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Boyle's law
- Gas pressure: forces required to compress and expand
- Pressure exerted by a stream of balls
- Massive beam and anvil to show pressure exerted by a stream of balls
- Boyle's law
- Three-dimensional model used to illustrate Boyle's law
- Why does reducing volume increase pressure?
- Larger kinetic model to illustrate Boyle's law
- Equi-partition of energy
- A simple theory of a gas
Boyle's Law
Properties of Matter
Boyle's law
for 14-16
Boyle developed a purely mathematical relationship between pressure and volume. His experiment still provides a good starting point for the study of the gas laws, and the underlying kinetic theory that explains them.
Properties of Matter
Gas pressure: forces required to compress and expand
Practical Activity for 14-16
Class practical
As with a spring, force is required to compress or to expand a gas.
Apparatus and Materials
Bicycle pumps or syringes.
Health & Safety and Technical Notes
Ensure that there are no needles available to fit on the syringes.
Read our standard health & safety guidance
Procedure
- Drive in the piston of the bicycle pump or syringe with the outlet open. Repeat with a finger placed over the outlet. Ask students for their ideas about what produces the force acting against the applied force.
- With the piston almost fully inserted in the syringe, place your finger over the outlet. Then try to pull the piston out. Ask students how the directions of the applied force and the force due to the gas have changed.
Teaching Notes
- If you judge your group to be sufficiently responsible to work with syringes, and enough are available, the activity can become a short class experiment.
- Note that, with the outlet blocked, the piston tends to return to its original position when you release it. Robert Hooke, the seventeenth century physicist, commented on the
springiness of air
. - You can use the activity as a reminder of the particulate nature of matter. Particles in a gas are much easier to push closer together or further apart than particles in a liquid or solid. This is because of the relatively large spaces and weak forces between them. Show the contrast between the behaviour of gas and liquid by filling a syringe with water, and then pushing on the piston. (But take care if you want to stay dry!)
- Any convenient solid object will illustrate the difficulty of pushing particles in a solid closer together. (If liquids and solids change shape when you exert a force on them, it is a result of rearrangement of particles rather than change in their spacing, unless the material is subject to high stress.)
This experiment was safety-tested in January 2006
Up next
Pressure exerted by a stream of balls
Demonstration
This demonstration models gas molecules hitting a wall.
Apparatus and Materials
- Toy shop marbles, steel balls or lead shot
- Spring balance, domestic or lever-arm balance
- Tray, a deep one, or lots of books
Health & Safety and Technical Notes
Read our standard health & safety guidance
Either a domestic balance or a lever-arm balance can be used for this experiment. Turn over the scale pan so that the balls bounce off without collecting on the pan. Place a deep tray under the balance (or set up a barrage of books round the balance) to catch the balls.
Procedure
Pour, by hand, a stream of balls, from a height of 30 cm or so, onto the inverted scale pan on the balance.
Teaching Notes
- As the balls hit the pan and bounce off they exert small impulsive forces. The comparatively great mass of the pan and balance smear out these forces into a steady push shown by the balance. Gas pressure results from impact forces like these spread over a surface.
- P = F/A, where P = pressure, F = force, and A = area over which force acts.
This experiment was safety-tested in March 2005
Up next
Massive beam and anvil to show pressure exerted by a stream of balls
Properties of Matter
Massive beam and anvil to show pressure exerted by a stream of balls
Practical Activity for 14-16
Demonstration
This is a larger, more dramatic version of:
Pressure exerted by a stream of balls
Apparatus and Materials
- Anvil and beam
- Marbles or 13 mm steel balls (not small steel balls)
Health & Safety and Technical Notes
Eye protection must be worn. The teacher must stand on a step-ladder to release the balls, not
on a stool or on a bench.
Read our standard health & safety guidance
Construct a see-saw with a massive elastic anvil at one end. You can make a very good version by placing a sheet of about 13-mm Perspex on top of a massive steel block, with a thin layer of glycerine between them. Screw the Perspex into the steel near the edges.
The anvil should be placed on a large wooden beam, which is pivoted near that end. The pivot could be a steel rod, fixed to the beam, free to roll on supports at the side. The other end of the beam must carry a counterweight and a pointer to indicate deflections.
Place a large tray under the apparatus (or make a barrage around it) to catch the balls. (An inflatable paddling pool may be suitable.)
Procedure
Pour a stream of marbles or steel balls from as high as possible above the anvil and the see-saw shows there is a deflecting force on the beam.
Teaching Notes
It helps if there is a release mechanism so the marbles or steel balls fall vertically onto the anvil. This is not an easy demonstration to set up but it is impressive when working.
This experiment was safety-tested in March 2005
Up next
Boyle's law
Demonstration
Apparatus and Materials
- Boyle's law apparatus
- Foot pump and adaptor
- Kinetic theory model kit (transparent cylinder with small steel balls)
Health & Safety and Technical Notes
It has been known for the glass tube to fly upwards when the gas is at maximum pressure. To prevent this, check the compression joint holding the tube and any tube supports before use. (The apparatus is filled and emptied by removing the pressure gauge.)
Read our standard health & safety guidance
The apparatus has been specially designed to give quick, clear readings which the class can see.
A sample of dry air is confined in a tall, wide glass tube by a piston of oil. The volume is found from the length of the air column, which should be clearly visible at the back of the class.
The pressure is read from a Bourdon gauge connected to the air over the oil reservoir. This is calibrated to read absolute pressure and is also visible from the back of the class.
The foot pump is attached to the oil reservoir and is used to change the pressure. The gauge reads up to 3 x 10 5 N m -2 and the pressure can safely be taken up to this value but must not be taken beyond.
To fill the apparatus with oil, unscrew the Bourdon gauge with a spanner and fill the chamber with a low vapour pressure oil. Tilt the apparatus in the final stage of filling in order to get enough oil into the main tube. When refixing the gauge, tighten the nut to get a good seal, but not so much that the thread is damaged.
Procedure
- Give a quick demonstration to show that doubling the pressure halves the length of the air column, and so its volume.
- Increase the pressure to its maximum value, and then record it and the (minimum) length of the air column.
- Next, disconnect the pump and release a little air using the valve on the oil reservoir, so that the oil level in the tube falls a few centimetres.
- Before taking the next pair of readings, wait a while so that the air temperature recovers and the oil left behind has fallen down the wall of the tube.
- Keep repeating step 3 until the gauge returns to atmospheric pressure.
Teaching Notes
- It is important to ensure that students have grasped that the volume of the air column is directly proportional to its length, so that the way the length changes tells us how the volume alters. (It is not hard to get a good estimate of the internal diameter of the tube, if finding the cross-sectional area of the air column would help.)
- It is helpful if students plot a graph of pressure ( P ) against lengths of air columns ( V ). This can lead them to see that trying a graph of P against I/length (I/V) might be a good idea.
- Students might then also use a spreadsheet to find how the product of pairs of values P x length (P x V) compare.
This experiment was safety-tested in January 2006
Up next
Three-dimensional model illustrating Boyle's law
Properties of Matter
Three-dimensional model used to illustrate Boyle's law
Practical Activity for 14-16
Demonstration
Apparatus and Materials
- L.T. variable voltage supply (capable of 8 A at 12 V)
- Kinetic theory model kit (transparent cylinder with small steel balls)
- OHP pen (soluble ink)
- Retort stand, boss, and clamp
Health & Safety and Technical Notes
Read our standard health & safety guidance
See the warning on the apparatus page on the use of a:
Electric motor, fractional horsepower
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 DC terminals of the variable voltage supply in parallel to the field and armature terminals of the motor. About three dozen small, phosphor bronze balls are needed. Put the paper disc, with wire attached, in the tube as a piston. The wire goes through the hole in brass cap which should be put over the top of the tube.
Add cardboard weights on top of the disc to increase the pressure
on the gas
.
(More modern versions of this apparatus are available, of course.)
Procedure
- Increase the voltage to about 6 volts, and mark the position of the piston on the cylinder with the OHP pen.
- Next, add more paper weights to the piston to show that, as the pressure increases, the volume decreases.
- Now turn off the motor and double the number of balls in the cylinder. Then switch on the motor again. The paper piston will now be seen to settle higher up the tube. Additional paper weights must be added to return it to its original position.
Teaching Notes
- The point of step 3 is to remind the class that Boyle's law applies only to a fixed mass of gas.
This experiment was safety-tested in March 2005
Up next
Why does reducing volume increase pressure?
Class practical
Apparatus and Materials
For each pair of students
- Kinetic model kit, two-dimensional
- Marbles, coloured, 20 - 24, about 1 cm diameter
- Metal tray lined with cork mat
Health & Safety and Technical Notes
Watch out for marbles which may roll accidentally onto the floor.
Read our standard health & safety guidance
Procedure
- Agitate the tray, listening to the sound of the marbles hitting the sides of the tray.
- Put a ruler across the tray to reduce the area occupied by the marbles. As it will not be easy to hold the ruler still, it helps to put a book in the tray and to hold the ruler firmly up against it.
- Now agitate the tray in the same way as earlier. You should hear an increase in noise as the marbles strike the tray walls at a greater rate than before.
Teaching Notes
- This model shows the increase in pressure caused by a decrease in volume.
- If students add a lot more marbles, they can listen to what happens to the pressure (it rises).
This experiment was safety-tested in March 2005
Up next
Larger kinetic model to illustrate Boyle's law
Demonstration
This experiment is quite elaborate, but it yields quantitative results. A beam balance weighs
the pressure.
Apparatus and Materials
- Vibration generator
- Signal generator
- Thread
- Aluminium sheet
- Beam balance
- Rubber sheet
- Cylinder, wide, 10 cm diameter
- Plastic balls, large
Health & Safety and Technical Notes
Read our standard health & safety guidance
Hang a light piston of aluminium sheet by a thread from one side of a beam balance. The thread needs to run through a hole in the floor of the balance.
The piston should fit loosely in a wide vertical cylinder, about 10 cm in diameter.
Fix a rubber sheet over the base of the cylinder and place some large plastic balls, such as those used for electrostatic experiments, into the cylinder.
Adjust the height of vibrator so that its vibrating rod is just a millimeter or two below the rubber sheet.
Procedure
- Balance the beam with the vibrator turned off.
- Turn on the vibrator - try 50 hertz - and add weights to the balance to measure the force exerted by the bombardment.
Teaching Notes
- If the vibrator and cylinder are raised, halving the volume, you should find that the pressure is doubled.
- If, instead, the number of balls is increased, you should find that the pressure increases proportionately.
This experiment was safety-tested in March 2005
Up next
Equi-partition of energy
Statistical studies, combined with the assumption that every molecular collision is elastic, lead to the conclusion that the molecules of all gases at the same temperature store the same amount of energy kinetically. This ignores one very important physics principle, the equi-partition of energy theorem.
The full form of this theorem states that each degree of freedom will on average have the same energy. The linear motion of molecules entails three degrees of freedom – motions in the x, y and z directions. A gas whose molecules are simple atoms, such as helium or neon, has only these three kinds of motion. A molecule made from two or more atoms, however, can move in additional ways: it will have rotations and vibrations.
At the beginning of the twentieth century, it seemed clear that equi-partition should apply to the energies of rotation and vibration. However, certain experiments, such as those measuring thermal capacities over a wide range of temperatures, threw increasing doubt on this. The full form of equi-partition theorem failed, and quantum theory explained why.
Equi-partition among linear motions still applies. All gas molecules, at a given temperature, have the same average kinetic energy.
Useful results
Average energy for molecules of gas A = average energy of molecules for molecules of gas B, at the same temperature. mA < vA2> = mB < vB2>
So you can compare molecular speeds if you know the relative molecular masses.
Another equation derived from the kinetic theory of gases: pV = 1/3 Nm < c 2 > where p is the gas pressure, V is gas volume, N the number of molecules, m their mass and < c 2 > their mean square speed. This equation tells you that equal volumes of gases at the same pressure and temperature must contain the same number of molecules (Avogadro’s rule).
Up next
A simple theory of a gas
The atoms or molecules in a gas are widely separated from one another and interact only when they collide. Each one changes its direction of travel only in collisions. This theory of a gas relates macroscopic quantities that we can measure (such as pressure, volume and temperature) to the motion of its molecules. Developed in the nineteenth century, it is called kinetic theory
because the molecules are always in motion.
Suppose the pressure of the gas on the walls is produced by the impact of bombarding molecules. Attach a pressure gauge to the box and read the pressure.
Now suppose that you put more and more molecules into the box until there are twice as many as before. The picture below shows a microscopic demon popping in additional molecules one by one, through a trap door.
When there are twice as many molecules as before, what pressure would you expect? With twice as many molecules to bombard the walls, you might expect double the pressure.
Of course with more molecules, collisions would also happen more often in the middle of the box. But those internal collisions would not affect the bombardment of the walls, for the following reason. Suppose there are two molecules moving in opposite ways, heading for opposite ends of the box, where each will add its contribution to the pressure. If they do not collide, but just pass each other, each will arrive at its target end. If they do collide head-on, they will rebound, elastically. Then each of them takes on the other one’s job and does what the other would have done without a collision.
Therefore, you might expect double the number of molecules to produce double the pressure. Yet all the pressure gauge can notice is a doubling of the local population of molecules, in other words, a doubling of density.
There is another way that you could double the density. Push the end wall of the box in, as a piston, so that the air occupies half the volume. Result: the pressure gauge would show the pressure doubling. So collision theory leads to a prediction: Halving the volume of a gas will double its pressure. Does experiment confirm this is true?
Robert Boyle did an experiment to investigate the relationship between pressure and volume more than three centuries ago. He was not testing a theory, but simply taking measurements. In 1661 he announced his result ‘concerning the spring of air’ to the Royal Society. It is now called ‘Boyle’s law’. Provided the temperature is kept constant, the product of gas pressure and volume is constant.
Real gases
Real gases do not behave in this ideal way. Molecules are not point-like particles, and there are likely to be so many of them in the box that space for movement is reduced. Molecules move a shorter distance to and fro. Bombardments happen a little more often, and the pressure is a little larger than for point-like particles.
Also molecules attract each other when they are fairly close, as surface tension shows. This effect decreases gas pressure when molecules are crowded close together and moving slowly, at low temperatures. Some of the slowest molecules are weeded out and never reach the walls. There is a less dense layer near the walls and that exerts smaller pressure.
In real gases, both of these effects are found at high pressure and small volumes, but they can be distinguished because they change in different ways with temperature. At low temperatures the effects of molecule size remain much the same, but the effects of attraction make themselves felt so strongly that gases can liquefy.