Lesson 4. IV - Temperature and Pressure

Umit Aslan, Nick LaGrassa
Chemistry
45-50 minutes
High School
v3

Overview

This lesson introduces a computer model that now includes the effect of warming up and cooling down the bike tire walls. They use this model to examine the relationships between speed of particles and the temperature of the gas as well as between temperature and pressure. Students use CODAP to collect data and then find a linear equation of the relationship between temperature and pressure. They use the equation to make predictions about what the pressure will be for temperature conditions.

Standards

Next Generation Science Standards
  • Physical Science
    • [HS-PS2] Motion and Stability: Forces and Interactions
  • NGSS Crosscutting Concept
    • Patterns
    • Systems
    • Structure and Function
  • NGSS Practice
    • Analyzing Data
    • Constructing Explanations, Designing Solutions
    • Asking Questions, Defining Problems
    • Using Models
    • Arguing from Evidence
    • Conducting Investigations
Computational Thinking in STEM
  • Data Practices
    • Analyzing Data
    • Collecting Data
    • Creating Data
    • Manipulating Data
    • Visualizing Data
  • Modeling and Simulation Practices
    • Assessing Computational Models
    • Designing Computational Models
    • Using Computational Models to Find and Test Solutions
    • Using Computational Models to Understand a Concept
  • Computational Problem Solving Practices
    • Assessing Different Approaches/Solutions to a Problem
    • Computer Programming
    • Troubleshooting and Debugging
  • Systems Thinking Practices
    • Investigating a Complex System as a Whole
    • Thinking in Levels
    • Understanding the Relationships within a System

Credits

The 2019 version of this unit is developed by Umit Aslan (umitaslan@u.northwestern.edu) and Nicholas LaGrassa (nicholaslagrassa2023@u.northwestern.edu).

Acknowledgement

A majority of this unit is adopted from the earlier Connected Chemistry units developed by Uri Wilensky, Mike Stieff, Sharona Levy, and Michael Novak (see http://ccl.northwestern.edu/rp/mac/index.shtml for more details). Some elements are also taken from the Particulate Nature of the Matter unit developed by Corey Brady, Michael Novak, Nathan Holbert, and Firat Soylu (see http://ccl.northwestern.edu/rp/modelsim/index.shtml for more details).

We also thank undergraduate research assistants Aimee Moses, Carson Rogge, Sumit Chandra, and Mitchell Estberg for their contributions.

Activities

  • 1. Why does the balloon expand?
  • 2. Let's talk about our balloon sketches
  • 3. Our experimental setup: the "warm up -- cool down" model
  • 4. Using CODAP to develop a mathematical Pressure-Temperature model
  • 5. Validating our mathematical model

Student Directions and Resources


In the previous two lessons, we used computational models of a bike tire to:

  • describe how "pressure" as a macro-level property emerges from the micro-level interactions between the gas particles and the container's walls
  • find a relationship between two variables, the number of particles and pressure, by conducting computational experiments and doing statistical analysis.

 

    

 

In this lesson, we are going to explore the relationship between temperature and pressure. To do so, we are going to use a new NetLogo model and the CODAP data analysis platform.

The goals of this lesson are:

  • Defining temperature in a gas container.
  • Understanding the relationship between gas particles' movement (kinetic energy) and gas temperature.
  • Analyzing the relationship between gas temperature (independent variable) and gas pressure (dependent variable).
  • Developing a mathematical model that defines the relationship between gas temperature and pressure quantitatively.

1. Why does the balloon expand?


Before moving on to our computational explorations, let us consider the GIF on the right, which shows a the result of an interesting real world experiment:

  1. The experimenter places a blown balloon inside liquid nitrogen*.
  2. The balloon shrinks while contacting the liquid nitrogen.
  3. He takes the shrunk balloon out and holds it in his hands.
  4. The balloon automatically expands.

 

Why does the balloon expand? Let's hypothesize.

*Liquid nitrogen is a very cold substance used in food industry to preserve food by freezing it quickly. It is also used in medicine to treat skin conditions.


Question 1.1

What is the difference when the balloon is contacting liquid nitrogen and when it is outside of the bowl? Draw a sketch for each condition. Things to consider: what is inside the balloon? how do the outside conditions affect the interior of the balloon? (please spend no more than 6 minutes on this task).

Note: please use colors other than black to differentiate with the balloon outline.

Note: Draw your sketch in the sketchpad below


Question 1.2

Please explain your sketch verbally. (min. 3 sentences)

  • Which shapes did you draw on the left? Why?
  • Which shapes did you draw on the right? Why? 


Question 1.3

Did "gas pressure" factor into your thinking? If yes, please elaborate. If no, why? (min. 2 sentences)



Question 1.4

If you were to develop a NetLogo model to explore this phenomena, how would you design it? Explain verbally (min 3 sentences/ideas):

  • What would the model's view look like?
  • What kind of elements would be in the model?
  • What kind of tools would you have (e.g., sliders, buttons)?

2. Let's talk about our balloon sketches


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.

 


Question 2.1

If the discussion has not started yet, start answering the following question (and the next 3 questions): Can you think of other real world objects that shrink due to outside temperature (except tires and ballons)?



Question 2.2

If the discussion has not started yet, please answer the following question: Watch the experiment on the right carefully. Why does the balloon explode? (min. 2 sentences)

 

 



Question 2.3

Before moving on, please reflect on the classroom discussion briefly: (1) How did your sketch compared to the other groups' sketches? (2) What were the similarities? (3) What were the differences?  (min 2. sentences)

3. Our experimental setup: the "warm up -- cool down" model


Let us begin our exploration of the relationship between gas pressure and gas temperature with another NetLogo model. In this model, we have a fixed-volume gas container similar to our previous Bike Tire model. However, this model allows us to warm up and cool down the walls of the container. 

When a particle hits the wall, two things may happen:

  • If it has more kinetic energy than the energy of the wall, it will loose some of its energy.
    • the loss of energy is dependent on the difference between the particle's energy and the wall's energy.
  • If it has less energy than the energy of the wall, it will gain some energy.
    • the gain of energy is dependent on the difference between the particle's energy and the wall's energy.
  • Particles only have kinetic energy. The higher a particle's kinetic energy, the faster it moves.
    • a particle will speed up if it gains energy from the wall
    • a particle will slow down if it looses energy to the wall

 

Now begin exploring the model:

  1. Run the model by clicking "setup" and then clicking "go".
  2. Wait until all three plots stabilize.
  3. Warm up the walls (at least 6).
  4. Observe the changes in plots.
  5. Repeat the same steps, but this time cool down the walls.

Some quick notes: The temperature of a gas is related to the average speed of the particles. When the average particle speed increases, the temperature also increases. However, this is not a linear relationship. Gas temperature is proportional to the square of the average particle speed. For example, if you double the average speed, you will quadruple the temperature.

Even though temperature and average particle speed are not directly proportional, when one increases the other will too. This means we can still use them to make comparisons and develop mathematical models.


Question 3.1

What happens to the particles when you warm up the walls of the container? Briefly describe the events you observe. (min. 2 sentences)

Quick tip: You can use the  slider.



Question 3.2

What happens to the particles when you cool down the walls of the container? Briefly describe the events you observe. (min. 2 sentences)

Quick tip: You can use the  slider.



Question 3.3

What changes did you observe in the plots? Briefly describe how each plot changes when you warm up the walls. (min. 3 sentences)



Question 3.4

In the next page, you are going to conduct another computational experiment. Once again, you will conduct an experiment to answer a pre-determined research question:

Dependent variable: (P)ressure
Independent variable: (T)emperature
Research question:

Is there any mathematical relationship between these two variables?

If yes, what is the nature of this relationship?

Note: Remember that you cannot manipulate the gas temperature directly. You can manipulate it only indirectly by manipulating the "outside energy" parameter. Hence, the table below does not have a "temperature" column. 

 

Also note: Remember the experiment you ran in the previous lesson and also remember that you will run this experiment within CODAP in the next page.

4. Using CODAP to develop a mathematical Pressure-Temperature model


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

Note: If you do not remember the exact details, you can see your experimental design below the CODAP window. If you are not sure about your experimental design, consult your teacher. Here are a few considerations to keep in mind:

  1. Run each experiment long enough so that all three plots stabilize before your model reports the data.
  2. Keep non-involved parameters (e.g., number of particles, ticks-to-run) fixed at all experiments.
  3. Run at least 3 trials (repetitions) for each combination.
  4. Try at least 5 different values for the independent variable (temperature/outside-energy).
  5. Speed up the model to conduct the experiments as fast as possible.

 

Did you also find a mathematical equation using CODAP's "movable line" tool? If you did not, please do it now.

If you do not remember exactly, here is how to do it:

  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.

Question 4.1

First and foremost, save your CODAP experiment and upload it using the "Browse" button below. You can do it as follows:

  1. Click the hamburger menu () icon on he top-left corner of the CODAP window.
  2. Click Save ().
  3. Choose the Local File option ()
  4. Click Download ().
Upload files that are less than 5MB in size.
File Delete
Upload files to the space allocated by your teacher.


Question 4.2

What is the mathematical equation you found?

Note: Remember that you can omit the last part of the equation (b, in y = mx + b).

5. Validating our mathematical model



Question 5.1

According to your mathematical model, what would be the pressure if your gas temperature was about 200 degrees?



Question 5.2

Given that you cannot set the temperature directly in this model, how can we test the validity of your prediction? Briefly describe your strategy. (min. 2 sentences).



Question 5.3

If you observe a pressure of 170, what should be gas temperature?



Question 5.4

Were you able to validate your mathematical model? Explain why and how. (min. 2 sentences).



Question 5.5

Optional question if you finished the activities early: Would your answer to the "balloon-in-liquid-nitrogen" experiment change after this lesson? If no, explain why. If yes, explain how. (min. 2 sentences)



Question 5.6

Optional question if you finished the activities early: Would you change your sketch, too? If yes, go ahead and draw a new one

Note: Draw your sketch in the sketchpad below