your mouse over the plot (as shown on the right) and see how the pressure has changed over time. Note down the final pressure of the system.
    
3. Repeat the same procedure with 200 particles and 15 ticks. Note the resulting pressure.
4. Repeat the same procedure with 300 particles and 15 ticks. Note the resulting pressure.
5. Answer the questions below the model.

In the previous lesson, we ran 3 experiments and then tried to plot the data by hand. Even with just three experiments, we  started noticing trends. However, we also noticed two important issues:

1. Reliability issue: The particles' random behavior may lead to fluctuations in our final pressure value.

2. Practicality issue: We might not be able to precisely plot the data by our hands.

Scientists try to overcome such issues by using an approach called "statistical mechanics 🔗". To put it simply, they collect lots of data and then use statistical methods to determine mathematical relationships between variables.

Below, you will see a CODAP workbench. CODAP is a web-based data analysis platform that will make it much easier for us to run many experiments at once. It will also make it much easier to plot our data and find out mathematical relationships between the variables.

Let's begin with familiarizing ourselves with the CODAP environment:

1. Run three experiments for 15 ticks: with 100 particles, with 200 particles, and with 300 particles. (p.s.: you can speed up the model to get the results more quickly)
2. Observe how the results of each experiment is automatically transferred to the "Experiment results" table on the right.
3. Drag the num_particles variable to the x-axis of the plot plot as shown in the GIF on the right.
4. Drag the last_pressure_value variable to the y-axis of the plot plot as shown in the GIF on the right.
5. Observe the resulting plot. Then answer the questions below the CODAP workbench.

Please set your computer aside briefly (do not close this page) and join the classroom discussion that your teacher is going to moderate.

Note: If your teacher did not initiate the discussion yet, you can start answering the first four questions below as you are waiting.

Now let's go ahead and conduct our fist computational experiment within CODAP!!!

Note: If you do not remember the exact details, you can see your initial experimental design below the CODAP window.

Also note: If you changed your mind after the classroom discussion, feel free to make changes to your experimental design.

A final note: Do not forget to drag variable names to the axes of your plot widget as you did in the Page 2.

So far, we collected many data points from the Bike Tire model, we plotted them, and saw a consistent relationship. We stated our findings verbally such as "the more particles in the box, the higher is the pressure".

However, verbal statements cannot help us answer questions such as: "What happens if I add 10 more particles to the box?" or "Approximately how many particles are inside the box if the pressure is 440?"

To answer such quantitative questions, we need to develop mathematical equations.

CODAP makes it trivially easy to develop such mathematical equations from data :

1. Load your CODAP savefile by clicking CODAP's hamburger menu () and then clicking "Open".
2. Open your file from the "Local File" section. You should have all your data back in the "Experiment Results" table, as well as your plot.
3. Click anywhere on the plot, and then click the ruler icon ().
4. Click the  option.
5. A line with three anchor points will appear. Move the line as shown on the right to fit the data as best as you can.
6. Note the linear equation 🔗 (with yellow background) that CODAP generates for us.

Congratulations to all of us!!! We developed a mathematical model using computational thinking!

• We analyzed a real world phenomenon using a computational model.
• We designed an experiment to find out the relationship between two variables.
• We collected data and plotted our data points on a graph.
• We used a computational data analysis tool to develop a mathematical equation.

We should now test the validity of our Pressure-Number equation through further experimentation! You can skip directly to the questions below.