VI. Archimedes` principle

advertisement
Pfizer Education Initiative
ala KaZOO ala KASAM
This lesson plan is based on Steve Spangler’s Fizz Factor. The following are some guidelines
but it is suggested that you look through the book and plan your own “party of fun”.
No soda or perishable items are supplied in this kit. If you wish to be reimbursed by PEI,
please submit an expense report to Connie Brennan.
Materials Supplied
Please review PEI safety
Demo Tank
guidelines and Soda Lab
Marshmallow Masher
Safety found on pg 9 in the
Floss
Fizz Factor book included
Caps with small holes drilled
Salt
in the kit prior to
Mento’s dispenser/Tube
performing any
Balloons
demonstrations or hands
Beaker
on experiments.
Hot Plate
Tongs
Steve Spangler’s book: Fizz Factor: 50 Amazing Experiments with Soda Pop
I.
Boyles Law
When you shake up a can of soda, bubbles collect on the side of the can. Opening the can
decreases the pressure, increasing the volume of the bubbles which rise to the top and causes
the soda to rush out.
In the mid 1600's, Robert Boyle studied the relationship between the pressure p and the volume
V of a confined gas held at a constant temperature. Boyle observed that the product of the
pressure and volume are observed to be nearly constant. The product of pressure and volume is
exactly a constant for an ideal gas.
Gases have various properties which we can observe with our senses, including the gas
pressure, temperature, mass, and the volume which contains the gas. Careful, scientific
observation has determined that these variables are related to one another, and the values of
these properties determine the state of the gas.
Boyle's Law states
PV = kT
where k is a constant, or
Pressure * Volume = Constant * Temperature
The value of the constant k depends on the units used for the other quantities but once the units are
fixed, k is also fixed. When any one of the quantities V, P, or T is changed, one or two of the
others must change so that the equation above still holds.
To demonstrate Boyle’s Law use the following exercises in the Fizz Factor Book:
1. Soda Can Shake-Up, pg 21
2. Baby Bottle Blow-up, pg 23
Temperature and cavitation site effects on carbonation:
3. Temperature Sensitive Fizz, pg 33
4. Just Add Ice, pg 34
5. Take a Peek inside, pg 35
II.
Learning more about Air Pressure
Atmospheric Pressure
 force exerted by the weight of the air
Atmospheric pressure is defined as the force per unit area exerted against a surface by the weight
of the air above that surface. In the diagram below, the pressure at point "X" increases as the
weight of the air above it increases. The same can be said about decreasing pressure, where the
pressure at point "X" decreases if the weight of the air above it also decreases.
Thinking in terms of air molecules, if the number of air molecules above a surface increases, there
are more molecules to exert a force on that surface and consequently, the pressure increases. The
opposite is also true, where a reduction in the number of air molecules above a surface will result
in a decrease in pressure. Atmospheric pressure is measured with an instrument called a
"barometer", which is why atmospheric pressure is also referred to as barometric pressure.
As an example, consider a "unit area" of 1 square inch. At sea level, the weight of the air above
this unit area would (on average) weigh 14.7 pounds! That means pressure applied by this air on
the unit area would be 14.7 pounds per square inch. Meteorologists use a metric unit for pressure
called a millibar and the average pressure at sea level is 1013.25 millibars.
Experiments demonstrating the affects of air pressure.
1.
2.
3.
4.
5.
6.
III.
The Big Squeeze, pg 59
Marshmallow Masher, pg 67
Diving for Ketchup, pg 74
Do Not Open! pg 89
The Quick-Pour Soda Bottle Race, pg 87
The Incredible Can Crusher, pg 49 (one of my favorites!)
Density of Liquids
Found on page 26 of the Fizz Factor Book.
We all know that certain things float in water while other things sink, but why? Do all heavy things
sink? Why does a penny sink and an aircraft carrier float? Think you know the answers?
Experiment:
1. Ask your audience the question: "Will this can of regular soda float or sink in the water?" After
gathering everyone's answer, place the can of regular soda in the water and notice that it sinks to
the bottom. Note: If the can of regular soda floats, you might have an air bubble trapped under the
bottom of the can.
2. Pick up a can of diet soda and pose the same question. Be sure to point out the fact that the cans
are exactly the same size and shape and contain the same amount of liquid (compare the number of
milliliters... probably 355 ml). Place the can of diet soda in the water and notice that it floats!
Show your audience that there are no bubbles trapped under the bottom. It still floats. Why?
How it works:
Take a look at the two boxes below. Each box has the same volume. If each ball has the same
mass, which box would weigh more? Why?
The box that has more balls has more mass per unit of volume. This property of matter is called
density. The density of a material helps to distinguish it from other materials. Since mass is usually
expressed in grams and volume in cubic centimeters, density is expressed in grams/cubic
centimeter.
Objects less dense than water float, and those denser than water sink. Empty cans float, rocks sink.
This is only possible because of differences in density.
Density= Mass/Volume
If both cans could be placed on a double pan balance, it would be clear that the regular soda is
heavier than the diet soda. This demonstrates the difference between mass and volume. Mass refers
to how much stuff exist within an object. If something is heavier than another object, it contains
more mass. Mass is measured in grams.
Volume, on the other hand, refers to how much space an object occupies. For fluids, volume is
usually measured in liters (L) or milliliters (ml). There are 1000 ml in one liter. Since both cans
have the same volume, the heavier can must have a greater mass. We can now conclude that the
heavier can is denser than the lighter can.
Diet sodas usually contain aspartame, an artificial sweetener, while regular sodas use sugar. Take a
look at the nutritional information on the side of the cans. Notice how much sugar is in a regular
soda (look under carbohydrates). The regular Coke has 39 grams of sugar. (Show how much 39
grams of sugar looks like). Diet soda is flavored with a relatively small amount of an artificial
sweetener (like aspartame) which is 200 times sweeter than an equal amount of sugar. Therefore,
only a tiny amount of aspartame is needed. (Show how much aspartame is needed to sweeten diet
soda). Both sugar and aspartame are denser than water, so it is actually a matter of how much of
each is used. The 39 grams of sugar added to a can of regular Coke makes it sink. The relatively
tiny amount of aspartame used in diet sodas will have a negligible effect on the mass, enabling the
can to still float.
So why then do cans of diet soda float? It is all due to the fact that there is a little bit of space,
called headspace, above the fluid in each can of soda. This space is filled with gas, which is much
less dense than the soda, itself. It is this space above the soda that lowers the density of diet drinks
just enough to make them float. Sugared drinks still have this headspace, but the excessive
amounts of sugar added makes the can denser than water.
Now freeze a can of regular Coke (make sure to put it in a plastic ziplock bag in case the can
explodes). By freezing the regular Coke, the can will be pushed out by the liquid expanding as it
freezes. Allow the can to defrost at room temperature. Now test to see if the defrosted can of
regular Coke floats. The extra headspace (volume) of the defrosted Coke is enough to allow the
regular Coke to float.
As you talk about the sugar amount and contents of soda, the following topics may be of use:
1. What’s in a soft drink? pg 12
2. How much soda pop do you drink? pg 13
3. Drinking Liquid Sugar, pg 13
More density experiments:
1. Take the Salt Water Plunge, pg 29.
2. The Floating Golf Ball, pg 85 (see below)
Do a similar experiment using regular water and showing
how the golf ball is denser than water. Ask if anyone has
swim in the ocean. Is it hard to sink? Ask what they think
will happen if we add the same golf ball to salt water?
Show that the salt water is denser than the golf ball so that
it floats.
IV.
Convection
Thermal energy can be transferred by three ways: conduction, convection, and radiation. The most
common way it is transferred in fluids is by convection. Teaching convection in relationship to
density of solutions can be assisted with using Melting Away experiment on pg 61-62.
Convection is the transfer of energy by the movement of matter. Convection and conduction are
similar. They both transfer energy from particle to particle. However, conduction transfers energy
without actually moving the particles. Conduction is the way energy is transferred in a solid. With
convection, the particles actually move from one place to another. They carry the energy with
them.
When heat is added to an object, whether a fluid or a solid, its particles begin to move faster.
However, the particles of a fluid have more freedom to move than those of a solid. The particles
begin to move apart, causing the fluid to expand. For example, what happens when you boil water
in a pot on the stove? The burner on the stove heats the bottom of the pot by conduction. The water
touching the bottom of the pot is also heated by conduction. As this water is heated, it expands.
This expansion causes the water to become less dense. Cooler, denser water at the surface sinks
and pushes the hot water upward. As the hot water rises, it cools by contact with the air and cooler
water at the top through conduction. This water becomes denser and sinks. This repetitive
movement creates convection currents. These currents transfer thermal energy from warmer areas
of the fluid to cooler areas.
In the case of the Melting Away experiment, the density of the regular soda inhibits the convection
currents, which causes the ice to melt much slower.
V.
Surface Tension and Nucleation Sites
Mentos Fountain
Materials needed:
 Rolls of Mentos
 2 liter bottles of Diet Soda
Either diet or regular soda will work but diet soda is less sticky to clean up.
1. This activity is best done outside in the middle of field.
2. Carefully open the 2 liter bottle of soda. Position the bottle on the ground so that it
will not tip over.
3. Unwrap the whole roll of Mentos. The goal is to drop all of the Mentos into the
bottle of soda at one time. Warn the spectators to stand back.
4. Use the tube, position the tube directly over the mouth and let the candies fall into
the bottle at the same time.
Explanation:
Soda pop is basically sugar or diet sweetener, flavoring, water and preservatives. The thing that
makes soda bubbly is carbon dioxide gas which is pumped into the bottle at the bottling plant using
tons of pressure. Ordinarily, water resists the expansion of bubbles in the soda. Water molecules
attract each other strongly, and they link together to form a tight mesh around each bubble. It takes
lots of energy to push water molecules away from each other to form a new bubble, or to expand a
bubble that has already been formed. The phenomenon is called "surface tension".
Mentos contain sugar, hydrogenated coconut oil, starch, gum Arabic, an emulsifier and natural
flavor. The gelatin and gum arabic from the dissolving candy disrupts the water mesh or surface
tension, so it takes less work to expand bubbles. At the same time, the roughness of the candy
surface provides many little nooks and crannies that allow new bubbles to form more quickly (a
process called nucleation). As more of the surface dissolves, both processes accelerate, and foam
rapidly begins to form. When all this gas is released, it thrusts the entire contents of the bottle
skyward.
You can see a similar effect when cooking potatoes or pasta in a pot of boiling water. The
water will sometimes boil over because organic materials that leach out of the cooking
potatoes or pasta disrupt the tight mesh of water molecules at the surface of the water,
making it easier for bubbles and foam to form. Root beer can also foam over if a scoop of
ice cream is added, for essentially the same reason. The surface tension of the root beer is
lowered by gums and proteins from the melting ice cream, and the CO2 out-gassing from
the root beer blows the foam.
See similar experiments:
1. Salty Soda, pg 32
2. Ultimate Eruption, pg 36
3. Ultimate Eruption II, pg 37(This is Awesome!!!)
VI.
Archimedes' principle
Use the Dancing Raisins (pg 43) experiment to explain Archimedes’ principle. See below for
more information.
It was the ancient Greek, Archimedes of Syracuse, who first discovered the law of buoyancy called
Archimedes's principle. The story of Archimedes discovering buoyancy while sitting in his bathtub
is described below which is from Book 9 of De architectura by Vitruvius. (See Appendix I)
Archimedes' principle states that a body immersed in a fluid is buoyed up by a force equal to the
weight of the displaced fluid. The principle applies to both floating and submerged bodies and to
all fluids, i.e., liquids and gases. It explains not only the buoyancy of ships and other vessels in
water but also the rise of a balloon in the air and the apparent loss of weight of objects underwater.
In determining whether a given body will float in a given fluid, both weight and volume must be
considered; that is, the relative density, or weight per unit of volume, of the body compared to the
fluid determines the buoyant force. If the body is less dense than the fluid, it will float or, in the
case of a balloon, it will rise. If the body is denser than the fluid, it will sink. Relative density also
determines the proportion of a floating body that will be submerged in a fluid. If the body is two
thirds as dense as the fluid, then two thirds of its volume will be submerged, displacing in the
process a volume of fluid whose weight is equal to the entire weight of the body. In the case of a
submerged body, the apparent weight of the body is equal to its weight in air less the weight of an
equal volume of fluid. The fluid most often encountered in applications of Archimedes' principle
is water, and the specific gravity of a substance is a convenient measure of its relative density
compared to water. In calculating the buoyant force on a body, however, one must also take into
account the shape and position of the body. A steel rowboat placed on end into the water will sink
because the density of steel is much greater than that of water. However, in its normal, keel-down
position, the effective volume of the boat includes all the air inside it, so that its average density is
then less than that of water, and as a result it will float.
In physics, buoyancy is an upward force on an object immersed in a fluid (i.e., a liquid or a gas),
enabling it to float or at least to appear lighter. Buoyancy is important for many vehicles such as
boats, ships, balloons, and airships. The buoyant force is equal to the weight of the displaced fluid.
The weight of the displaced
fluid is directly proportional
to the volume of the displaced
fluid (specifically if the
surrounding fluid is of
uniform density), in addition
to the volume of fluid above
the object (if the object is
completely immersed in the
fluid). Thus, among objects
with equal masses, the one
with greater volume has
greater buoyancy.
If the weight of an object is less than the weight of the fluid the object would displace if it was
fully submerged, then the object is less dense than the fluid and it floats at a level so it displaces
the same weight of fluid as the weight of the object.
If the object has exactly the same density as the liquid, then it will stay still, neither sinking nor
floating upwards, just as the liquid nearby stays still.
An object made of a material of higher density than the fluid, for example a metal object in water,
can still float if it has a suitable shape (e.g. a hollow which is open upwards or downwards) that
keeps a large enough volume of air below the surface level of the fluid. In that case, for the
average density mentioned above, the air is included also, which may reduce this density to less
than that of the fluid.
VII. Hydrophobic versus hydrophilic
Demonstrate hydrophobic properties (water repelling properties) and hydrophilic (water loving
properties) with The Great Grape Debate, pg 47.
See Appendix II for Information from Planet Water.Au.com
Hydrophilic ('Water Loving') and Hydrophobic ('Water Hating') Molecules.
VIII. Learn more about Carbon Dioxide
1. What is Carbonation? pg 15
2. The Explosive Soda Secret, pg 17
3. Fizz or Flat? pg 19
4. The Expanding Balloon, pg 72
5. The Expanding Balloon: Part II pg 73
6. Fizz Fire Extinguisher pg 31
IX.
Conductors and Insulators
In performing The Quicker Cooler experiment on pg 65, try and get the volume of can and
plastic soda as close as possible.





Thermal conductor = something that lets heat move through itself.
Thermal Insulator = something that stops heat from moving through itself.
Good thermal conductors are things like: metals (iron, aluminum, copper, steel,
titanium...). Good thermal conductors heat up and cool down very quickly.
Poor thermal conductors are things like: plastics (polystyrene, polyester, rubber,
PVC, PVA...); fabrics (wool, cotton, leather, silk...); rocks & minerals (stone, chalk,
marble, slate...) etc. Poor thermal conductors heat up and cool down very slowly.
A good thermal conductor is a poor thermal insulator, and vice versa. For example:
copper is good thermal conductor, so it is a poor thermal insulator; wool is a good
thermal insulator, so it is a poor thermal conductor.
X.
pH of Soda
The pH of soda is also demonstrated in the Acid-Base or pH Kit. The following
experiments, discussing the pH of soda, are as follows:
1.
2.
3.
4.
XI.
The pH of Soda, pg 51
The pH of Soda – Part II, pg 53
The World’s best Copper Cleaner, pg 56 (based on acidity of soda)
Soda Acid Magic, pg 77
Learn to differentiate between a suspension, colloid and solution
The Solution or Suspension, pg 63 demonstrates the difference of a suspension and
solution. The following information is supplemental to what is discussed in the Fizz
Factor book.
A suspension, in chemistry, is a mixture of two substances, one of which is finely
divided and dispersed in the other. Common suspensions include sand in water,
fine soot or dust in air, and droplets of oil in air. A suspension is different from a
colloid or solution. Particles in a suspension are larger than those in colloids or
solutions; they are visible under a microscope, and some can be seen with the
naked eye. Particles in a suspension precipitate if the suspension is allowed to
stand undisturbed.
A colloid (kol'oid) [key] [Gr., =glue-like] is a mixture in which one substance is
divided into minute particles (called colloidal particles) and dispersed throughout a
second substance. The mixture is also called a colloidal system, colloidal solution,
or colloidal dispersion. Familiar colloids include fog, smoke, homogenized milk, and
ruby-colored glass.
A solution, in chemistry, is a homogeneous mixture of two or more substances.
The dissolving medium is called the solvent, and the dissolved material is called the
solute. In most common solutions, the solvent is a liquid, often water, and the
solute may be a solid, gas, or liquid. For example, syrups are solutions of sugar, a
solid, in water, a liquid; household ammonia is a solution of ammonia gas in water;
and vinegar is a solution of acetic acid, a liquid, in water. When two liquids, e.g.,
water and ethanol, can be mixed in any proportions, the solvent is commonly
considered to be the one present in greater proportion.
References
Rohrig, Brian. Fizz Factor: 50 Amazing Experiments with Soda Pop, Wren Publishing, 2003.
The National Aeronautics and Space Administration
www.grc.nasa.gov/WWW/K-12/airplane/boyle.html
Copyright c 1997 by Frank Wattenberg, Department of Mathematics, Montana State
University, Bozeman, MT 59717
http://www.math.montana.edu/frankw/ccp/before-calculus/function/boyle/body.htm
Lee Marek of Naperville North High School Author FredSenese Why do Mentos mints foam when
you drop them into soda pop?
Bill Thayer’s Website, Vitruvius: On Architecture
http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Vitruvius/9*.html
Planet Water.au.com
http://www.ozh2o.com/h2chem.html
Credits and Acknowledgments for Atmospheric Pressure:
Department of Atmospheric Sciences (DAS) at www.atmos.uiuc.edu, the University of Illinois
at Urbana-Champaign.
APPENDIX I
The story of Archimedes discovering buoyancy from Book 9 of De architectura by Vitruvius
Though Archimedes discovered many curious matters which evince great intelligence,
that which I am about to mention is the most extraordinary. Hiero, when he obtained
the regal power in Syracuse, having, on the fortunate turn of his affairs, decreed a
votive crown of gold to be placed in a certain temple to the immortal gods, commanded
it to be made of great value, and assigned an appropriate weight of gold to the
manufacturer. He, in due time, presented the work to the king, beautifully wrought, and
the weight appeared to correspond with that of the gold which had been assigned for it.
10. But a report having been circulated, that some of the gold had been abstracted, and
that the deficiency thus caused had been supplied with silver, Hiero was indignant at the
fraud, and, unacquainted with the method by which the theft might be detected,
requested Archimedes would undertake to give it his attention. Charged with this
commission, he by chance went to a bath, and being in the vessel, perceived that, as his
body became immersed, the water ran out of the vessel. Whence, catching at the method
to be adopted for the solution of the proposition, he immediately followed it up, leapt out
of the vessel in joy, and, returning home naked, cried out with a loud voice that he had
found that of which he was in search, for he continued exclaiming, in Greek, εὑρηκα,
(I have found it out).
º
11. After this, he is said to have taken two masses, each of a weight equal to that of the
crown, one of them of gold and the other of silver. Having prepared them, he filled a
large vase with water up to the brim, wherein he placed the mass of silver, which caused
as much water to run out as was equal to the bulk thereof. The mass being then taken
out, he poured in by measure as much water as was required to fill the vase once more
to the brim. By these means he found out what quantity of water was equal to a certain
weight of silver.
12. He then placed the mass of gold in the vessel, and, on taking it out, found that the
water which ran over was lessened, because, as the magnitude of the gold mass was
smaller than that containing the same weight of silver. After again filling the vase by
measure, he put the crown itself in, and discovered that more water ran over then than
with the mass of gold that was equal to it in weight; and thus, from the superfluous
quantity of water carried over the brim by the immersion of the crown, more than that
displaced by the mass, he found, by calculation, the quantity of silver mixed with the
gold, and made manifest the fraud of the manufacturer.
APPENDIX II
Hydrophilic Molecules
Substances that dissolve readily in water are termed hydrophilic. They are composed of ions or polar molecules that attract
water molecules through electrical charge effects. Water molecules surround each ion or polar molecule on the surface of a
solid substance and carry it into solution. Ionic substances such as sodium chloride dissolve because water molecules are
attracted to the positive (Na+) or negative (Cl_) charge of each ion. Polar substances such as urea dissolve because their
molecules form hydrogen bonds with the surrounding water molecules.
Hydrophobic Molecules
Molecules that contain a preponderance of nonpolar bonds are usually insoluble in water and are termed 'hydrophobic'.
This is true, especially, of hydrocarbons, which contain many C-H bonds. Water molecules are not attracted to such
molecules as much as they are to other water molecules and so have little tendency to surround them and carry them into
solution.
But the so-called 'Hydrophobic Effect' does not mean that nonpolar molecules are not attracted to water! We have all seen
what happens after vinegar and oil salad dressing are vigorously shaken; one does get a mixture of sorts, but after a little
time the ingredients separate with the lighter oil on top and a denser vinegar/water solution on bottom This is an illustration
of an important chemistry principle expressed by the rule that 'like dissolves like.' This refers to the phenomena that when
two liquids made of molecules of similar size and polarities are mixed, they will usually form a single phase solution, no
matter what the relative number of moles of each species. This is expressed by the jargon that the two substances are
miscible in all proportions.
In contrast, when a highly polar substance, such as water, is mixed with a nonpolar or weakly polar substance, such as most
oils, the substances will separate into two phases. This phenomenon is usually rationalized in introductory chemistry text
books by saying that oil is hydrophobic, and thus does not make solutions with water, while polar small organic acids (such
as acetic acid from which house vinegar is made) are hydrophilic, and thus are miscible with water.
This explanation almost universally leads people to believe that individual water and oil repel each other, or at least attract
each other very weakly. Nothing can be further from the case! An individual oil molecule is attracted to a water molecule by
a force that is much greater than the attraction of two oil molecules to each other. We can observe the consequence of this
greater attraction when we put a drop of oil on a clean surface of water. Before hitting the surface, the oil will be in the
shape of a spherical droplet. This is because the oil molecules are attracted to one another and a spherical shape minimizes
the number of oil molecules that are not surrounded by other molecules. When the oil hits the surface of the water, it
spreads out to form a thin layer. This happens because the attractions between the oil and water molecules gained by
spreading over the surface is larger than the oil-oil attraction lost in making a large oil surface on top of the water. If a
sufficiently small drop of oil is put on the surface, it will spread to form a single molecular layer of oil. By measuring the
area produced, one can get a simple estimate for the size of each oil molecule and thus Avogadro's number.
Given these strong interactions, why does not each oil molecule dive into the water solution? and surround itself with the
favorable water attractions? The reason is that to do so, it must come between water molecules that are already attracting
each other! The strength of water-water attraction is much higher than water-oil interactions, and thus there is a net cost of
energy in putting the oil molecules into a water solution. Thus the vast majority of oil molecules stay out of the water,
though as many as will fit will hang on to the surface water molecules that do not have a full complement of partners. The
meniscus is the curved surface of a liquid in a graduated cylinder or any other small diameter glassware. Water adheres to
the sides of any container creating a "cup" of surface tension.
This induced structure is very important is it related to the structure and function of membranes which are very
characteristic of life as we know it. Membranes in bacteria are composed of phospholipids and proteins. Phospholipids
contain a charged or polar group (often phosphate, hence the name) attached to a 3 carbon glycerol back bone. There are
also two fatty acid chains dangling from the other carbons of glycerol. The phosphate end of the molecule is hydrophilic and
is attracted to water. The fatty acids are hydrophobic and are driven away from water.
Because phospholipids have hydrophobic and hydrophilic portions, they do remarkable things. When placed in an
aqueous environment, the hydrophobic portions stick together, as do the hydrophilic. A very stable form of this
arrangement is the lipid bilayer. This way the hydrophobic parts of the molecule form one layer, as do the hydrophilic.
Lipid bilayers form spontaneously if phospholipids are placed in an aqueous environment. The cytoplasmic membrane is
stabilized by hydrophobic interactions (i.e. water induced) between neighboring lipids and by hydrogen bonds between
neighboring lipids. Hydrogen bonds can also form between membrane proteins and lipids. These are known as membrane
vesicles and are used to study membrane properties experimentally. There is some evidence that these structures may form
abiotically and may occur on particles that rain down on earth from space.
Download