Continual movement of atoms results in motion that looks random and causes kinetic energy to be distributed evenly among the atoms in a gas.
Part A: Students kinesthetically model a gas, by role playing atoms moving around in a container. By doing this students gain an understanding about the behavior of lots of atoms bouncing around and exchanging kinetic energy.
Part B: Students observe a computer model of a gass (in spatial and thermal equilibrium). They experiment with varying initial conditions (# of atoms, masses of atoms, initial velocity of atoms) to see what kind of predictions the model makes about the eventual state of the total system and each individual atom. They should eventually observe that the kinetic energy [energy of motion] is distributed evenly among atoms and comes to a state of equilibrium.
- Demonstrate, using a computer model, that all initial states result in a similar equilibrium distribution of kinetic energies and spatial locations of atoms.
- Predict what will happen given some random initial state of a computer model depicting a gas at the atomic level.
- Describe what it means to be in a state of thermal equilibrium.
- Describe what it means to be in a state of spatial equilibrium.
- Define general equilibrium in very simple terms.
The model of many atoms in a box is a good depiction of a gas. Using the models in this activity students will start to get an idea of how the air in the hot air balloon is behaving. All of the air molecules are bumping into each other exchanging kinetic energy with each other and with the fabric of the balloon. Air inside the balloon spreads out and reaches various states of equilibrium both spatially and thermally [see science concepts below]. Understanding how kinetic energy gets distributed among all of the atoms in the balloon is important to the overall picture of how the balloon eventually flies. Later, students will learn that the kinetic energy of atoms is related to their temperature, so understanding the distribution of kinetic energy will give students an understanding of how heat is distributed throughout the balloon.
Other Macro connections:
- Air inside a room reaches a state of equilibrium such that the atoms* are spread out evenly and have about the same kinetic energy.
- Clouds are made of tiny droplets (much bigger than atoms) which are kept aloft by collisions with air molecules all around them.
*Air is actually made of a mixture of molecules (tightly bound groups of atoms) not single atoms.
When atoms collide with each other, the total amount of kinetic energy [energy of motion] they have is conserved [remains constant]. Typically, when one atom collides with another of the same mass, the faster atom, the one with more energy, will slow down and consequently now have less kinetic energy. The other atom with which it collided will speed up and consequently now have more kinetic energy. The total energy of the atoms before and after the collision is the same.
As the number of atoms being modeled increases, patterns and certain statistical behaviors emerge that are not easily observed in simpler models. Using a computer model with many atoms, we begin to approach the modeling of macro scale phenomena (e.g., the behavior of gasses). With many atoms, we can now study the statistical behavior of molecules in a gas. Specifically, the following can be observed:
- Eventually, if the atoms are allowed to collide randomly, the system reaches a state of dynamic equilibrium. Equilibrium is a state in which measurements of the system or any part of the system remain constant, but not due to reaching some endpoint where everything stops. For example, imagine two sets of people on opposite sides of a bridge. They begin to walk across in such a way that for every person who crosses from side A to side B, one crosses from side B to A. If you were to measure how many people are on either side of the bridge you would always get the same number. However, the specific people are always changing. This is a state of dynamic equilibrium.
- Two kinds of equilibrium will occur:
- Spatial equilibrium: when the number of atoms in any one part of the box is, on average, the same over time. In other words, the atoms are spread out evenly in the box.
- Thermal equilibrium: when the kinetic energy of every atom is, on average, the same over time. In other words, when the kinetic energy is spread out evenly among the atoms.
- The starting location or starting kinetic energy will have no effect on the eventual equilibrium of the system.
- Atoms move in straight lines until they collide with other atoms. Because of numerous collisions between atoms, the motion of individual atoms appears random.
- All atoms of a gas have the same average kinetic energy, even if this gas contains a mixture of atoms with different masses. The heavier ones will move more slowly, but they will have the same average kinetic energy as the lighter faster moving particles.
- Equilibrium is an endpoint when everything stops.
- Equilibrium is a dynamic state in which measurements on the system or parts of the system remain constant. However, the constant measurements are due to many counterbalancing fluctuations of individual elements that comprise the system.
Activity Design and Execution
Major Science Concepts: kinetic energy
Assumed Previous Knowledge: Experience with a computer model of two atoms in a container.
That atoms bounce off of each other with 100% elasticity.
That atoms have kinetic energy [energy of motion] which is related to mass and velocity [speed].
That the total energy in a collision between two atoms is conserved [the same before and after].
That energy can be transferred between atoms through collisions.
Time: Part A: approximately 50 minutes
Part B: approximately 100 minutes (50 min x 2)
Materials: Popsicle sticks (a box)
Computers with Workbench Software
Advanced Preparation: (if any) None
Investigative Question: How do the atoms of a gas share space and kinetic energy?
Part A :
For the position drop down menu:
- Close to the center.
- Close to a corner.
- Spread evenly.
For the kinetic energy drop down menu:
- Same kinetic energy.
- Random kinetic energy.
- Half high, half low kinetic energy.
Have students write several things in their notebooks:
- Imagine you are at a party where someone dared you to pop one of the helium balloons in a room that has all the windows and doors closed. Describe what would happen to those Helium atoms once they have been released from the balloon. Specifically talk about their eventual position inside the room and what their kinetic energies would be like if you could actually measure them.
- Define spatial equilibrium.
- Define thermal equilibrium.
- The term equilibrium can apply to many different things. Think about what is similar between spatial and thermal equilibrium and give a general definition of equilibrium.
- When the burner of the hot air balloon is turned on, the kinetic energy of atoms near the burner is greatly increased. This makes the air inside the balloon go out of thermal equilibrium. Explain what will happen to all the atoms in the balloon as they eventually come back to thermal equilibrium.
The running average exercise could be done by individual students (or pairs) using spreadsheets. In this way they get experience using spreadsheets and graphing.
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