Kinetic Theory of Gases Model
Properties of Matter

Physical models for kinetic theory

for 14-16

Models enable students to visualize what might be happening to particles in different states of matter. They can also lead to predictions, against which real behaviour provides a crucial test.

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Kinetic theory: two-dimensional model

Kinetic Theory of Gases Model
Properties of Matter

Kinetic theory: two-dimensional model

Practical Activity for 14-16

Class practical

Students use marbles in a tray to explore models.

Apparatus and Materials

For each pair of students

  • Metal tray lined with cork mat
  • Marbles, coloured, 20 - 24, about 1 cm diameter

Health & Safety and Technical Notes

Beware of marbles on the floor.

Read our standard health & safety guidance


The metal tray should have near-vertical sides and a thin cork base. Each tray should contain 20 to 24 coloured marbles.

The marbles need to be of random colours so the students can concentrate on a particular one if they wish. The thin cork base reduces the noise and helps students distinguish between collisions between marbles and those with the walls.

Procedure

  1. Shake the tray in a random motion, on the table.
  2. To model a solid: Tilt the tray so the marbles are at the bottom and the marbles are able to vibrate but not change places.
  3. To model a liquid: Vibrate the tray more violently so the marbles occupy approximately the same space but are free to move around. These energetic marbles are modelling particles that do not spend long enough near any one particular particle to get locked into a crystal array.
  4. To model a gas: Vibrate the tray more violently, keeping it flat on the table. This will cause particles to spread out more. Some particles may spill over the tray wall: diffusion.

Teaching Notes

  • Students should be able to hear the difference between the glass-glass collisions of atoms colliding with each other and the glass-metal edges of the tray of the atoms colliding with the walls, modelling pressure of a gas.
  • Students may ask why the tray needs to be continuously agitated. You do not need to continually 'heat' a real gas. The model can only tell so much of the real story: the walls of all containers, on a molecular scale, are themselves in constant agitation.
  • Heating a gas causes the particles to move faster with translational random motion. The energy stored kinetically increases.
  • Molecules also spin and vibrate. Transferring energy to a gas will increase the energy stored in a variety of ways.

This experiment was safety-tested in January 2005

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Kinetic theory model for a gas

Kinetic Theory of Gases Model
Properties of Matter

Kinetic theory model for a gas

Practical Activity for 14-16

Class practical

Here phosphor bronze balls model a small volume of a gas.

Apparatus and Materials

Health & Safety and Technical Notes

Read our standard health & safety guidance


See apparatus page for

Electric motor, fractional horsepower


Photo courtesy of J Kinchin

The model kit may include its own motor.

Fix the rubber base over the lower end of the tube, which is held as shown in the diagram. Adjust the height of the tube until the rubber base is a millimetre or two above the vibrating rod in its mean position. Connect the d.c. terminals of the variable voltage supply in parallel to the field and armature terminals of the motor. Add the small phosphor bronze ball bearings until they cover about two-thirds of the base. Put the cap over the top of the tube to prevent the balls escaping and to cut down the noise.

More modern versions of this apparatus are available, from scientific suppliers.

Procedure

  1. Turn the voltage up so the vibrator is set in motion, and you have simulated kinetic theory motion.
  2. Gradually increase the motion to show that the kinetic energy of the particles increases.
  3. To aid visibility for a class, place a translucent screen behind the model. Put a lamp behind the screen to form a silhouette.

Teaching Notes

  • Students should notice fewer particles in the higher parts of the tube.
  • You can put a cardboard disc in the tube to act as a lid. The disc will fall to the bottom when the vibrator is switched off. When the vibrator is switched on again, the disc rises to a position where its weight is just balanced by the force of the particles' bombardment, the pressure of the gas. More discs can be added on top of the first one, so increasing the pressure of the gas. It is easy to model gas law behaviour with this model.
    • The higher the temperature (and kinetic energy of particles), the larger the volume, at fixed pressure.
    • The higher the pressure, (weight of the disc), the smaller the volume at a fixed temperature.
    • The higher the temperature, the greater the pressure (number of collisions with the wall) for a fixed volume.
  • Notice too the density of particles at various heights which models the atmosphere.

This experiment was safety-tested in February 2006

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Modelling for Brownian motion

Kinetic Theory of Gases Model
Properties of Matter

Modelling for Brownian motion

Practical Activity for 14-16

Demonstration

Apparatus and Materials

  • Metal tray lined with cork mat
  • Marbles, coloured, 20 - 24, about 1 cm diameter
  • Marbles, large, several, about 2 cm diameter
  • Three-dimensional kinetic model kit
  • Electric motor, fractional horsepower


  • Power supply, low-voltage, variable
  • Retort stand, boss, and clamp
  • Polystyrene, expanded, piece of

Health & Safety and Technical Notes

See apparatus entry for:

Electric motor, fractional horsepower


Beware of marbles on the floor.

Read our standard health & safety guidance


If a different vibrator is used with the original tube and rubber-sheet base from the 3-dimensional kinetic model kit, the base can soon be damaged. However, the life of the base can be prolonged considerably by sticking a small disc of aluminium foil on the rubber.

Alternative methods Adapt this experiment by adding a small piece of expanded polystyrene and following its path:

Kinetic theory model for a gas


Closely observe a suspension containing mm scale polystyrene spheres, projected onto a screen using a visualiser with a data projector.

Procedure

  1. Add to the tray of marbles one or two larger marbles used in this experiment, and compare their motion with that of the smaller ones:

    Kinetic theory: two-dimensional model


  2. Alternatively, add a small piece of polystyrene to the 3D model, as used in this experiment:

    Kinetic theory model for a gas


Teaching Notes

  • The random path of a larger marble buffeted by the smaller ones suggests what you might see if you looked at, say, bits of ash in the air.
  • Similarly, the movement of the small piece of expanded polystyrene in the tube used for the experiment...

    Kinetic theory model for a gas


    ...shows a similar effect. However, here buoyancy and gravity play more noticeable parts than they would for ash in air. Nonetheless, taking the opportunity to try different sized scraps of expanded polystyrene, the students can predict the ways that smaller and larger fragments of ash will be seen to move in air, and even to realise why Brownian motion is only observed with microscopically small particles.

This experiment was safety-tested in December 2004

  • This video shows how Brownian motion can be observed in a suspension containing micrometre diameter polystyrene spheres. Using a microscope and video camera, students can observe the motion of the polystyrene spheres. The video also shows how Brownian motion can be simulated using a vibrating loudspeaker, table tennis balls and a small balloon.

  • This video shows footage of the movement of particles by Brownian motion and can be used in the classroom with your students:

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Model of expanding liquids and gases

Kinetic Theory of Gases Model
Properties of Matter

Model of expanding liquids and gases

Practical Activity for 14-16

Class practical

Students use marbles in a tray to model the expansion of liquids and gases.

Apparatus and Materials

  • Metal tray lined with cork mat
  • Marbles, coloured, 20 - 24, about 1 cm diameter

Health & Safety and Technical Notes

Beware of marbles on the floor.

Read our standard health & safety guidance


The metal tray should have near-vertical sides and a thin cork base. Each tray should contain 20 to 24 coloured marbles.

Procedure

  1. Add a few marbles to the tray and incline the tray slightly so that the marbles are touching, representing a liquid.
  2. Agitate the tray.
  3. Remove some of the marbles so that the model represents a gas.
  4. Again agitate the tray.

Teaching Notes

  • When the tray representing the liquid is agitated, the marbles move around each other and the volume they occupy increases a little.
  • In liquids the expansion is easier to explain. Heating raises the speed of the molecules which are in constant, colliding turmoil. Molecules push each other further apart, on the average, against those fairly long-range attractive forces which still hold the liquid together.
  • In the case of gases the picture of expansion is clearer still. Heating a gas makes its molecules move faster and so they transfer more momentum at each impact. If the gas is in a container that allows expansion then the bigger pressure will drive the walls of the container outwards until the pressure is the same as before but the gas has a bigger volume. The molecules are further apart and, having longer to travel, they bombard the walls less frequently though each impact is more violent.
  • If the heated gas is in a container which does not allow expansion, then the pressure of the gas on the container walls increases.

This experiment was safety-tested in March 2006

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Kinetic theory models

Kinetic Theory of Gases Model
Properties of Matter

Kinetic theory models

Teaching Guidance for 14-16

Students will probably have met the simple molecular picture of solids, liquids and gases. Matter is, in every case, made up of atoms or molecules, but with different amounts of arrangement (‘order’) and different types of motion.

The story of the development of the kinetic theory is too good a story to split up and tell as individual experiments. It demonstrates the interaction between observation and experimentation. Thinking about the causes of observed behaviour involves model-building and theorizing.

Show your students models, preferably in several forms, but murmur gentle warnings that a model is not the real thing. This kind of reservation is discouraging when young people first meet it. But they can learn to enjoy devising models and thinking in terms of them with much greater freedom and skill and imagination once they realize the scope of scientific models as scientists use them.

Show your students real balls as models of gases. Imagining their paths and collisions will help in thinking about gases, to suggest a line of investigation, or to illustrate a technical term such as ‘mean free path’. You might contrast such molecular models with mock-up models, such as a tiny wooden model of a fission reactor or a huge wax model of a flower. The latter models are used to aid people in visualising; the former are used for constructive thinking.

Discussion of physical models can lead on to an algebraic model developed from the kinetic theory for the pressure of a gas. The algebraic model can be used to make predictions. The equation of the pressure of a gas can be used, for example, to estimate the molecular speed and mean free path of the molecules. It could also lead to an estimate of Avogadro’s number from some simple measurements. Teaching-models such as these cannot prove a theory right. But they help students to visualize and understand the theory.

All theoretical physics uses models as essential parts of the framework of knowledge, but with great care to remember where the words, phrases, descriptions, are only parts of models. All models have their limitations as well as strengths, and it is vital to understand both. Without imaginative thinking in terms of models, scientific knowledge would be merely a pile of facts, codified here and there in laws, little more than a handbook of data.

Even if you cannot put these ideas over to students, think about the nature of science and the part played by models in it when you use demonstration models as part of your teaching.

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Estimate of molecular size: a more formal method

Kinetic Theory of Gases Model
Properties of Matter

Estimate of molecular size: a more formal method

Teaching Guidance for 14-16

Imagine molecules in a gas; dots spaced far apart. Add arrows to show the random motion, not all speeds (arrows) the same but speeds around the average. You could say:

'Here is a snapshot of air molecules in this room with the camera focused at one distance. To find how one molecule would move through this vast array of moving neighbours is too difficult a business. Instead, pretend that we freeze all the molecules except one and watch that one molecule go hurtling through the crowd.'

Redraw the picture showing each molecule as one round blob without any indication of velocity. Draw the path of the chosen molecule, as it moves to collide with another, as a cylinder swept out between the two molecules. The diameter of the cylinder is equal to the diameter of the molecule and its length is equal to the mean free path. Bend the path at the collision and another cylinder is swept out as shown this diagram:

The mean free path is many times longer than the separation between molecules and so the cylinder should pass many other molecules on the way to a collision.

Now move off to a separate preparatory discussion looking at such a collision in detail. Draw a large round molecule bouncing against another molecule.

'How far apart are the molecules, centre to centre, at the collision? One diameter.'

'I am now going to show you a trick for finding out how far a molecule goes before hitting another. This trick has been invented by scientists and is not what really happens but gives good results. When two molecules collide they must be 2 radii, or 1 diameter apart. Instead of drawing the collision like that, I could pretend that the molecule flying along to make the collision is much bigger, and any other molecule that it hits is much smaller. We get the same result as long as we have the centres of the two molecules 1 diameter apart at the collision. I am now going to push this to the limit and make the flying molecule have double the radius, equal to 1 diameter, and the molecule it hits have no radius at all.'

'Now we start this story all over again. Here is the artificial molecule flying along with radius equal to one molecular diameter. It sweeps out a cylinder of 1 molecular diameter in radius and collides with the artificial point sized molecule where it bends its path.'

'Think about the path swept out by this flying molecule which is possessively patrolling its "share" of the volume of the box. This volume is equal to d2x 10-7m.'

For justification of mean free path being 10-7m, see Guidance note...

Further discussion of mean free path


'We need to know the volume of space that belongs to one molecule of air in this room. The volume change from liquid air to air is about 1:750. If for liquid air each molecule of diameter, d, occupies a cubical box of side d, then the volume occupied is d 3on the average.'

750d3= d2x 10-7

d = 4 x 10 -10m

'We have found the diameter of a typical molecule of air. An atom is probably about half that size. This is certainly a rough estimate because our measurements were difficult and we made all kinds of risky moves carrying out our calculations. Yet this is a very good estimate for many working purposes. It is the right order of magnitude.

All we are really measuring here is an order-of-magnitude distance of approach at which inter-molecular forces grow large enough to have a noticeable effect. Air of course is a mixture of different gases, mainly nitrogen (about 78%) and oxygen (about 21%).

Careful measurements for particular molecules give different diameters according to the experiment chosen and the method of interpretation used. After all, the diameter of a molecule is not as definite a thing as the diameter of a steel ball. Both nitrogen and oxygen are diatomic molecules. Not only are diatomic molecules oblong but they behave as if squashy, so more violent collisions are likely to reveal a smaller effective diameter. Nitrogen molecules are very slightly larger than oxygen molecules; in their gaseous state both have effective diameters of about 3 x 10-10m.

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