2

HEAT

Although heat at first appears to have nothing to do with motion, it is now understood that heat is the motion of molecules. The connection between heat and motion was provided by Benjamin Thompson (1753-1814), an American who sympathized with the British during the Revolutionary War and eventually settled in Bavaria and became Count Rumford[1]. While watching the boring of artillery cannons in Munich in 1798, he concluded that motion could be transformed into heat and estimated the mechanical equivalent of heat.* Half a century later the experiment was refined and repeated by James Prescott Joule (1818-1889), the son of an English brewer. Joule's careful quantitative measurements became a model for modern science[2]. For our purposes, we will include in the chapter on heat such topics as fluid mechanics, phase transitions, cryogenics, thermodynamics, kinetic theory and combustion.

*Now defined as 4.186 joules/calorie

REFERENCES

1. S. C. Brown, Benjamin Thompson, Count Rumford, MIT Press: Cambridge, Massachusetts (1979).

2. H. J. Steffens, James Prescott Joule and the Concept of Energy, Science History Publications: New York (1979).

Table 2.1

Physical Properties of Selected Gases

                             Molecular  Freezing Boiling  Density
                             Weight     Point    Point    (g/liter)
Gas                  Formula (g/mole)   (°C)     (°C)     (1 atm)

Argon                Ar      39.95      -189.2   -185.9   1.633
Carbon dioxide       CO2     44.01                -78.5a  1.799
Helium               He       4.00      -272.2b  -268.9   0.164
Hydrogen             H2       2.02      -259.1   -252.9   0.082
Methane              CH4     16.04      -182.6   -161.5   0.656
Neon                 Ne      20.18      -248.7   -246.1   0.825
Nitrogen             N2      28.01      -209.9   -195.8   1.145
Oxygen               O2      32.00      -218.4   -183.0   1.308
Sulfur hexafluoride  SF6    146.05                -63.7a  5.970
Xenon                Xe     131.30      -112.0   -108.1   5.367
aSublimation point.
bAt 26 atmospheres. 4He will not freeze below a pressure of about 20 atmospheres.

General Safety Considerations

The demonstrations in this chapter present special hazards, since most involve very hot or extremely cold substances, volatile chemicals, fragile glassware, high pressure gases or evacuated containers. Procedures should be developed to ensure that the demonstration can be done without danger to the audience or to one's self. Hot and cold substances should be handled with tongs or with special, thermally insulated gloves. Eye protection should be worn not only to avoid personal injury but to set a proper example for the audience. A fire extinguisher, first aid kit, safety shower and telephone should be available nearby.* The person performing the demonstrations should know where these are located and how to use them. An assistant trained in first aid and CPR provides an extra measure of protection. If there are children in the audience they should be cautioned not to attempt certain of the demonstrations at all and not to do others unless a parent or another adult is present. The reason for the precaution should be explained to them.

*Available from Lab Safety Supply, P. O. Box 1368, Janesville, WI 53547-1368 (608) 754-2354

In the event of a burn, the burned skin should be put under cold water until the pain goes away. If blisters are present, they should be covered with a sterile gauze. If the burn is severe or if a large area is involved, one should see a doctor. With frostbite, the area should be warmed slowly with lukewarm (about 106°F) water or with another part of the body, such as putting a finger under an armpit. Cuts and abrasions should be cleaned with soapy water, dried and covered with sterile gauze. If bleeding is severe, apply pressure to the cut and/or the pulse point above the cut. Elevate the cut above the level of the heart. If bleeding persists or if the cut is severe, one should see a doctor within a few hours to have the cut stitched.

Safety considerations specific to sound, electricity and lasers will be covered in subsequent chapters.

2.1

Liquid Nitrogen Cannon

The rapid evaporation of liquid nitrogen inside a steel cylinder exerts enough pressure to blow a cork stopper off the cylinder.

MATERIALS

PROCEDURE

A spectacular demonstration involving the vaporization of liquid nitrogen can be done by lowering a small stainless steel cup (~30 milliliters) suspended by a wire and filled with liquid nitrogen into a larger steel cylinder (40 cm long × 5 cm i.d.) sealed on one end. A cork stopper is pounded into the other end with a mallet. Then the whole device is picked up and shaken in order to spill the nitrogen from the cup. When the liquid nitrogen strikes the wall of the cylinder it rapidly evaporates, causing a large and sudden pressure increase which blows the cork off with great force and noise. A heavy base on the cylinder helps to absorb the shock of the recoil. Liquid nitrogen can be procured by hospital supply sources. If a Dewar flask is not available, an ordinary thermos bottle can be used to store the nitrogen if it is made of metal or Pyrex glass. Ordinary glass can shatter at the low temperature of liquid nitrogen, and the container should not be sealed tightly lest the thermos bottle explode as the nitrogen evaporates. If liquid nitrogen is not available, a piece of dry ice can be used instead[1].

DISCUSSION

When a liquid evaporates, the resulting gas occupies a much larger volume than the liquid from which it came if the pressure is the same in both cases. The expansion typically amounts to about a factor of 1000 for most liquids (compare the density of the gas with the density of the liquid from which it came). If the gas is not allowed to expand, the pressure will increase by the same factor. The increased pressure raises the boiling point and inhibits the boiling, as in a pressure cooker, but not enough to prevent a large pressure buildup, as demonstrated here. In the liquid nitrogen cannon, only a small fraction of the liquid nitrogen needs to boil in order to blow the cork off with considerable force.

HAZARDS

Liquid nitrogen boils at a temperature of -196°C (-321°F, 77K) and can cause severe frostbite. Care should be taken to avoid contact with the liquid and with anything that has been cooled by it. Aside from making sure the cylinder is quite strong, the only other precaution is to aim the cannon above the heads of the audience. The cork can travel several hundred feet, but is relatively harmless after it bounces off a wall or the ceiling.

REFERENCE

1. J. S. Miller, Physics Fun and Demonstrations, Central Scientific Company: Chicago (1974).

2.2

Collapsing Can

A small amount of water is placed in an aluminum, soft-drink can and brought to a boil over a Bunsen burner and then inverted in a bath of cold water, causing the can to instantly collapse as a result of the rapid condensation of the steam.

MATERIALS

PROCEDURE

Put about 15 milliliters of water in an empty, 12-ounce, aluminum, soft-drink can (one with "Crush" in its name is good) and heat it over a Bunsen burner or hot plate until a cloud of condensed water vapor escapes from the mouth of the can for about 20 seconds. One should point out that the cloud is not "steam," which is an invisible gas or smoke which is a collection of tiny solid particles. Using tongs, quickly lift the can from the burner and invert it in a tray containing cold water to a depth of a few centimeters. The can will collapse instantly[1,2].

DISCUSSION

When the can cools, the water vapor condenses, reducing the pressure inside the can from which most of the air has been expelled. The surface area of the can is about 0.031 m2 (or 48 in2). In the most extreme case, a pressure difference of 1 atmosphere (14.7 lb/in2) would apply a total force of about 700 pounds which is far in excess of what the can is able to sustain. One might suspect that the water would be drawn up into the can. However, since the hole in the can is small and the condensation occurs quickly, the viscosity of the water inhibits it from entering the can. Some water does spray up into the can, and it is this water that causes the steam to condense so rapidly.

HAZARDS

The can contains boiling water at 100°C and can cause burns to the skin if it is touched with unprotected hands. Be sure the outside of the can is clean to prevent it from catching fire.

REFERENCES

1. G. Kauffman, Journ. College Sci. Teach. 14, 364 (1985).

2. B. Z. Shakhashiri, Chemical Demonstrations, The University of Wisconsin Press: Madison, Wisconsin, Vol 2 (1985).

2.3

Carbon Dioxide Trough

Carbon dioxide from a glass beaker is poured down a trough containing a number of candles which are successively extinguished by the invisible gas.

MATERIALS

*Available from Frey Scientific Company

PROCEDURE

A V-shaped metal or plexiglas trough inclined at an angle of about 30° contains about five candles mounted vertically within the trough with their wicks below the top of the trough. The candles are lit in honor of someone's birthday. There is a better than even chance that someone in the audience will have a birthday on any given day if there are at least 250 people in the audience (see Table 2.2). A 2-liter glass beaker containing carbon dioxide gas is removed from behind the lecture table and poured down the trough. The candles go out one by one as if water were pouring down the trough, but the beaker is apparently empty since carbon dioxide is a colorless, odorless gas.

The carbon dioxide was produced by placing a piece of dry ice in the beaker before the lecture with a piece of cardboard on the top to cover the beaker. The cardboard is removed, and the dry ice is lifted out with tongs just before the beaker is shown to the audience. The beaker can be stored on a slightly warm, electric hotplate to prevent the formation of water ice on its exterior and to ensure the rapid evaporation of the dry ice. Dry ice can often be procured from ice cream vendors.

DISCUSSION

This demonstration illustrates the necessity of oxygen for sustaining combustion. It also demonstrates sublimation, the process in which a liquid changes directly from a solid to a gas without going through the liquid phase. Dry ice is called "dry" because, unlike ordinary water ice, it sublimates at atmospheric pressure. Ordinary ice sublimates (and hence is also dry) when the vapor pressure of the water above the liquid is below 4.58 torr (or 0.006 atmospheres). This condition can exist on a dry day and is the reason why snow and ice eventually disappear even when the temperature is below freezing (0°C). Liquid carbon dioxide cannot exist below the triple point pressure of 5.1 atmospheres and temperature of -56.2°C. The carbon dioxide remains in the beaker because it is about 50% more dense than air. Some types of fire extinguishers use carbon dioxide.

HAZARDS

Dry ice sublimates at a temperature of -78.5°C and can cause frostbite. Thus it should not be allowed to touch the bare skin.

Table 2.2

Probability that Someone in an Audience of a Given Size Will Have a Birthday on a Given Day

     Audience Size       Probability
          10                  3%
          20                  5%
          30                  8%
          70                 13%
         100                 24%
         150                 34%
         200                 42%
         250                 50%
         300                 56%
         400                 67%
         500                 75%

2.4

Exploding Soap Bubbles

Soap bubbles blown with natural gas or hydrogen are ignited with a candle as they rise toward the ceiling.

MATERIALS

PROCEDURE

Soap bubbles can be made by filling a glass pipe with a small amount of soap solution (sold in toy stores). Suitable solutions can also be made by adding a few drops of sodium or potassium oleate or liquid dish detergent to a beaker of warm, distilled or very soft, pure water. A small amount of glycerine and a few drops of ammonia water greatly improves the lasting quality of the bubbles[1].

The pipe is supported by a ring stand and connected to a source of compressed gas. A gas lighter than air, such as helium,* allows the bubbles to rise to the ceiling as they are released from the pipe. The gas should be allowed to flow through the pipe briefly before filling it with soap solution in order to expel the air. If the bubbles are blown with hydrogen, they can be ignited with a candle held in the hand as they rise[2,3]. Some oxygen can be mixed with the hydrogen, using the arrangement shown in the figure, to make a much louder explosion. The loudest explosion will occur when the hydrogen-to-oxygen ratio has a stoichiometric value of 2:1 so as to produce pure H2O. Natural gas, often conveniently available on the lecture bench, makes a very beautiful and quiet flame. Natural gas consists primarily of methane (CH4) which is slightly less dense than air. Mixtures of methane and oxygen will rise only if the ratio of CH4 to O2 is large. The effect is best if viewed against a dark background in subdued light.

*Specialty gases and equipment can be procured from Matheson Gas Products, P. O. Box 1587, Secaucus, NJ 07094.

DISCUSSION

This demonstration illustrates a number of physical concepts. The very existence of bubbles is a dramatic demonstration of surface tension. A bubble consists of a thin film of liquid, held together by surface tension. It has elastic properties similar to those of a balloon. The size of the bubble is determined by the pressure of the gas inside it and the radius and thickness of the water film. That the gas inside a bubble is under pressure can be illustrated by blowing a bubble with a pipe, but before the bubble is released, allowing it to deflate and blow out a candle near the stem of the pipe. A smaller bubble has a higher pressure than a larger bubble for the same reason that a balloon is hard to blow up at first but becomes easier as it gets larger. This can be illustrated with a T-shaped pipe in which two bubbles of different size are blown and then connected together by way of the pipe. The larger bubble will get larger, and the smaller bubble will get smaller.

The tendency of a bubble to rise when filled with a gas lighter than air illustrates Archimedes' principle. The bubble will rise if its weight plus the weight of the gas inside is less than the weight of the air displaced. At room temperature and atmospheric pressure, a cubic meter of air weighs almost three pounds. A bubble filled with air will slowly drop to the floor because of the weight of the film of water. The weight of the air inside approximately cancels the weight of the air displaced, neglecting the small difference in pressure. From the radius of the bubble and its terminal velocity as it falls (see the discussion in section 1.4), one can estimate the weight of the water and hence the thickness of the water film (the density of water is 1000 kg/m3). An air-filled bubble can be made to float in a bath of carbon dioxide produced by dry ice in the bottom of a transparent container such as a fish tank.

Bubbles are very fascinating and instructive. Entire lectures can be given on the properties and behavior of bubbles, and such demonstrations[4-7] inevitably enthrall the audience.

HAZARDS

Aside from the normal precautions involved with flames, the oxygen mixtures can make quite a loud explosion. The demonstrator should use ear plugs and caution the members of the audience to hold their hands over their ears.

REFERENCES

1. C. L. Strong, Scientific American 220, 128 (May 1969).

2. B. Z. Shakhashiri, Chemical Demonstrations, The University of Wisconsin Press: Madison, Wisconsin, Vol 1 (1983).

3. H. A. Robinson, ed., Lecture Demonstrations in Physics, American Institute of Physics: New York (1963).

4. C. V. Boys, Soap Bubbles and the Forces Which Mould Them, Educational Services Incorporated, Doubleday Anchor Books: Garden City, New York (1959).

5. C. Isenberg, The Science of Soap Films and Soap Bubbles, Tiesto Ltd.: Clevedon (1978).

6. S. Simon, Soap Bubble Magic, Lathrop, Lee and Shepard: New York (1985).

7. A. Ward, Experimenting with Surface Tension and Bubbles, Dryad Press: London (1985).

2.5

Hero's Engine

A specially constructed, glass flask containing water and suspended from above by a chain spins rapidly when heated from below.

MATERIALS

*Available from Carolina Biological Supply Company, Central Scientific Company, Edmund Scientific, Fisher Scientific, Frey Scientific Company and Sargent-Welch Scientific Company

PROCEDURE

A glass flask with glass tubes connected to the neck and bent to one side, suspended by a bead chain, containing a small amount of water and heated from below by a Bunsen burner, spins rapidly as the water is brought to a boil. The glass tubes act as jets releasing the steam in one direction. A bead chain provides freedom to rotate since it will not wind up. The amount of water used is not critical. Enough should be used so that it doesn't all boil away, but if too much is used, it will take a long time to begin to boil. The speed of rotation can be adjusted by varying the amount of heat provided from below. A more rugged version can be constructed using an aluminum cylinder[1]. The device is called "Hero's engine" after the Greek philosopher Hero of Alexandria who in the first century B.C. wrote about it but apparently never actually made one. An analogy could be made to a rotating lawn sprinkler which can also be demonstrated in a lecture room using compressed air in place of water.

DISCUSSION

This demonstration illustrates the conservation of angular momentum, Newton's third law (action and reaction) and the principle of a rocket engine. As the water vapor is expelled, it imparts an equal and opposite momentum to the flask causing it to rotate in the opposite direction. It illustrates the transformation of heat energy into mechanical energy and shows the large amount of steam that can be produced from a small amount of water. Note the great simplicity of this engine as compared to other forms of steam engines which have many complicated moving parts. Perhaps it would be more widely used were it not for the fact that it is enormously inefficient at converting heat into motion because the exhaust velocity its relatively low and much heat is wasted (exhausted to the air).

HAZARDS

The flask should be of the type that is designed to be heated with a burner. Care should be taken not to boil the water too rapidly lest the flask begin to spin uncontrollably. The flame should be extinguished before the water has completely boiled. The flask should be allowed to cool before it is touched with unprotected hands.

REFERENCE

1. L. Hirsch, Am. Journ. Phys. 46, 773 (1978).

2.6

Model Geyser

A model geyser consisting of a column of water heated from below with a Bunsen burner erupts periodically and shoots water up to the ceiling.

MATERIALS

PROCEDURE

A working model of a geyser can be rather easily constructed[1]. It requires only a long, vertical, water-filled tube with a constriction at the top, a supporting structure, a Bunsen burner to heat the tube from below and a catch basin to collect the water and return it to the tube after an eruption. Depending on the length and volume of the tube and the amount of heat used, it can be made to erupt every few minutes. A water column of about 2 meters height works well since it makes the boiling point about 5°C higher at the bottom than at the top. If the tube is made of pyrex glass, the activity in the whole geyser tube can be observed. One can contrast the turbulent nature of the boiling to the regular periodic nature of the eruptions.

DISCUSSION

The geyser operates by heating the water at the bottom of the tube to a superheated state (greater than the boiling point of water at atmospheric pressure). The water does not immediately boil, however, since the boiling point is elevated by the pressure of the water column above. When it finally does begin to boil, the pressure of the water column is relieved, and the boiling vigorously ensues, causing the eruption. The ejected water cools upon contact with the air and the catch basin and runs back down the tube, and the heating process begins again.

In addition to the eruption, it should be possible to observe tremors of various types as well as a water-hammer effect that occurs just after an eruption when the water is momentarily prohibited from running down the tube by the pressure of the steam remaining in the tube. As the steam condenses, a partial vacuum forms in the geyser tube and audibly "sucks" the pool of water from the catch basin into the tube with great force. The resulting noise sounds like a belch and invariably elicits a reaction from the audience. A similar effect can be produced by pouring water into a funnel inserted through a rubber stopper into an empty flask.

HAZARDS

The geyser is relatively safe if one exercises normal caution in not touching the Bunsen burner or the tube containing the hot water. The water can cause burns if one gets too close when it erupts, but by the time the water has sprayed into the air and fallen back down, it is no more dangerous than a hot shower. Some water may miss the catch basin and damage other nearby equipment.

REFERENCE

1. L. W. Anderson, J. W. Anderegg, and J. E. Lawler, American Journal of Science 278, 725 (1978).

2.7

Magdeburg Hemispheres

Two hemispheres when placed together and evacuated cannot be pulled apart because of the atmospheric pressure.

MATERIALS

*Available from Central Scientific Company, Fisher Scientific and Frey Scientific Company

PROCEDURE

The large force that the atmosphere can exert is vividly demonstrated with a pair of Magdeburg hemispheres, named after the city of Magdeburg in Germany where Otto von Guericke (1602-1686), a physicist and politician, while mayor of the city in 1657, entertained the local people by having two teams of eight horses each try to pull apart two, half-meter-diameter, copper hemispheres held together only by the pressure of the atmosphere[1]. Otto von Guericke devised one of the first vacuum pumps in about 1641 and was largely responsible for dispelling the medieval view that "nature abhors a vacuum."

For a more modest demonstration, one can use steel hemispheres with a diameter of about 12 centimeters and a gasket of some sort to prevent leakage of air around the joint. If a good vacuum pump is not available, one can use larger hemispheres and a water aspirator or hand pump to produce a partial vacuum. One of the hemispheres should have a lip around the edge to prevent the hemispheres from being slid across the gasket. The hemispheres are placed together and evacuated with a vacuum pump through a hose connected to a valve on the side of one of the hemispheres. The valve is then shut and the hose removed. The hemispheres are usually equipped with handles so that two volunteers from the audience can try to pull them apart. It is safe to offer them a sum of money if they succeed (without opening the valve!).

In a variation of the demonstration, one can use two disks with the same projected area as the hemispheres to show that the volume of the evacuated space is not the relevant factor. Rubber suction cups of various types can be shown. A bathroom plunger is a familiar example. A pair of such plungers can be used as an inexpensive version of the Magdeburg hemisphere demonstration.

DISCUSSION

The atmosphere exerts a force of (pi)r2p or 6.25(pi) sq in × 14.7 pounds/sq in = 290 pounds for a 5-inch diameter sphere completely evacuated. Even with only a partial vacuum, it is nearly impossible for two people of normal strength to separate them. One can hang weights from one of the hemispheres with the other attached to a secure hook in the ceiling to get a quantitative measure of the atmospheric pressure. With Otto Von Guericke's half-meter hemispheres, the force is over two tons!

HAZARDS

Assuming the spheres are made of a material sufficiently strong not to be crushed by the atmosphere, the only danger is from one of the volunteers falling if the other pulls too hard or lets go. A suitable conclusion to the demonstration is to open the valve and let air in while the volunteers are still pulling, in which case they should be instructed not to pull too hard.

REFERENCE

1. J. Higbie, Am. Journ. Phys. 48, 987 (1980).

2.8

The Impossible Balloon

A specially constructed balloon appears to have a lifting power far beyond what is permitted by Archimedes' principle.

MATERIALS

PROCEDURE

Professor Ed Miller of the University of Wisconsin likes to perform a demonstration involving a buoyancy scam in which a half-meter-diameter balloon is against the ceiling with a weight hanging below it. After explaining all about buoyancy, Professor Miller goes into an enthusiastic spiel about the exciting development by some of his colleagues of a new gas with 47 times the lifting power of hydrogen and how we are very fortunate to get an advance demonstration. Then he hangs several more, obviously heavy weights to the string from the bottom of the balloon. Eventually someone wakes up and tries to argue that this is inconsistent with all he has been saying. He doesn't say a word, just turns around, reaches up and pulls out the cork to release the gas from the balloon. The balloon "flooffs" out its gas and droops down to nothing, but the weights stay hanging there. Obviously there is a string through the balloon to a small hook in the ceiling that holds the weights up. Finally a ring on top of the balloon, that kept it steady, falls down around the collapsed balloon onto the weights with a clatter as a humorous climax to the scam.

DISCUSSION

The amount of weight that a balloon can lift is equal to the weight of the air displaced by the balloon minus the weight of the balloon and the gas that it contains (Archimedes' principle). Thus hydrogen (H2) with a molecular weight of 2 grams per mole compared to air with an average molecular weight of 29 grams per mole is close to the best that one can do. Even a gas with zero molecular weight (a vacuum) could provide a lift only 7% greater than hydrogen. The use of an evacuated balloon is, of course, impractical since the balloon would be much too heavy if made of a material sufficiently strong to support the pressure of the atmosphere. The pressure in a hydrogen-filled balloon is actually slightly greater than the pressure of the surrounding atmosphere (typically 5-10%), and so such a balloon would contain more moles of hydrogen than the air that is displaced, which reduces its buoyancy slightly.

HAZARDS

The only hazard in this demonstration is the string breaking and dropping the weights on one's foot.

2.9

Boiling with Ice

Water in a sealed flask is made to boil by inverting the flask and holding an ice cube against its bottom.

MATERIALS

PROCEDURE

Water can be made to boil at a temperature well below 100°C by reducing the pressure of the atmosphere above the water[1-5]. A 1-liter, thick-walled, round-bottomed boiling flask is filled about half way with water. A two-hole rubber stopper is used to seal the flask. A thermometer is placed in one hole of the stopper. In the other hole is a glass tube connected to a rubber hose which can be sealed with a pinch clamp. The water is brought to a boil with a Bunsen burner. The water is then allowed to cool for one minute. The pinch clamp is then used to seal the flask, the flask is inverted, and an ice cube is held against its bottom. The water in the flask will boil for several seconds.

DISCUSSION

The temperature at which a liquid boils depends upon the pressure of the atmosphere above it. The water will boil when its vapor pressure (see Table 2.3) exceeds the pressure of the surrounding gas. In this demonstration, the pressure is lowered from normal atmospheric pressure (760 torr) by cooling the air in the flask and by condensing some of the water vapor in the flask. As the water boils, the pressure in the flask increases to the point where it is greater than the vapor pressure of the liquid, and the water stops boiling. The flask should be no more than half full of water to provide space for the vapor produced by boiling. If too little space is provided, the vapor pressure of the liquid water may be reached before boiling is apparent.

HAZARDS

In addition to the hazard of burns from the Bunsen burner and the hot flask, the flask may implode if the pressure is lowered sufficiently. This risk is minimized by using a thick-walled boiling flask rather than a standard round-bottomed one.

REFERENCES

1. D. Baisley, The Science Teacher 47, 45 (May 1980).

2. A. Joseph, P. F. Brandwein, E. Morholt, H. Pollack and J. F. Castka, A Sourcebook for the Physical Sciences, Harcourt, Brace and World: New York (1961).

3. H. A. Robinson, ed., Lecture Demonstrations in Physics, American Institute of Physics: New York (1963).

4. B. Z. Shakhashiri, Chemical Demonstrations, The University of Wisconsin Press: Madison, Wisconsin, Vol 2 (1985).

5. J. P. VanCleave, Teaching the Fun of Physics, Prentice Hall Press: New York (1985).

Table 2.3

Temperature Dependence of the Vapor Pressure of Water

          Temperature (°C)         Pressure (torr)
                 0                      4.579
                 5                      6.543
                10                      9.209
                15                     12.788
                20                     17.535
                25                     23.756
                30                     31.824
                35                     42.175
                40                     55.324
                45                     71.88
                50                     92.51
                55                    118.04
                60                    149.38
                65                    187.54
                70                    233.7
                75                    289.1
                80                    355.1
                85                    433.6
                90                    525.76
                95                    633.90
               100                    760.00

2.10

Freezing by Evaporation

Water at room temperature in a flask boils vigorously and then turns into ice when the pressure in the flask is reduced.

MATERIALS

PROCEDURE

With the use of a mechanical vacuum pump, water in a flask can be made to boil so vigorously at room temperature that the loss of heat due to evaporation causes the water to freeze[1]. Apparatus for such a cryophorus demonstration can be purchased or constructed.If constructed, one should use a thick, round-bottom boiling flask and a trap which can be filled with strong sulfuric acid to isolate the flask from the vacuum pump. The acid absorbs the water vapor thereby increasing the rate of boiling as well as preventing the pump oil from being contaminated with water. The use of distilled water is recommended. The water can be brought to a boil more quickly if it is preheated. A large pressure gauge visible to the audience is a useful addition.

This demonstration is best introduced by asking the audience at what temperature water will boil. Most people will answer with 212°F or 100°C. One should point out that this answer is correct only at atmospheric pressure (760 torr), and that it is well-known by the residents of high-altitude cities that it takes longer to cook a boiled egg there because water boils at a lower temperature at higher altitude. It's not accurate to say that it takes longer to boil an egg there because the water is actually brought to a boil more quickly. The barometric pressure drops by about 3% for each 1000 feet above sea level. A city such as Denver, Colorado is at an altitude of about 5000 feet, and thus the average barometric pressure is around 660 torr, and the boiling point of water is about 96°C. On top of Mt. Everest (29,028 feet) it's a chore to make a pot of tea. One can point out that a boiling liquid tends to maintain a constant temperature, and this is why many foods are cooked in boiling water. In a pressure cooker, the boiling point is raised by the increased pressure.

One then turns on the vacuum pump and lets the audience watch while the water boils furiously. One can touch the flask and point out that it isn't hot at all, and, in fact, if anything, it feels a bit cool. While holding a hand on the flask, ask the audience at what temperature water will freeze. If this is timed properly, the water will freeze on cue into a slushy form of ice. In a large hall, the ice can best be seen in silhouette on a screen illuminated by an arc lamp or by a slide projector.

DISCUSSION

The heat of vaporization of water is 540 calories per gram, and the heat of fusion of water is 80 calories per gram. The density of water is 1 gram per milliliter. When the water evaporates, a large amount of heat is thus extracted from the water, causing the cooling. The evaporation of each milliliter of water is capable of freezing almost seven milliliters once the temperature of the water has decreased to 0°C. As the temperature drops, the vapor pressure of the water drops, and the boiling is greatly reduced. This heat loss is why we feel cool when we get out of the bath or swimming pool. Animals perspire in order to keep cool by the same process. If our perspiration evaporated too rapidly, we would freeze to death!

HAZARDS

The major hazard is implosion of the flask if it is not designed to withstand atmospheric pressure or if it is dropped or struck with a heavy object. Sulfuric acid can also cause burns and should be handled with great caution.

REFERENCE

1. H. A. Robinson, ed., Lecture Demonstrations in Physics, American Institute of Physics: New York (1963).

2.11

Nonburning Handkerchief

A cotton handkerchief is doused in a liquid and set on fire, but the handkerchief doesn't burn.

MATERIALS

PROCEDURE

A brightly colored, cotton handkerchief is taken from the pocket, or better yet, from a volunteer planted in the audience and is soaked in a liquid and set on fire[1]. While holding the handkerchief with tongs and watching the blue flame, one points out that the handkerchief is not burning. Finally the handkerchief is snuffed out with a quick jerk or doused in a bucket of water and passed around for inspection or returned to the volunteer. For more drama, an assistant can put out the flame with a fire extinguisher. The volunteer can be asked to hold up the handkerchief for everyone to see.

In this demonstration, the liquid used is a 50/50 mixture of isopropyl alcohol and water. Methanol or ethanol can be substituted for the isopropyl alcohol. Some salt in the solution will help to make the flame more visible. Other combustible materials, such as paper, can also be used in place of the handkerchief[2]. A dollar bill provided by someone in the audience is especially effective. Note carefully the purity of the alcohol before mixing. Rubbing alcohol as sold in drug stores is often 30% or more water. One could repeat the demonstration with varying mixtures of alcohol and water. Too much water will prevent the alcohol from burning, and too little water will allow the cloth or paper to char.

In a variation of the demonstration, a dry cotton cloth is wrapped tightly around a coin, and a lighted cigarette is touched to the cloth. The coin absorbs the heat and keeps the temperature below the point where the cloth burns.

DISCUSSION

This demonstration illustrates the variation in the temperature required to support combustion in different substances. The alcohol burns at a temperature below the kindling temperature of the cotton. In addition, the heating and vaporization of the water removes heat and prevents the cloth from burning.

HAZARDS

Although the flame is relatively cool, it is capable of producing severe burns. Hold the handkerchief with a pair of very long tongs (30 cm or more) while it is ignited. Plan ahead to have a way to extinguish it before the water is completely vaporized or if it inadvertently drops to the floor while burning. Isopropyl alcohol can damage the eyes severely.

REFERENCES

1. B. Z. Shakhashiri, Chemical Demonstrations, The University of Wisconsin Press: Madison, Wisconsin, Vol 1 (1983).

2. J. Jardin, P. Murray, J. Tyszka, and J. Czarnecki, Journ. of Chemical Education 55, 655 (1978).

2.12

Liquid Nitrogen Cloud

Liquid nitrogen induced to vaporize rapidly by expelling it from a large Dewar under pressure cools the air and causes the formation of a large, dense cloud.

MATERIALS

PROCEDURE

An impressive cloud can be produced by the rapid boiling of liquid nitrogen. Suitable apparatus consists of a large (25-liter) Dewar filled with liquid nitrogen. A two-hole rubber stopper plugs the mouth of the Dewar. In one hole of the stopper is placed a tube connected to high-pressure air or through a pressure regulator to a cylinder of compressed nitrogen. In the other hole is placed a tube that leads to the center of a meter-long, thick-walled, horizontal, copper pipe, sealed at the ends, with a dozen or more small (1/8" diameter) holes in the top through which the nitrogen can escape into the room. Electrical heating tapes surrounding the pipe can be used to warm the pipe prior to use. If a pipe with sufficiently thick walls is unavailable, a solid cylinder of copper can be fit loosely inside the pipe. The aim is to provide a warm orifice of high heat capacity to cause rapid boiling of the nitrogen for as long as possible. Depending upon the heat capacity of the pipe and the flow rate of gas into the Dewar, a cloud reaching from the floor up several meters into the air can be sustained for a good fraction of a minute until the pipe cools to too low a temperature. The demonstration cannot be repeated for about an hour or so because the pipe has to warm back up to room temperature.

The operation of the device involves forcing the liquid nitrogen from the Dewar up into the warm pipe where it rapidly boils and exits from the holes in the pipe as cold nitrogen gas. The cold gas then condenses moisture from the air in the room above the apparatus and forms the cloud. Thus the demonstration works best when the humidity is high. If there is a ventilation system in the room, it can be turned off a few minutes before the demonstration to allow the humidity to rise. After 30 seconds or so the pipe will cool to the point where fountains of liquid are emitted from the holes. The liquid is not nearly so effective as the cold gas in cooling the air, and the cloud slowly subsides. Colored lights illuminating the cloud provides extra visual appeal. The demonstration is an effective conclusion to a presentation, and the demonstrator can disappear in the cloud and perhaps exit the room through a nearby door unseen by the audience.

DISCUSSION

Although this demonstration is done mostly for the drama, a number of physical principles are illustrated including Pascal's law, heat of vaporization, heat capacity, heat transport, and the condensation of water vapor in air as the temperature is lowered. The mechanism is similar to the way clouds in the sky are formed by cooling of the air to a temperature below which the air becomes saturated with moisture (100% relative humidity). The cloud consists of extremely small droplets of liquid water and is not steam or smoke as many people will respond if asked.

HAZARDS

A possible hazard is explosion of the Dewar due to over-pressurization. The exit holes should not be obstructed, and pressures higher than about 30 psi should not be used unless the Dewar is known to be of adequate strength. It is wise to test the Dewar behind a suitable barricade at a pressure about 50% greater than what one intends to use. Some liquid nitrogen will exit from the holes especially after the device has run for a while, and thus to avoid frostbite, the face and other parts of the body should not be directly above the holes in the pipe when it is turned on.

2.13

Heat Transmitter

A match at the focal point of a parabolic reflector is ignited by the radiation from an electrical heating element placed at the focal point of a second parabolic reflector across the room and aimed at the first.

MATERIALS

*Available from Central Scientific Company, Edmund Scientific, Fisher Scientific, Frey Scientific Company and Sargent-Welch Scientific Company

PROCEDURE

The transfer of heat by radiation can be effectively demonstrated with two parabolic reflectors preferably of 20 centimeters or more diameter. Near the focus of one reflector is placed an electrical resistive heating element. At the focus of the other reflector is placed a wooden match. The reflectors are then placed several meters apart and aimed at one another. When the heating element is energized, the match should burst into flame in a few seconds. One can show that it is safe to stand in the beam, since the power flux (watts per square meter) is quite low. The reflectors need not be of optical quality since the heat source is quite spread out, but the surfaces should reflect infrared radiation with high efficiency. Chrome plating of the reflectors is helpful. A less effective variation uses a single reflector the focus an image of the lamp on the match[1]. A piece of paper can be used in a dimly lit room to view the red spot on which the heat is focused to place the match in the optimal location. Avoid bumping either of the reflectors after they have been aligned. For a bit more drama the match can be replaced with a small amount of gunpowder as Sir Humphry Davy (1778-1829) was fond of doing in his public lectures at the Royal Institution in London[2].

DISCUSSION

Radiation is one of the three ways in which heat can be transferred. The others are conduction and convection. Only radiation can take place in a vacuum. The others require a material medium. This is the means by which the sun heats the earth. Heat radiation is a form of electromagnetic wave in the infrared portion of the spectrum. It is of the same form as light, microwaves, radio waves, X-rays, and so forth, except of a different wavelength. When the temperature of a body increases, it emits successively shorter and shorter wavelengths, first giving off heat and then light. Most materials melt before they can give off significant amounts of ultraviolet. The amount of energy radiated by a body is proportional to the fourth power of its absolute temperature (Stefan's law). Infrared radiation obeys the same laws of geometrical optics as does light, and thus it can be focused by mirrors and lenses as in this demonstration. Radiation can also be described in terms of the emission and absorption of individual photons.

HAZARDS

The heating element can cause burns and electrocution if operated directly from the power lines. A bad burn can result if any part of the body or clothing is placed in the focus of the receiving reflector. Don't try to align the reflectors by placing the eye at the focus; rather, observe the spot on a piece of paper. A means should be provided to safely extinguish the match once it is lit and to avoid dropping the match onto something that might catch fire. Experiment with small amounts of gunpowder to get an explosion that is impressive but safe.

REFERENCES

1. R. E. Berg, Phys. Teach 28,56 (1990).

2. J. Tyndall, Heat; a Mode of Motion, third edition, Longman: London (1868).

2.14

Ethanol Vapor Explosion

A small amount of ethanol placed in a bottle is made to explode and blow a cork a considerable distance by means of an electrical spark.

MATERIALS

*Available from Fisher Scientific and Sargent-Welch Scientific Company

PROCEDURE

Two to three milliliters of >95% ethanol (C2H5OH) is placed in a 250-milliliter polyethylene bottle with two nails or screws through the sides as shown in the illustration[1]. The tips of the nails or screws are pointed and come within a few millimeters of touching. The bottle is sealed with a cork or rubber stopper. The bottle can be shaken briefly to ensure that the liquid ethanol has come to equilibrium with its vapor. The nails are then connected to a high-voltage (>1000 volts), low-current source. The resulting spark ignites the ethanol and blows the stopper off. Alternately, a hand-held Tesla coil can be held near one of the nails. Even with the second nail disconnected, there is enough capacitance between the nails to cause a spark to jump across the gap. The capacitance can be increased, causing a more intense spark, by connecting the second nail to ground or to any conductor with a large surface area. A number of such bottles can be placed in series electrically, causing all the stoppers to blow off at the same time. Larger bottles can be used for more impressive explosions. One can point out that cars can use ethanol as fuel and that the reaction in the cylinders of the engine is the same as the one illustrated here.

DISCUSSION

In this demonstration, some of the liquid ethanol evaporates and mixes with the air in the bottle. The reaction that takes place is C2H5OH + 3O2 --> 2CO2 + 3H2O. Thus there is an increase both in the number of moles of gas (4 to 5) and in its temperature as a result of the energy released in the exothermic reaction. The increased pressure causes the stopper to blow off the bottle. The demonstration cannot be repeated without flushing the bottle, because the explosion consumes all the oxygen in the bottle.

HAZARDS

The stopper is expelled with considerable force, and thus care should be taken to avoid damage to light fixtures or other objects. Keep the area above the bottle clear of obstructions. The voltage used to produce the spark should be either of a high frequency, as with the Tesla coil, or a low current to avoid electrocution.

REFERENCE

1. B. Z. Shakhashiri, Chemical Demonstrations, The University of Wisconsin Press: Madison, Wisconsin, Vol 2 (1985).

2.15

Heat Convection

A candle is extinguished when a tightly-fitting glass cylinder is placed over it unless a T-shaped piece of metal is lowered into the cylinder.

MATERIALS

PROCEDURE

The convection of heated air can be demonstrated quite simply and effectively with a candle[1]. The candle is lit to show the audience that it is quite ordinary. Then a glass cylinder, about 30 cm long and 3 cm in diameter, open at both ends, is lowered over the candle, making a tight seal at the base so that air cannot be drawn up from below. After a few seconds, the candle will go out. Then a thin, tightly-fitting partition made out of copper or some similar metal is lowered into the cylinder to within a few centimeters of the top of the candle. The partition can be held in place by a T-shaped extension at its top. The cylinder is lifted, the candle relit, and the cylinder put back over the candle. The candle continues to burn with a flickering flame while the cylinder is in place. Finally, after awhile, the partition is removed, and the candle goes out. For each case, the audience can be asked to predict whether the candle will continue to burn. With a bit of practice, one can let the candle apparently go out and then revive it by quickly lowering the partition.

As a frill, the candle can also be extinguished by abruptly touching a coil of copper wire to the flame[2]. The copper conducts the heat away and lowers the temperature below the kindling point of the candle wax.

DISCUSSION

In the absence of the partition, the upward rising warm air interferes with the downward falling cool air near the top of the cylinder, and the convection pattern does not reach down to the level of the candle. With the partition in place, the warm air rises up one side of the partition and the cool air falls down the other side and replenishes the candle with oxygen. Whether the convection goes clockwise or counter-clockwise around the partition depends on small asymmetries when the convection starts. Once the convection starts in one direction, it will tend to continue in that direction as long as the candle burns, much as the direction of the swirling water leaving the drain in a bathtub depends mainly on the small vorticity present in the water when the plug is pulled.*

*The coriolis force due to the rotation of the earth will determine the direction of the swirl if the initial vorticity is sufficiently small. This force is in opposite directions in the northern and southern hemisphere.

Along with radiation and conduction, convection is one of the ways in which heat is transported from one place to another. Convection can occur in gases and liquids. The convection is driven by pressure gradients in the fluid. With the candle, the pressure gradient is small, and so the warmer air is less dense than the colder air and thus is not as strongly attracted to the earth by gravity. The burning of a candle requires gravity as can be demonstrated by observing that a candle in free-fall will extinguish[3].

HAZARDS

The hazards in this demonstration are rather obvious and include burns from the candle and cuts from the glass.

REFERENCES

1. J. S. Miller, Physics Fun and Demonstrations, Central Scientific Company: Chicago (1974).

2. T. L. Liem, Invitations to Science Inquiry, Ginn Press: Lexington, Massachusetts (1981).

3. B. Z. Shakhashiri, Chemical Demonstrations, The University of Wisconsin Press: Madison, Wisconsin, Vol 2 (1985).

2.16

Exploding Balloons

Helium and Hydrogen-filled balloons tethered by strings above the lecture bench are burst with a match on the end of a stick.

MATERIALS

PROCEDURE

Two identical balloons are filled, one with helium, the other with hydrogen. The balloons are attached to either end of the lecture bench with thin strings that allow them to float about ten feet above the floor. The balloons should be filled within about an hour of being used since the gas will gradually diffuse through the balloons, and they will lose their buoyancy.

The audience is asked to guess what is in the balloons. Most people will assume they are filled with helium. The audience is then asked to predict what will happen when a lighted match is touched to one of the balloons. Most people will say the balloon will burst.

A match is lit and attached with an alligator clip on the end of a wooden stick about a meter long. The match is touched to the helium balloon causing it to burst. The members of the audience are then asked if they would like to see it repeated with the other balloon. One then repeats the demonstration with the hydrogen balloon, causing a large explosion and ball of flame.

When the audience regains its composure, one can explain the importance of taking nothing for granted in science. Helium is only one example of a gas that is lighter than air. In fact, hydrogen is lighter yet (about half as heavy). The upward buoyant force, however, is only slightly different since it is given by the difference between the weight of the gas in the balloon and the weight of the air displaced by the balloon. On can proceed to discuss Archimedes' principle, chemical combustion, or the scientific method. Mention of the Hindenburg and the reasons hydrogen is no longer used in dirigibles is appropriate. The operation of hot-air balloons can be discussed.

The demonstration can also be done using other gases such as air and oxygen if the balloons are suspended in some way such as with a ring stand. A stoichiometric mixture (2:1) of hydrogen and oxygen can also be used if proper precautions are taken to protect one's ears from the loud explosion that results[1]. If hydrogen gas is not available, it can be produced in a 250 ml pyrex Erlenmeyer flask to which 10 to 15 grams of mossy zinc and 65 ml of 3M hydrochloric acid has been added[2]. One can increase the amount of sound released in the explosion of the hydrogen balloon by putting some air in the balloon before it is filled with hydrogen. Experiment to get an appropriately dramatic but not dangerously loud explosion.

DISCUSSION

The tendency of a balloon to rise when filled with a gas lighter than air illustrates Archimedes' principle. The balloon will rise if its weight plus the weight of the gas inside is less than the weight of the air displaced. At room temperature and atmospheric pressure, a cubic meter of air weighs almost three pounds. An air-filled balloon or soap bubble can be made to float in a bath of carbon dioxide produced by dry ice in the bottom of a transparent container such as a fish tank.

The combustion of the gas in a balloon is an illustration of a chemical reaction, in this case hydrogen in the balloon reacting with oxygen in the surrounding air to form water with the release of 232 kJ/mole of water formed. The reaction ensues much more violently if oxygen is mixed with the hydrogen than if it has to mix with oxygen from the air. This gives some indication of the rate with which gases diffuse when the partition between them (the balloon) is suddenly removed.

HAZARDS

This demonstration looks more dangerous than it is. If the area around and especially above the balloon is clear of obstructions and if the balloon is ignited using a stick at least a meter long at arm's length, it is relatively safe. One should practice with small balloons to gain confidence. Remember that the volume of hydrogen is proportional to the cube of the diameter of the balloon, and thus the demonstration quickly scales up to quite dramatic proportions. Hydrogen-oxygen mixtures require ear protection for both the demonstrator and the audience.

REFERENCES

1. B. Z. Shakhashiri, Chemical Demonstrations, The University of Wisconsin Press: Madison, Wisconsin, Vol 1 (1983).

2. S. Isom and C. Lail, The Science Teacher 56, 45 (March 1989).

2.17

Smoke Rings

A cardboard box with a hole in one side is used to produce smoke vortices.

MATERIALS

PROCEDURE

One of the six faces of a cardboard box of arbitrary size is removed and replaced with a sheet of thin rubber or plastic. A plastic shower curtain or even a sheet of cloth will suffice. The sheet is taped to the box to make as nearly an air-tight fit as possible. A circular hole about 10 cm in diameter is cut in the cardboard on the side of the box opposite the sheet. The box is filled with smoke. A good way to do this is to paint the rim of the hole with an aqueous solution of titanium tetrachloride (TiCl4) using a cotton swab. Alternately the box can be filled with smoke from the combustion of some suitable material or, perhaps more safely, with chalk dust or talcum powder. If a spotlight or other bright light is available, it should be aimed at the hole in the box from across the room.

The box is placed on its side, and the side with the sheet is given a tap with the hand as one would beat a drum. A smoke ring vortex should be emitted from the hole and travel across the room. The process can be repeated as often as desired so long as some smoke remains. After a while the whole room becomes smokey, and visibility is impaired. The first few rings are usually the most dramatic. A fast-moving ring can be produced immediately after a slower one so that it catches up and overtakes the slower one. Two such vortex generators can be constructed and the rings projected toward one another to study their interaction. It should be pointed out that the vortices are there even in the absence of the smoke, whose sole purpose is to render them visible. This can be illustrated by blowing out a candle from across the room.

The construction of such a vortex generator makes an ideal home project for people of all ages. The audience can be encouraged to try making one and to investigate the effect of using holes of different sizes and shapes. Would a square hole make a square ring? What happens when the ring is projected upward?

DISCUSSION

The mechanism whereby the vortex ring is generated is easy to understand. When the air exits the hole, it is retarded by friction with the rim of the hole causing the air in the center to move forward faster than the air at the edge. If you imagine riding along with the vortex, the air at the center is moving forward and the air at the edge is moving backwards. This leaves a region of reduced pressure in front of the ring at the edge and behind the ring in the center. The extra air in the center front curves outward, and the extra air at the edge in back curves inward to equalize the pressure thus forming the ring.

Vortex rings are quite a common occurrence in nature. Flowing liquids form vortices when they flow too fast down a narrow channel as can be seen by watching a fast-flowing river. Vortices off the wing tips of fast-moving aircraft are a hazard to other planes that inadvertently fly through them. Most people have seen someone who smokes make vortex rings by shaping the mouth in the form of a circle and exhaling gently. It was once thought (incorrectly) that the interaction of atoms and their spectral emission could be understood in terms of vortex motion inside the atom.

HAZARDS

The hazards are mostly in producing the smoke. One should not place ignited materials inside the box. When blowing out a candle from across the room, the candle should be kept well away from anything flammable.

2.18

Bell Jar

Object placed in a bell jar connected to a vacuum pump expand when evacuated and contract when air is readmitted.

MATERIALS

*Available from American Scientific Products, Carolina Biological Supply Company, Central Scientific Company, Fisher Scientific, Frey Scientific, Nasco and Sargent-Welch Scientific

PROCEDURE

A balloon is inflated with air to about half the diameter of the inside of the bell jar and tied off. It is placed inside the bell jar. The audience is asked to predict what will happen when the air is removed from the bell jar. A vacuum pump is turned on, evacuating the bell jar. The balloon expands. Then the audience is asked to predict what will happen when air is readmitted to the bell jar. The pump is turned off, and air is admitted, causing the balloon to return to near its original size. The procedure can be repeated with other objects such as a carbonated beverage, marshmallows or shaving cream[1]. When done with a liquid, a sulfuric acid trap should be used to prevent the pump oil from becoming contaminated.

DISCUSSION

The size of a balloon is determined by an equilibrium between the pressure of the internal gas and the combined effects of the pressure of the external gas and the elasticity of the balloon material[2]. The balloon expands when the external pressure is reduced and contracts when the external pressure is increased. A balloon with a diameter of six inches at sea level has a total external force in excess of three tons! Consequently, even a partial vacuum will significantly change its size. The balloon may not return to quite its original size because the balloon material may become permanently deformed when it expands. It is for this reason that a balloon is easier to inflate the second time than the first. A balloon is also easier to inflate if it is stretched first.

A marshmallow can be considered as a large number of very small balloons. Most people know a marshmallow is mostly air. If the marshmallow is left in the evacuated bell jar for a few minutes, the air will mostly leak out of the trapped pockets, and it will be compressed to about half its original size when air is readmitted quickly enough that the pockets don't refill. With a carbonated beverage, the carbon dioxide comes out of solution because of the reduced pressure of the external gas. The liquid will begin to boil if the pump is left on too long.

HAZARDS

The main hazard with this demonstration is implosion of the bell jar which has many tons of atmospheric pressure on it while evacuated. Use only bell jars designed to be evacuated, and be careful not to drop the bell jar or strike it with any hard objects.

REFERENCES

1. J. D. Wilson, College Physics, Allyn and Bacon: Needham Heights, MA (1989).

2. J. Walker, Scientific American 261, 136 (Dec 1989).

2.19

Liquid Nitrogen

Objects placed in liquid nitrogen change their physical properties because of the reduced temperature.

MATERIALS

*Liquid nitrogen is available from hospital supply houses. An ordinary thermos bottle serves as an adequate Dewar if it is made of metal or Pyrex glass (ordinary glass can shatter).

PROCEDURE

A bit of liquid nitrogen is poured onto the table, and the audience is asked to note that the table didn't get wet. The substance that looks like water is the major constituent (80%) of the air that we breathe, but at a reduced temperature of -196°C (-321°F, 77K). It is probably the coldest substance most people have ever seen. One can explain that it boils without evident heating because even ordinary materials like the table have quite a lot of heat, and not much heat is needed is boil nitrogen.

One explains that most materials change their physical properties when they get cold. Most people have noticed how hard the seats of their cars are on a cold morning. A plastic hose it dipped into the Dewar of liquid nitrogen until the boiling stops and then shattered with a hammer. While the nitrogen is boiling, a small cloud appears above the Dewar. The audience can be asked what it is. Many will say "steam" or "smoke," but of course steam is invisible and smoke is the product of combustion. The cloud actually consists of small particles of liquid water condensed from the air above the Dewar by the cooling effect of the boiling of the nitrogen.

One can take a rubber ball, bounce it a few time on the floor and then drop it into the liquid nitrogen. When the boiling stops, the ball is removed with tongs, and then, while wearing thermally insulating gloves, throw it to the floor causing it to shatter. Alternately, a banana is left in the liquid nitrogen for a few minutes and then used to drive a large nail into a block of styrofoam. The banana has a tendency to shatter and leaves quite a mess when it thaws.

A balloon is blown up to about six inches in diameter, tied off and placed in a glass dish. Liquid nitrogen is poured over the balloon causing it to shrivel to negligible size. It is then removed from the dish with tongs or gloves and held while it slowly reinflates. If one looks carefully, it is possible to see some liquid air inside the balloon. The audience can be asked to explain what is happening.

DISCUSSION

The temperature of liquid nitrogen is suffiently low that most materials have significantly different and sometimes surprising properties. Few elastic materials retain their elasticity at this temperature. Electrical resistance is much lower, and some materials in fact become superconductors and lose all electrical resistance.

When the air in a balloon is cooled, its pressure decreases, and the pressure of the external atmosphere crushes it. Some of the nitrogen and most of the oxygen in the balloon may liquefy.

HAZARDS

Liquid nitrogen is potentially very dangerous since it can cause instant frostbite. Never allow it to come into contact with bare skin. Objects should be lowered into the liquid nitrogen and removed with tongs. Be careful that it doesn't splash into the eyes. Gloves and protective eyewear are recommended. When objects are shattered with a hammer or by throwing them against the floor or wall, the resulting projectiles can easily injure someone unless proper precautions are taken.

2.20

Kinetic Theory Simulator

A collection of small ball bearings in an enclosure one side of which is connected to a loudspeaker exhibit motion analogous to the molecules in a gas.

MATERIALS

*Commercial versions, sometimes called "molecular motion demonstrators" are available from Central Scientific Company, Carolina Biological Supply Company, Frey Scientific, PASCO Scientific, and Sargent-Welch Scientific.

PROCEDURE

A dozen or more small plastic or steel balls are placed in a transparent container, one boundary of which is made to oscillate rapidly back and forth by a vibrator or loudspeaker connected to a high power audio oscillator at a frequency of a few Hertz. A larger version can be made with ping-pong balls in a large plexiglas cylinder with a motor-driven piston. For a large audience, the apparatus is placed on an overhead projector, shadowed with an arc lamp against a screen or viewed with a television camera and monitor. The amplitude or frequency of the driving oscillation can be changed to illustrate the effect of changing the temperature of a gas. A lid resting on the balls but free to move upward illustrates the pressure exerted by molecules in motion as they bombard the walls of their container. One should emphasize that this demonstration is merely a simulation since typical molecules in a gas are about ten million times smaller than the balls used in the demonstration.

DISCUSSION

Simulations such as this provide a useful means for visualizing the motion of molecules[1]. An ideal gas obeys the ideal gas law

pV = NkT

where p is the pressure, V is the volume, N is the number of molecules in the volume, k is Boltzmann's constant (1.38 x 10-23 J/K) and T is the temperature (in Kelvin). Thus with a given number of molecules (N) in a constant volume (V) the pressure increases in proportion to the temperature. If the volume (V) is allowed to change but the pressure (p) is kept constant by having a movable lid of given weight, the volume (V) increases in proportional to the temperature. This is known as Charles's Law after Jacques Alexandre Cesar Charles (1746-1823).

Real gases would typically be in thermal equilibrium with the walls of their container, and thus the molecules would on average gain as much energy as they lose upon collision with the walls and with one another. In this case, the kinetic energy of the balls is considerably greater than their thermal energy at room temperature (about kT) and thus the balls lose energy every time they collide. Hence it is necessary to provide energy input to keep the balls moving. The effective "temperature" of the simulated gas can be calculated from

kT = mv2

where m is the mass of the balls and v is their velocity. If the balls are 0.01 kg and their velocity is 10 m/s, the temperature is about 1023 degrees!

This demonstration also illustrates how apparent randomness can arise from simple equations of motion if there are many particles interacting. Even without gravity and with perfectly elastic collisions (no energy loss), the motion is very complicated and effectively unpredictable after many collisions. If one of the balls were painted red and its motion followed through many collisions, it would execute a random walk (Brownian motion).

HAZARDS

Take care not to burn out the speaker with too large of an input voltage. A handful of ball bearings carelessly spilled on the floor can make for treacherous walking!

REFERENCE

1. B. Z. Shakhashiri, Chemical Demonstrations, The University of Wisconsin Press: Madison, Wisconsin, Vol 2 (1985).

2.21

Firehose Instability

A rubber hose connected to a source of compressed air dangles from the ceiling and flails about in a complicated fashion.

MATERIALS

PROCEDURE

A rubber hose is suspended from the ceiling with one end open and just above head level. The other end is connected to a source of compressed air. The audience is asked what would happen if they were to turn on a garden hose full blast without holding on to the end of it. Most people answer by flailing their arms wildly. Point out that this effect is called the "firehose instability," and that it can be very dangerous with a large hose such as used by firefighters. Then turn on the compressed air to illustrate that the same thing happens with gases as with liquids. Point out that it is the same compressed air that one would use to inflate an automobile tire or bicycle tire. Try hoses of different diameters and with different nozzles to get the best effect for the length and pressure used. A similar phenomenon is observed when a balloon inflated with air is released.

DISCUSSION

A hose with fluid coming out one end is unstable in the same way a pencil balanced on its point is unstable. If the hose were perfectly straight, the reaction force of the exhausted fluid would be along the axis of the hose and would simply compress it without any sideward motion. With a stiff hose or pipe, this is just what would happen. This condition is one of unstable equilibrium just as a pencil balanced vertically on its point has all the force along its axis. However, if the hose bends slightly, there is a horizontal component of the force that causes it to bend more, and the bend continues to grow. In the same way, if the pencil is not exactly vertical, there is a component of the force that causes it to continue moving away from the vertical.

The instability actually explains only the initial motion. Thereafter there is a complicated interplay of the reaction force, gravity and elastic forces in the hose that result in chaotic motion. In principle, it would be possible to calculate the resulting motion, and with a computer, it would even be practical, but the prediction would be precise only for short times because of the extreme sensitivity to the initial conditions and to the exact nature of the forces. Like all chaotic processes, this demonstration illustrates apparently random behavior of deterministic systems.

HAZARDS

Hanging the hose above head level prevents it from hitting anyone in the face. Be sure it is suspended securely. Scaled-up versions of this demonstration using high pressure gases and liquids and large hoses are impressive but entail considerable obvious dangers.

2.22

Dripping Faucet

A dripping faucet illustrates periodic and chaotic behavior and the period doubling route to chaos.

MATERIALS

PROCEDURE

Place an aluminum pie pan, bottom-side up, about half a meter below a water faucet whose drip rate can be controlled. The pie pan makes the dripping water audible. A microphone placed under the pie pan and connected to the an amplifier and speaker makes an impressive sound easily heard by a large audience. The output of the microphone can also be connected to an oscilloscope adjusted to a slow sweep rate (about 1 Hz) and set to trigger on the input sound. A television camera aimed at the point where the drops are released improves visibility.

At a low drip rate (once per second, say) the dripping is perfectly periodic. As the drip rate is slowly increased, there comes a point where a bifurcation occurs and the dripping suddenly changes to a period twice as long. The bifurcation is evident in the sound, which should change from "drip - drip - drip" to "drip drip - drip drip - drip drip." Careful adjustment and patience is required to detect the bifurcation. At a slightly larger drip rate, a second bifurcation occurs (four times the period), and so forth, but these longer periods are difficult to observe. At the end of this infinite, period-doubling sequence, the dripping is chaotic, and has no detectable pattern. It should be easy to hear and observe on an oscilloscope the chaotic condition.

DISCUSSION

The dripping faucet is one of the simplest and most common examples of the period-doubling route to chaos. It has been extensively studied[1-5], and an entire scientific book[6] has been written about it. Its simplicity makes it ideal for home experimentation.

The mechanism is as follows. There is a maximum size that a drop can have for its weight to be less than the surface tension that holds it together and holds it attached to the rim of the faucet. When it reaches this critical size, the drop splits into two parts, one of which falls while the other is left behind. The drop left behind then begins to grow, and the process repeats. If the drop fills with water at a constant rate, the time required for it to reach this critical size is a constant, and the drops are released periodically. However, the drop left behind will oscillate up and down a few times before coming to rest, and inertia of this moving mass will either encourage or discourage the next release of a drop depending on the phase of the oscillation when the drop reaches its critical size. A drop released early will leave more water behind for the formation of the next drop and vice versa. It is reasonable that there might be a condition in which alternate drops are in and out of phase with the oscillation, respectively, and this is the situation that leads to period doubling. Chaos occurs when the drip rate is faster than the oscillation frequency so that the phase of the oscillation is different each time a drop is released. The oscillation can be easily seen if the faucet is observed closely.

Water drops are a useful analogy to nuclear processes. There is a maximum size of the nucleus determined by a competition of the electrostatic repulsion between the protons and the short-range attractive nuclear force that behaves somewhat like surface tension. When a nucleus exceeds a certain critical size, it splits by the fission process with a large release of energy. The fission fragments are of varying size, probably determined by the phase of oscillations within the nucleus when the fission occurs.

HAZARDS

The only hazards are from spilled water and perhaps water damage to the microphone.

REFERENCES

1. P. Martien, S. C. Pope, P. L. Scott and R. S. Shaw, Phys. Lett 110Z, 399 (1985).

2. X. Wu, E. Tekle and Z. A. Schelly, Rev. Sci. Instr. 60, 3779 (1989).

3. X. Wu and Z. A. Schelly, Physica D 40, 433 (1989).

4. H. Yepez, N. Nuniez, A. L. Salas Brito, C. A. Vargas and L. A. Vicente, Eur. J. Phys. 10, 99 (1989).

5. R. F. Calalan, H. Leidecker and G. D. Cahalan, Comp. in Phys. 4, 368 (1990).

6. R. Shaw, The Dripping Faucet as a Model Chaotic System, Ariel Press: Santa Cruz, CA (1984).

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J. C. Sprott