Ideal Gas Model
Properties of Matter

Gas laws and absolute zero

for 14-16

Here are class experiments to find how the volume and the pressure of a fixed mass of gas vary with temperature, and how pressure and volume vary at fixed temperature. They also provide a means of introducing absolute zero and the Kelvin temperature scale.

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Pressure of air at constant volume

Pressure Law
Properties of Matter

Pressure of air at constant volume

Practical Activity for 14-16

Demonstration

Measuring the change in pressure when air is heated at constant volume.

Apparatus and Materials

  • Crushed ice
  • Bourdon gauge
  • Round-bottomed flask, 250 ml
  • Rubber bung and tubing
  • Aluminium container or water bath
  • Tripod
  • Electric kettle to provide hot water OR Bunsen burner and tripod
  • Stand and clamp to hold the flask down
  • Heatproof gloves
  • Rotary vacuum pump (optional)
  • Thermometer -10°C to 110°C

Health & Safety and Technical Notes

Heatproof gloves will be needed to handle the flask and water bath after the experiment unless they can be left to cool down.

If a rotary vacuum pump is used, remember that it is too heavy for one person to lift or carry.

Read our standard health & safety guidance


You can improve the accuracy of measurements in this demonstration by ensuring that the neck of the flask is in the water. This probably means using a clamp to hold the flask in the water.

Procedure

  1. Connect the Bourdon gauge to the flask.
  2. Note the gauge reading when the flask is first immersed in cold water (preferably at or near the freezing point). Then note it with the flask in hot water (preferably at or near the boiling point).

Teaching Notes

  • As the air inside the flask is cooled, its molecules move more slowly. Collisions with the walls become less frequent and less violent, meaning pressure falls. When the air is warmed, molecules move faster. Collisions with the walls become more frequent and more violent, meaning pressure rises.
  • If you measure the water temperature, you can take a set of pressure readings against temperature and plot a graph. The Bourdon gauge scale will probably have to be interpolated because it may not be sensitive enough. About 40 kN m -2 pressure change should be obtained between 0 and 100°C. If you start counting temperature at minus 273°C the line will pass through the origin, showing that pressure is proportional to temperature.
  • If you attach a T-piece and tap or clip to the flask, you can pump out about two-thirds of the air. Then you can try the experiment at another density. The change in pressure should be in the same proportion.
  • Having noticed that the pressure falls as the temperature decreases, ask whether we could predict a temperature at which the pressure would be zero. (To get students to see this is not a daft idea, get them to consider what happens to the motion of the molecules as the temperature falls.)
  • Either by calculation or - better - by drawing onto an extra sheet of graph paper, get them to extrapolate to find values of the temperature at which the pressure would be zero. Discuss its significance.
  • The Bourdon gauge may be calibrated in a variety of units, lb in -2 , kg m -2 , N m -2 , etc. Check that you can translate these into units your students are used to. See CLEAPSS Laboratory Handbook, section 20.24.

This experiment was safety-tested in August 2007

Up next

Expansion of a gas at constant pressure

Ideal Gas Model
Properties of Matter

Expansion of a gas at constant pressure

Practical Activity for 14-16

Class practical

Apparatus and Materials

For each group of students

  • Washing-up bowls with hot and cold water from taps
  • Round-bottomed flask
  • Bung with narrow-bore tubing to fit
  • Access to lubricating oil

Health & Safety and Technical Notes

Warn the class to handle the long glass tubes carefully as they are (relatively) easily broken.

Read our standard health & safety guidance


Glass test-tubes and corks with capillary tubing can be used in place of the flasks. The drop of oil is added to the bung-end of the tube before insertion into the flask.

Procedure

  1. Trap the air in the flask with a small bead of oil in the glass tubing. Gently heat the flask with your hand. This will produce a sufficient temperature rise for the oil index to move up the tubing.
  2. Plunge the flask first into cold and then into warm (not hot) water.

Teaching Notes

  • The oil plug will rise up the glass tube as the air in the flask expands (in warm water) and fall as the air contracts (in cold water). The volume expansion of a gas is approximately 500 times that of glass, so it is unlikely that the expansion of the flask will have any noticeable effect.
  • Students may already know that a gas is made up of rapidly moving molecules which hit the surfaces of the container and exert a force on the container so creating a pressure. If the temperature of the container is raised, molecules move faster. The pressure exerted by the gas will therefore increase.
  • Plunging the flask into hot water may increase the volume of the gas so much that either the oil plug flies out of the tube, or it breaks up and runs down the inside of the tube.

This experiment was safety-tested in August 2006

Up next

Thermal expansion of air - Charles' law

Charles' Law
Properties of Matter

Thermal expansion of air - Charles' law

Practical Activity for 14-16

Class practical

Expansion of air at constant pressure and an indication of absolute zero (-273°C).

Apparatus and Materials

For each group of students

  • Concentrated sulfuric acid
  • Beaker, deep (see technical note)
  • Bunsen burner
  • Capillary tube with liquid index (see technical note)
  • Tripod
  • Thermometer -10°C to 110°C
  • Ruler, 300 mm
  • Lab oven (if available)
  • Rubber bands

Health & Safety and Technical Notes

When you seal the tubes, avoid a long taper at the end.

Take care when handling concentrated sulfuric acid.

Read our standard health & safety guidance


It is almost impossible to obtain tubing with this bore and not a very thick wall: 3 mm outer diameter and 1 mm inner diameter is ideal. If suppliers will not stock it, this experiment could be omitted.

The beaker should be deep enough for all the air column in the tube to be immersed in water.

The capillary tubes should be about 20 cm long and 1 mm bore, closed at one end and open at the other.

To insert the index:

  1. Put all the tubes into a deep beaker of strong brine and bring it to the boil. This will ensure that the tubes are dry internally as well as hot.
  2. Whilst hot, dip the open end of each tube into a small beaker containing concentrated sulfuric acid, so that a 5 mm length of acid is drawn in to the tube as it cools.
  3. Leave the tube to cool further. The index will be drawn to a suitable position just over halfway along.

If a laboratory oven is available, the tubes can be heated to 120°C for about 20 minutes instead of using brine.

Sulphuric acid is hydrophilic; it removes water vapour from the air trapped in the capillary tube. If you do not like working with acid, the experiment could be tried with an oil plug but the water vapour pressure in the air column would then distort the results.

Procedure

  1. Fix the capillary tube and thermometer to the ruler with rubber bands at each end. Measurements are easier if the end of the air column inside the tube coincides with the zero of the centimetre scale on the rule.
  2. Put the tubes into the deep beakers with the open end free to the air.
  3. Add water, or water and crushed ice, to the beaker, always ensuring the trapped air column is under the surface of the water in the beaker. Stir.
  4. Record the temperature and length of the air column.
  5. Repeat for about four more temperatures, plotting the graph as the experiment proceeds.

Teaching Notes

  • Students need to appreciate that the way the length of column changes reveals how the volume of the air alters ( volume = length x cross-sectional area).
  • The data should give straight-line graphs, although there may be a need to discuss the uncertainties in the readings.
  • Once students recongnize that the length/volume of the air column decreases as the temperature falls, ask whether they could predict a temperature at which the pressure would be zero.
  • An alternative method could use a test-tube with a capillary tube through its bung, as in the experiment:

    Expansion of a gas at constant pressure


This experiment was safety-tested in August 2006

Up next

Gas pressure rises with temperature

Pressure Law
Properties of Matter

Gas pressure rises with temperature

Practical Activity for 14-16

Demonstration

A quick, dramatic demonstration to show the pressure of a fixed volume of gas increases with temperature.

Apparatus and Materials

  • Tin with lid
  • Bunsen burner
  • Tripod
  • Safety screen
  • Heatproof gloves

Health & Safety and Technical Notes

Safety screens are needed with the class sitting well back.

Heat-proof gloves should be available for retrieving the lid and the hot tin.

Read our standard health & safety guidance


The tin should have a well-fitting, push-in lid.

To ensure a reliable result, it is not unknown for teachers to secrete a small amount of water in the tin before sealing with the lid. It is helpful to try out this demonstration before the lesson, allowing enough time for the tin to cool down again! (It has not been unknown for the lid to stay fixed in place even after several minutes heating of dry air only.)

Procedure

  1. Show the tin to contain (or appear to contain) only air before gently pushing in the lid.
  2. Place on the tripod and then heat using the Bunsen burner until the lid is blown off.

Teaching Notes

  • Apart from being dramatic - and thus memorable - this demonstration provides an opportunity to get students thinking about what has happened in terms of molecules.
  • Help students to understand that as temperature increases the particles move ever faster, hitting the walls of the tin, and its lid, both harder and more often. This means the pressure rises. Pressure rises until it is sufficient to force the lid off.

This experiment was safety-tested in March 2006

Up next

Variation of gas pressure with temperature

Pressure Law
Properties of Matter

Variation of gas pressure with temperature

Practical Activity for 14-16

Class practical

This experiment leads to the concept of absolute zero. Students investigate the effect of temperature on the pressure of a fixed volume of gas.

Apparatus and Materials

For each student group

  • Bourdon gauge
  • Flask, 250 ml, fitted with bung, glass tube and polythene or rubber tubing
  • Metal container for flask, fitted with wire stirrers
  • Thermometer -10°C to 110°C
  • Crushed ice
  • Electric kettle to provide hot water OR Bunsen burner and tripod
  • Retort stand, boss, and clamp

Health & Safety and Technical Notes

Ensure that the can support can be removed, so that the can may be lowered safely without moving the flask.

Read our standard health & safety guidance


School kitchens might be a source of deep tins large enough to contain the flasks, stirrers and thermometers.

The flasks need to be immersed up to their bungs. Wire each bung to the neck of its flask so it cannot easily be dislodged. The stirrers need to be able to move past the flasks; their use is vital to the success of this experiment.

Procedure

  1. Ensure the tubing from the flask fits tightly onto its Bourdon gauge and is as narrow and short as possible. Using stands, bosses and clamps, if necessary, hold the bung and the Bourdon gauge.
  2. Put a small amount of ice into the container, add the stirrer and bring it up around the flask before adding some more ice. Then top up the water so all the air in the flask is immersed.
  3. Stir and record the temperature and corresponding pressure.
  4. Carefully remove the can and empty it of ice. Replace and add cold water.
  5. Stir and record the temperature and corresponding pressure.
  6. Repeat with mixtures of cold and hot water, and finally with just hot water. Aim to get five sets of readings with roughly evenly separated temperatures.
  7. Plot a graph of pressure against temperature.

Teaching Notes

  • The data should give straight-line graphs, although there may be a need to discuss the uncertainties in the readings.
  • Once students recognize that the pressure falls as the temperature decreases, ask whether we could predict a temperature at which the pressure would be zero. Get them to consider what happens to the motion of the molecules as the temperature falls.
  • Either by calculation or - better - by drawing onto an extra sheet of graph paper, get them to extrapolate to find values of the temperature at which the pressure would be zero. Discuss its significance.
  • With an able group, this provides an opportunity to discuss the benefits and dangers of both extrapolation and interpolation. Interpolation can be safe but dull. Extrapolation is rash but sometimes very fruitful.
  • A discussion with students could follow:
  • "What happens to the pressure of air when heated like that? If pressure is just the result of molecules bombarding the walls, why does the pressure change?"
  • "How can the molecules make a bigger pressure? There are just as many as before. (Heating cannot manufacture more molecules.) So the same lot of molecules make more pressure. How?"
  • You hope that students will say "the molecules must bombard the walls more often and more violently".
  • Coax students to statements like: "thus if more often, the molecules must be moving faster; and if more violently, something must have changed to make the collision more violent".
  • Suggest that "if a gas molecule makes a more violent collision when it hits the wall, that must be because it is moving faster."
  • Both suggestions, more frequent collisions and more violent collisions lead to the idea of molecules moving faster in a hotter gas.
  • Then reverse the story: "If molecules move faster, they will make more violent collisions (change more momentum) and they will arrive back at the wall for another bang more often. So you might expect the speed to appear twice over as a factor in the pressure. Pressure varies as temperature, and as (speed) 2 . Energy stored kinetically also varies as (speed) 2 . Temperature is related to the energy stored kinetically.

This experiment was safety-checked in August 2006

Up next

Warming up a gas by speeding up its particles

Ideal Gas Model
Properties of Matter

Warming up a gas by speeding up its particles

Practical Activity for 14-16

Demonstration

Apparatus and Materials

  • Metal-bodied bicycle pump
  • Thermocolour film, cut to suitable size

Health & Safety and Technical Notes

Read our standard health & safety guidance


ALTERNATIVE method: demonstrates how compressing a gas increases its temperature. A small piece of cotton wool is placed into the bottom of a narrow plastic tube. When the air is rapidly compressed by a piston, the air temperature increases and the cotton ignites. The 'fire piston' can be used to illustrate the transfer of energy, kinetic theory and Charles' law.

Procedure

  1. Fully extend the pump and block the hole at the bottom with a close-fitting bolt and PTFE tape. Attach the thermocolour film to the sides of the cylinder near the bolt.
  2. Make sure that the bicycle pump is cool. The temperature should be at the bottom of the range that the film will indicate.
  3. Fully extend the pump and squash the air up rather suddenly with one good push. Leave the piston at the position of maximum compression.
  4. Watch for the temperature rise of the cylinder, as shown by the thermocolour film attached to it.

Teaching Notes

  • This is another simple experiment that can be explained through kinetic theory. Ask students to explain what an increase in temperature of a gas suggests about the particles of the gas. Follow this up by asking for explanations of the increased particle speed. It may take some time before the class is happy that collisions with the approaching piston increase the velocities of the gas particles. (Consider the momentum changes of an air particle as it rebounds from the approaching piston.)
  • This experiment comes from AS/A2 Advancing Physics. It has been re-written for this website by Lawrence Herklots, King Edward VI School, Southampton:

    AS/A2 Advancing Physics


This experiment was safety-tested in June 2004.

  • This video shows how to set up a 'fire piston' to illustrate the transfer of energy, kinetic theory and Charles' law:

 

 

Up next

Theoretical thoughts: extrapolation

Ideal Gas Model
Properties of Matter

Theoretical thoughts: extrapolation

Teaching Guidance for 14-16

A risky guess

When students continue their graph (or calculate) on down to find absolute zero, they are making a risky guess that the behaviour of a gas would stay the same. Explain that continuing beyond all measurements like that is called extrapolation.

You could say that:

Extrapolation is a risky business, trusting or pretending that what you have observed continues on and on.

Did the Sun rise in the East this morning? Did it rise in the East yesterday? Did it rise in the East many a morning before that? Are you willing to extrapolate these observations into the future and say that you are sure the Sun will rise in the East tomorrow? Are you quite sure?...

Suppose you were not a human being but were a butterfly who emerged from a chrysalis on a warm day in early summer and flew about from flower to flower, day after day. What would you observe about the weather? A fine day, another fine day, another fine day, ... If you were that insect, you might extrapolate and predict that every day in the future would be fine. You would not foresee the wintry day which would end your happy flights.

Extrapolation and interpolation

Extrapolation would be very risky if we trusted it for the molecules of a real gas like air or carbon dioxide. If we cool any gas enough, it fails to remain a gas, for example carbon dioxide becomes cold solid crystals of dry ice. Air that has been cooled down and pushed together so that its molecules (moving relatively slowly at that low temperature) hang together in a liquid.

You could say:

Yet we can safely make the extrapolation in imagination and find a useful absolute zero as a starting point for the grand Kelvin scale of temperature.

Interpolation means reading something off a graph between two measured points on it. (Or you can calculate an intermediate value between two values given in some table.) Interpolation is useful in science and engineering; and, if carefully done, it is safe. But in developing new science and technology, extrapolation is more important.

Although extrapolation is risky, it is the way in which some of the great discoveries have been made. Scientists guess what might happen if they continued our knowledge into an unknown region, then they try to test their guess by experiments. And sometimes, those experiments lead them in quite a new direction of knowledge.

Extrapolation is rash but sometimes very fruitful; interpolation is safe but dull.

Up next

From the pressure law to the Kelvin scale

Ideal Gas Model
Properties of Matter

From the pressure law to the Kelvin scale

Teaching Guidance for 14-16

The experimental graph of pressure against temperature is likely to be straight enough to justify asking whether the plotted points (the true results of the experiment) fit closely to an ideal simple law. This is what we would like to find because it makes our description of nature easy and simple. If some students have graphs that do not seem to suggest a straight line, then a picture gallery of everybody's graph can be organized. That will enable the class to extract a general conclusion, as in a professional research team's work.

Then suggest each student should extend the line backwards to look for absolute zero. They can either draw new axes so the temperature scale can be extended backwards to about 300ºC below the ice point or pages of graph paper stuck to the original graph until the line cuts the temperature axis. It is also possible to calculate the position of absolute zero algebraically, using the slope of the line.

Get students to think on these lines:

"What happens to the motion of the molecules when you cool the air? Think of cooling the air more and more... could you cool it until its molecules had no motion at all? Suppose there was such a temperature: somewhere far down on the scale of the thermometer at which molecules would have no motion at all. What would the pressure be like at that temperature? If we trust our picture of gas models we expect the pressure to fall to nothing."

Students should emerge with a clear idea that, judged by a mercury thermometer, gas pressure runs down an almost straight line as temperature falls. The straight line reaches zero pressure at a temperature somewhere between -250ºC and -300ºC (-273°C), called absolute zero. Tell them this process of extending the graph backwards beyond the reading is called extrapolation. It is a risky process because we do not know if the gas will continue to behave in the same way.

You could ask students to imagine an ideal gas and discover what the temperature would be at which that gas would collapse with no useful motion.

Say:

"The absolute scale of temperature can be defined by shifting the zero from the ice point to this new zero and reckoning all temperatures from there. All we do is add 273 to all Celsius temperatures in order to create the temperature on this new Kelvin scale. The close agreements amongst many gases persuade us to redefine our temperature measurement for gas thermometers and then finally move to the Kelvin scale. The Kelvin scale has several advantages:"

  • If you keep the volume of a sample of gas constant, its pressure goes up in direct proportion to the Kelvin temperature. This is automatically true for an ideal gas; fortunately many gases have almost identical behaviour, except at very low temperatures.
  • For standard thermometers, you can change from ordinary mercury thermometers, which are convenient, to a gas thermometer. This is a bulb and pressure gauge similar to the class experiment. Instead of using it to investigate a sample of air, turn the argument round and say:

"'Henceforth we choose to measure temperatures on a scale that uses a gas thermometer with an ideal gas in it"

  • There is a very fruitful theory of heat engines, thermodynamics, which offers many remarkable predictions, all of which necessarily use the Kelvin scale. Without the idea of that scale, and without practical gas thermometers for measurements, the predictions of thermodynamics would be useless, just hot air.

"You will find that real gases give an almost straight line graph when their pressure is plotted against Kelvin temperature. The expansion of mercury happens, by a lucky chance, to give a fairly straight line when plotted against Kelvin temperature measured by a gas thermometer. That lucky chance makes it comfortable to use mercury thermometers for measuring ordinary temperatures in the laboratory. For higher temperatures, Bunsen flames, mercury thermometers are useless and in very cold weather the mercury freezes. The Kelvin scale extends from zero as high as you like, millions of degrees in nuclear fusion."

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