Freezing of Water

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Water is an unique substance that consists of many unusual properties. The two elements making u

water are Hydrogen and Oxygen. There are two Hydrogen atoms per Oxygen atom. Hence the

Molecular Formula of water is H2O. This makes water a polar compound and soluble with many

substances. As hydrogen and oxygen are both non-metals, covalent bonding is used to form the

compound. In covalent bonding the more electronegative (ability to attract electrons) atom has a

slightly negative charge and the less electronegative is slightly positively charged. Polar molecules a

attracted to one another by dipole interaction. Hydrogen has an electronegativity of 2.1 and Oxyge

3.5. Therefore the difference in electronegativity is 1.4. The negative end of one molecule of water

attracted to the positive end of another. This results in hydrogen bonding.

Hydrogen bonding occurs when the hydrogen bonds with a highly electronegative element e.g. O, F

The Hydrogen (slightly positive charge) is attracted to the lone pair of electrons in the nearby atom

Oxygen (the highly electronegative element). This Hydrogen bond has about 5% of the strength of

standard covalent bond. Hydrogen bonds are the strongest of all intermolecular forces.

Hydrogen bonding in water is the only reason why it has such a high specific heat. Specific heat can

defined as the amount ofheatrequired to change a unit mass ( such as a mole) of a substance by o

degree in temperature. Hydrogen bonding weakens as the temperature rises, therefore much of the

energy is used into breaking hydrogen bonds instead of raising the temperature. This causes water

have a higher heat capacity, In fact it is the second highest among all the heteroatomic species (aft

ammonia).

According to Josh Willis, ofNASA'sJet Propulsion Laboratory, the oceans absorb one thousand time

more heat than the atmosphere (air) and are holding 80 to 90% of the heat ofglobal warming.

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Ice is water frozen into the solid state. It can appear transparent or opaque bluish-white color,

depending on the presence of impurities or air inclusions. The addition of other materials such as soil

further alter the appearance.

The molecules in solid ice may be arranged in different ways, called phases, depending on the

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temperature and pressure. Usually ice is the phase known as ice Ih, which is the most abundant of t

varying solid phases on the Earth's surface. The most common phase transition to ice Ih occurs

when liquid water is cooled below 0C (273.15K, 32F) at standard atmospheric pressure. It can also deposit fr

vapour with no intervening liquid phase, such as in the formation of frost.

As a naturally occurring crystalline inorganic solid with an ordered structure, ice is considered

a mineral.[1] It possesses a regular crystalline structure based on the molecule of water, which consists o

single oxygen atom covalently bonded to two hydrogen atoms, or H-O-H. However, many of the physical

properties of water and ice are controlled by the formation ofhydrogen bonds between adjacent oxy

and hydrogen atoms. It is a weak bond, but is critical in controlling the structure of both water and

An unusual property of ice frozen at atmospheric pressure is that the solid is approximately 8.3% less dense than liquid w

The density of ice is 0.9167 g/cm at 0 C, whereas water has a density of 0.9998 g/cm at the same temperature. Liquid w

is densest, essentially 1.00 g/cm, at 4 C and becomes less dense as the water molecules begin to form

the hexagonal crystals[2] ofice as the freezing point is reached. This is due to hydrogen bonding dominating the intermole

forces, which results in a packing ofmolecules less compact in the solid. Density of ice increases slightly with decreasing

temperature and has a value of 0.9340 g/cm at 180 C (93 K).[3]

The effect of expansion during freezing can be dramatic, and is a basic cause offreeze-thaw weathering ofrock in naturealso a common cause of the flooding of houses when water pipes burst due to the pressure of expanding water when it

freezes, then leak water after thawing.

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Any substance can exist in three different physical forms; solid, liquid and gas. Water is the only substance onearth that naturally occurs in all three states. Temperature reflects the amount of kinetic energy of molecules ormore simply, the motion of the molecules. The faster the molecules are moving the higher their temperature. Thisis similar to how the faster you move, the hotter you get! When moving, the hydrogen bonds between themolecules of water can break. The water molecules in the liquid phase can move so fast that they break theirhydrogen bonds and go from a liquid to a gas phase. If temperatures get hot enough, the molecules all move fastenough to break their hydrogen bonds and move into the gas phase. We see this happening when water boils!When liquid cools the molecules have less kinetic energy, slowing down and packing closer together. Volume is

decreasing without mass changing so the water gets more dense. As seawater gets more dense, it sinks to thebottom of the ocean. This sinking of cold water at the poles creates global circulation of seawater.

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Credit NASA

As water continues to cool the hydrogen bonds form and hold the water molecules in place as a solid. This solidform of water is ice. Ever notice that ice cubes float in your drink? That is because fresh water gets denser as itcools until it reaches about 4C, (39F). Below that temperature ice gets less dense as it cools. This happensbecause water expands as it freezes. If you have ever made ice cubes you have seen this happen. Since the massremains the same, but the volume of the solid is greater, ice is less dense than liquid water ~ so it floats! Becauseof this, bodies of water such as lakes and bays freeze at the surface. This property allows fish living in lakes andponds to survive the winter. The ice that freezes on the surface insulates the water below so it stays warmer! Ingeneral, it is extremely unusual for the solid phase of a substance to be less dense than its liquid phase, but luckyfor aquatic life it is!

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Changes of Phase (or State)Heat and Temperature Energy Mechanics Contents Index Home

The term 'change of phase' means the same thing as the term 'change of state'.

SolidLiquidGasPlasma

There are four states, or phases, of matter. They are:

We will not be discussing the plasma state here.When a substance changes from one state, or phase, of matter to another we say that ithas undergone a change of state, or we say that it has undergone a change of phase.These changes of phase always occur with a change of heat. Heat, which is energy,either comes into the material during a change of phase or heat comes out of thematerial during this change. However, although the heat content of the material

changes, the temperature does not.Here are the five changes of phase. They are diagrammed in the above animation andlisted below.

Description ofPhase Change

Term for PhaseChange

Heat MovementDuring PhaseChange

TemperatureChange DuringPhase Change

Solid to liquid Melting Heat goes into thesolid as it melts.

None

Liquid to solid Freezing Heat leaves theliquid as it freezes.

None

Liquid to gas Vaporization, whichincludes boiling andevaporation

Heat goes into theliquid as itvaporizes.

None

Gas to liquid Condensation Heat leaves the gasas it condenses.

None

Solid to gas Sublimation Heat goes into thesolid as itsublimates.

None

So, how could there be a change in heat during a state change without a change intemperature? During a change in state the heat energy is used to change the bonding

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between the molecules. In the case of melting, added energy is used to break the bondsbetween the molecules. In the case of freezing, energy is subtracted as the moleculesbond to one another. These energy exchanges are notchanges in kinetic energy. Theyare changes in bonding energy between the molecules.If heat is coming into a substance during a phase change, then this energy is used tobreak the bonds between the molecules of the substance. The example we will usehere is ice melting into water. Immediately after the molecular bonds in the ice arebroken the molecules are moving at the same average speed as before, so their

average kinetic energy remains the same, and, thus, their Kelvin temperature remainsthe same.Look at the following diagram and continue to read the text below it. The molecule of iceand the molecule of water (the black balls) are moving with the same rate of vibration inthis diagram. This is meant to show that they have the same average speed and thusthe same average kinetic energy (since they have the same mass) and thus the sameKelvin temperature. The motions are, though, greatly exagerated. Actually, the motionsof the molecules should be considered tiny vibrations.In the ice the molecules are strongly bonded to one another, thus forming a rigid solid.When heat is added to the ice it melts, and these bonds are broken, The moleculesafterward bond to one another with less strength, and water is formed.Now, before the melting, the molecules were actually moving when in the solid state.They were vibrating back and forth. They had an average kinetic energy. So they had aKelvin temperature proportional to this average kinetic energy.After the melting the water molecules are moving, also. And they have the sameaverage kinetic energy as they had before the melting. So, the water is at the sametemperature the moment after the melting that the ice was at the moment before themelting.Heat came into the situation, but it was not used to change the kinetic energy of themolecules. It was used to change the bonding between the molecules. Breaking thebonds between the molecules of the ice requires energy, and this energy is the addedheat.In a similar way heat enters a liquid to change the molecular bonding when the liquid

boils or evaporates into a gas, and heat enters a solid to change the molecular bondingwhen it sublimates into a gas.In an inverse way heat leaves a gas to change the molecular bonding when the gascondenses into a liquid, and heat leaves a liquid to change the molecular bonding whenit freezes into a solid.In none of these changes of state is the heat (energy) that is input or output used tochange the speed of the molecules. The average speed of the molecules is the samebefore and after a phase change, and so is the average kinetic energy. And so, again,note that the temperature does not change during a change in phase, since it isproportional, in Kelvin degrees, to the average kinetic energy, which does not change.

Heat and Temperature Energy Mechanics Contents Index Home

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Convection

Conduction

Evaporation

Radiation

The rate at which ice is formed, is directly proportional to the temperature gradient applied

to the system. Thermodynamically the environment is in a state of lower entropy than the

water and the water dissipates entropy through collisions at its boundary. The bump

represents the energy released as the water goes to a lower enthalpy state, or a lower

internal energy state. This rate is also depended on other factors such as the methods of

heat transfers, that can change the rate of freezing. Water in freezer is cooled by four mainways in standard atmospheric pressure. These are:-

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Hot Water will freeze faster than cold water

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Convection effects the rate at which water freezes


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Conduction also effects at the rate of freezing


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Evaporation effects the freezing of the water


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Conduction

Much of the cooling is done by conduction.

Container

The container is is direct contact with some cold material, such as the freezer shelf. The container getscold and also cools the water by conduction.

Metal is a good conductor, so a metal pail would speed up cooling the water by conduction. On theother hand, wood is a poor conductor of heat. A wooden pail would require other heat transfermethods to cool the water.

Air

Cold air is in contact with both the container and the water. The water transfers heat to the cooler airby means of conduction, thus lowering the temperature of the water.

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ConductionFouriers Law of Conduction

Screen clipping taken: 15-08-2012 15:17

Good conduction and good contact

One theory is that frost on a container can slow down the cooling process.

If hot water is placed in the freezer in a small container that is a good conductor of heat (or cold), thewarmth of the container can melt any frost that collects on its surface. This includes the ice on thebottom surface. When this ice refreezes, it creates a good connection between the container and thesurface, allowing much better conduction of cold than a container of cold water that has frost on itssurface, including its bottom. As a result, heat is drawn out of the warmer container more rapidly thanthe one with cold water in it.

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ConvectionConvection is the transfer of energy through the movement of currents of a gas or liquid. You can seethis motion when heating a pot of water on a stove.

Different densities cause water convection

Since cold water is more dense than warm water, it will sink to the bottom of the container, causingsome convection currents during the freezing process. When the temperature of the water gets below

39oF or 4oC, it becomes less dense and will float to the top until the water finally freezes.Slowing freezingIn some situations when water is moving, it can actually increase the time it takes to freeze ascompared with still water. For example, ducks often paddle around in a pond in the winter to keep itfrom freezing over.

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Convection and insulating surfaceJust as a layer of frost on the surface of a container can slow down the conduction of heat from the water, a layeron the upper surface of the water can insulate the water from the from the colder air currents.

Since water becomes less dense between 37oF and 32oF (3oC and 0oC), it will float to the top and then finally fre

This thin layer of ice will then act as an insulator protecting the water below from freezing rapidly and will slow dofreezing process of cold water.

In the case of warm water, the convection currents will cause that ice to melt, allowing the water to cool more rap

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Convection is heat transfer by mass movement. You've probably heard the saying that"hot air rises." This happens because it is less dense than colder air. As the hot air rises, it

creates currents of air flow. These circulating currents serve to transfer heat, and are an

example of convection.

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Convection

It has also been proposed that the Mpemba effect can be explained by the fact that the temperature of the water becomesnon-uniform. As the water cools, temperature gradients and convection currents will develop. For most temperatures, thedensity of water decreases as the temperature increases. So over time, as water cools we will develop a "hot top"the


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surface of the water will be warmer than the average temperature of the water, or the water at the bottom of thecontainer. If the water loses heat primarily through the surface, then this means that the water should lose heat faster thanone would expect based just on looking at the average temperature of the water. And for a given average temperature, theheat loss should be greater the more inhomogenous the temperature distribution is (that is, the greater the range of thetemperatures seen as we go from the top to the bottom).

How does this explain the Mpemba effect? Well, the initially hot water will cool rapidly, and quickly develop convectioncurrents and so the temperature of the water will vary greatly from the top of the water to the bottom. On the other hand,the initially cool water will have a slower rate of cooling, and will thus be slower to develop significant convectioncurrents. Thus, if we compare the initially hot water and initially cold water at the same average temperature, it seemsreasonable to believe that the initially hot water will have greater convection currents, and thus have a faster rate ofcooling. To consider a concrete example, suppose that the initially hot water starts at 70C, and the initially cold water

starts at 30C. When the initially cold water is at an average 30C, it is also a uniform 30C. However, when the initiallyhot water reaches an average 30C, the surface of the water is probably much warmer than 30C, and it will thus lose heatfaster than the initially cold water for the same average temperature. Got that? This explanation is pretty confusing, soyou might want to go back and read the last two paragraphs again, paying careful attention to the difference between initialtemperature, average temperature, and surface temperature.

At any rate, if the above argument is right, then when we plot the average temperature versus time for both the initially hotand initially cold water, then for some average temperatures the initially hot water will be cooling faster than the initiallycold water. So the cooling curve of the initially hot water will not simply reproduce the cooling curve of the initially coldwater, but will drop faster when in the same temperature range.

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Types of convection

Natural Convection

Forced Convection

Granular Convection

Thermo magnetic convection.

Gravitational Convection

Natural Convection or

Free Convection

Occurs due to temperature differences affecting density resulting in buoyancy (more orless dense)

This leads to bulk fluid movement.

More rapid movement between two fluids of large density differences.

Larger acceleration occurs through greater mediums

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Gravitational

ConvectionInduced by buoyancy variations resulting from material properties other than

temperature.

Variable salinity in water is a frequent cause of ocean convection.

Dependant on the effects of gravity and does not occur in micro gravity environments

http://theory.uwinnipeg.ca/physics/fluids/node10.html

http://www.bakker.org/dartmouth06/engs150/13-heat.pdf

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Evaporation

When a liquid evaporates, the higher energy molecules leave the lower energy molecules behind,resulting in lowering the temperature of the material. You can experience that by spreading some

water on your skin and blowing across it to enhance evaporation. there is more evaporation from hotwater than from cold.

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Evaporation

It is thought that evaporation is one factor that allows warm water to freeze faster than cold water.There is more evaporation from warm or hot water than from cold water. Thus the evaporation notonly carries off some of the water, resulting in slightly less water to freeze in the warm watercontainer, but it also causes the temperature of the warm container to drop due to heat lost.

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Evaporation is another method of heat transfer. When molecules of a liquid vaporize, they

escape from the liquid into the atmosphere. This transition requires energy, since a molecule in

the vapor phase has more energy than a molecule in the liquid phase. Thus, as molecules

evaporate from a liquid, they take away energy from the liquid, cooling it.

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Evaporation

One explanation of the effect is that as the hot water cools, it loses mass to evaporation. Withless mass, the liquid has to lose less heat to cool, and so it cools faster. With this explanation, thehot water freezes first, but only because there's less of it to freeze. Calculations done by Kell in1969 [11] showed that if the water cooled solely by evaporation, and maintained a uniformtemperature, the warmer water would freeze before the cooler water.This explanation is solid, intuitive, and undoubtedly contributes to the Mpemba effect in mostphysical situations. However, many people have incorrectly assumed that it is therefore "the"explanation for the Mpemba effect. That is, they assume that the only reason hot water canfreeze faster than cold is because of evaporation, and that all experimental results can beexplained by the calculations in Kell's article. However, the experiments currently do not bearout this belief. While experiments show evaporation to be important [13], they do not show thatit is the only mechanism behind the Mpemba effect. A number of experimenters have arguedthat evaporation alone is insufficient to explain their results [5,9,12]; in particular, the originalexperiment by Mpemba and Osborne measured the mass lost to evaporation, and found itsubstantially less that the amount predicted by Kell's calculations [5,9]. And most convincingly,an experiment by Wojciechowski observed the Mpemba effect in a closed container, where nomass was lost to evaporation.

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Evaporation As the initially warmer water cools to the initial temperature of the initially

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http://www.electronicsteacher.com/succeed-in-physical-science/heat-and-thermodynamics/the-mpemba-effec.phphttp://www.electronicsteacher.com/succeed-in-physical-science/heat-and-thermodynamics/the-mpemba-effec.phphttp://www.electronicsteacher.com/succeed-in-physical-science/heat-and-thermodynamics/the-mpemba-effec.phphttp://www.electronicsteacher.com/succeed-in-physical-science/heat-and-thermodynamics/the-mpemba-effec.phphttp://www.electronicsteacher.com/succeed-in-physical-science/heat-and-thermodynamics/the-mpemba-effec.phphttp://www.electronicsteacher.com/succeed-in-physical-science/heat-and-thermodynamics/the-mpemba-effec.phphttp://www.sciencebuddies.org/science-fair-projects/project_ideas/Phys_p032.shtmlhttp://www.sciencebuddies.org/science-fair-projects/project_ideas/Phys_p032.shtmlhttp://math.ucr.edu/home/baez/physics/General/hot_water.html#Experimentshttp://math.ucr.edu/home/baez/physics/General/hot_water.html#Experimentshttp://math.ucr.edu/home/baez/physics/General/hot_water.html#Experimentshttp://math.ucr.edu/home/baez/physics/General/hot_water.html#Experimentshttp://math.ucr.edu/home/baez/physics/General/hot_water.html#Experimentshttp://math.ucr.edu/home/baez/physics/General/hot_water.html#Experimentshttp://math.ucr.edu/home/baez/physics/General/hot_water.html#Experimentshttp://math.ucr.edu/home/baez/physics/General/hot_water.html#Evaporationhttp://math.ucr.edu/home/baez/physics/General/hot_water.html#Evaporationhttp://math.ucr.edu/home/baez/physics/General/hot_water.html#Evaporationhttp://math.ucr.edu/home/baez/physics/General/hot_water.html#Evaporationhttp://math.ucr.edu/home/baez/physics/General/hot_water.html#Evaporationhttp://math.ucr.edu/home/baez/physics/General/hot_water.html#Experimentshttp://math.ucr.edu/home/baez/physics/General/hot_water.html#Experimentshttp://math.ucr.edu/home/baez/physics/General/hot_water.html#Experimentshttp://math.ucr.edu/home/baez/physics/General/hot_water.html#Experimentshttp://www.sciencebuddies.org/science-fair-projects/project_ideas/Phys_p032.shtmlhttp://www.electronicsteacher.com/succeed-in-physical-science/heat-and-thermodynamics/the-mpemba-effec.phphttp://www.electronicsteacher.com/succeed-in-physical-science/heat-and-thermodynamics/the-mpemba-effec.phphttp://www.electronicsteacher.com/succeed-in-physical-science/heat-and-thermodynamics/the-mpemba-effec.phphttp://www.electronicsteacher.com/succeed-in-physical-science/heat-and-thermodynamics/the-mpemba-effec.php


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cooler water, it may lose significant amounts of water to evaporation. The reduced mass will

make it easier for the water to cool and freeze. Then the initially warmer water can freeze

before the initially cooler water, but will make less ice. Theoretical calculations have shown

that evaporation can explain the Mpemba effect if you assume that the water loses heat solely

through evaporation [11]. This explanation is solid, intuitive, and evaporation is undoubtedly

important in most situations. However, it is not the only mechanism. Evaporation cannot

explain experiments that were done in closed containers, where no mass was lost to

evaporation [12]. And many scientists have claimed that evaporation alone is insufficient to

explain their results [5,9,12].

Pasted from

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Radiation13 August 2012

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Newton's Law of Cooling13 August 2012

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Inroduction Page 18


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FREEZING RATE OF WATER

VARIABLES

INDEPENDENT DEPENDENT CONTROLLED

Initial Temperature

(oC)

- 25

- 50

- 75

- 100

Surface Area

- Cup

- Bowl

- Plate

Container Material

- Plastic

- Styrofoam

- Stainless Steel

Freezing rate of

water

Refrigerator type

Volume of water 100mL

AIM To investigate the effect of the initial temperature, surface area and container

material type on the freezing rate of water in a refrigerator

1 Refrigerator

1 Bunsen Burner

1 Tripod

1 Gauze Mat

1 Pair of Tongs

3 Measuring Cylinders (100 mL)

1 Glass Beaker (500 mL)

1 Thermometer

1 Gram Scales

1 Plastic Cups

1 Stainless Steel Cup

1 Styrofoam Cup

MATERIALS

13 August 2012

18:19

Materials and method Page 19


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1 Styrofoam Cup

1 Plastic Plate

1 Stainless Steel Plate

1 Styrofoam Plate

The apparatus was set up as shown in diagram 1.1.500 mL of tap water was poured into the glass beaker.2.

Using a Bunsen burner, the water in the glass beaker was heated to 100 oC.3.

The heated water was carefully and accurately poured into the three (3) 100 mL

measuring cylinders.

4.

The measured volumes of water were placed into three (3) different material

cups plastic, stainless steel and Styrofoam.

5.

Making sure that no large amounts of heat was lost, each cup containing the

liquid was weighed and the results were recorded.

6.

The cups were placed inside the freezer.7.

At the same time, three (3) temperature probes were connected and placed,along with the cups, inside the freezer as shown in diagram 2.8.

Three (3) hours after placing into the fridge, the cups were taken out and the

temperature probe recordings were noted and transferred onto the computer.

9.

Each cup was weighed and the results were recorded.10.

The process in steps 1-8 was repeated using different material bowls and plates.11.

The process in steps 1-9 was repeated using different initial water temperatures

such as 75 oC, 50 oC and 25 oC.

12.

METHOD

Diagram 1 Diagram 2



21/54

METHODS

PREPARATION

1 Roll of Sticky Tape

1 Roll of Aluminium Foil

2 Plastic Cups

2 Styrofoam Cups

2 Stainless Steel Cups

6 Plastic Temperature Probes

Materials:

Three (3) different material cups were wrapped once in aluminium foil using sticky tape as

shown in diagram ___

1.

NOTE: The use of sticky tape was kept to a minimum as sticky tape is made of plastic.

Therefore, an overuse would alter the heat transfer rate as plastic acts as an insulator

Using sticky tape, one plastic temperature probe was attached to each cup. They were

placed so that they were positioned in the centre of the volume of water

2.

Procedure:

WATER AT 85 oC

1 Plastic Cup.

1 Plastic Cup with Al. Foil

1 Styrofoam Cup

1 Styrofoam Cup with Al. Foil


1 Stainless Steel Cup with Al. Foil

1 Freezer

1 Data Logger

1 Kettle

1 Half Cup (125 mL) Measuring Cup

1 Gram Scale

Materials:

The apparatus was set up as shown in diagram __1.

Using a kettle an approximated amount of water (from the tap) was boiled2.

Procedure:

New19 August 2012

17:31



22/54

The boiling water was measured accurately to 125 mL (half a cup) using a measuring cup3.

The measured amount of water was then transferred into the styrofoam cup4.

The mass of the cup containing the water was weighed and the results were recorded5.

The process in steps 3-5 was repeated for the styrofoam cup with aluminium foil6.

Two probes (one from each cup) were connected to the data logger7.

Both cups were placed in the freezer8.

Using a data logger, the temperature drop in both cups was recorded over a time length

of five (5) hours

9.

After five (5) hours, the cups were weighed and the results were recorded10.

The process in steps 2-10 was repeated using plastic and stainless steel cups11.

WATER AT ROOM TEMPERATURE

1 Plastic Cup.

1 Plastic Cup with Al. Foil

1 Styrofoam Cup1 Styrofoam Cup with Al. Foil


1 Stainless Steel Cup with Al. Foil

1 Freezer

1 Data Logger

1 Half Cup (125 mL) Measuring Cup

1 Gram Scale

Materials:

The apparatus was set up as shown in diagram __1.125 mL of water (from the tap) was measured and poured into each styrofoam cup2.

The weight of the cups was measured individually and the results were recorded3.

Both cups were placed in the freezer4.

Using a data logger, the temperature drop in both cups was recorded over a time length

of five (5) hours

5.

After five (5) hours, the cups were weighed and the results were recorded6.

The process in steps 2-6 was repeated using plastic and stainless steel cups7.

Procedure:



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AVERAGE

RESULTSTIME (mins) PLASTIC

CUP (oC)

PLASTIC

CUP

+

Aluminium

Foil (oC)

STYROFO

AM CUP

(oC)

STYROFOAM

CUP +

Aluminium

Foil (oC)

STAINLESS

STEEL

CUP (oC)

STAINLESS

STEEL CUP +

Aluminium

Foil (oC)

Room. 85 oC Room. 85 oC Room. 85 oC Room. 85 oC Room. 85 oC Room.

0 17.31 85.87 17.67 85.13 17.28 85.91 17.23 85.94 17.83 85.02 17.97

3 14.42 71.51 16.71 72.10 16.81 73.35 16.78 71.92 16.94 61.53 15.51

6 12.78 62.97 14.95 62.55 14.37 63.42 15.84 64.49 15.61 54.18 14.79

9 8.18 54.62 13.46 55.29 12.83 55.63 14.92 57.40 14.60 45.68 14.32

12 5.81 47.76 12.11 49.30 10.02 49.02 13.97 51.46 13.27 38.18 12.9615 3.18 41.91 10.99 44.27 8.66 43.57 13.26 46.78 12.06 33.15 11.68

18 2.55 36.74 9.91 39.94 7.35 38.96 12.46 42.74 10.93 29.60 10.44

21 1.32 32.22 9.01 36.18 6.09 34.97 11.79 39.33 9.84 26.32 9.40

24 0.36 28.43 8.22 32.86 4.86 31.47 11.07 36.30 8.46 24.25 7.62

27 0.34 25.49 7.25 28.51 3.35 28.54 10.28 33.20 6.13 22.06 6.05

30 0.31 22.96 6.01 24.32 2.96 26.16 9.37 29.98 5.36 20.26 3.96

33 0.31 20.74 4.75 20.42 2.70 23.85 8.36 26.78 4.57 18.28 2.32

36 0.30 18.70 3.60 16.86 2.21 22.03 7.32 24.12 3.01 16.81 1.10

39 0.30 16.85 3.32 13.58 1.72 20.19 6.30 21.29 1.84 14.98 0.51

42 0.29 15.21 2.21 10.57 1.27 18.54 5.42 19.02 1.12 13.66 0.40

45 0.30 13.56 1.17 7.92 1.87 16.78 4.67 16.69 0.75 10.43 0.34

48 0.29 11.72 0.71 3.95 1.50 14.97 2.69 14.63 0.48 7.75 0.30

51 0.29 9.83 0.49 3.21 1.81 13.31 1.73 12.68 0.44 5.82 0.28

54 0.29 7.98 0.38 3.55 1.13 11.49 1.18 10.75 0.39 3.22 0.27

57 0.28 6.29 0.27 3.17 0.91 9.82 0.89 9.13 0.35 0.95 0.26

60 0.28 4.67 0.25 2.20 0.92 8.17 0.63 7.41 0.32 -0.75 0.26

63 0.27 3.25 0.19 1.31 0.82 6.67 0.45 6.00 0.31 -1.63 0.25

66 0.27 1.53 0.21 0.51 0.83 5.14 0.38 4.78 0.30 -2.00 0.24

69 0.26 0.56 0.20 0.24 0.84 3.25 0.35 3.99 0.29 -1.09 0.24

72 0.26 0.20 0.18 0.08 0.84 2.66 0.34 3.31 0.28 -1.03 0.24

75 0.25 0.18 0.17 0.15 0.73 1.90 0.33 2.41 0.28 -0.90 0.23

78 0.24 0.20 0.16 0.16 0.73 1.06 0.33 1.99 0.28 -0.87 0.24

81 0.24 0.18 0.19 0.17 0.67 0.41 0.33 0.95 0.28 -0.81 0.24

84 0.25 0.17 0.18 0.17 0.63 -0.01 0.32 0.51 0.28 -0.87 0.23

87 0.24 0.16 0.17 0.17 0.64 0.07 0.31 0.33 0.28 -0.71 0.24

90 0.24 0.16 0.17 0.17 0.57 0.20 0.31 0.23 0.29 -0.74 0.25

93 0.24 0.16 0.17 0.17 0.44 0.21 0.31 0.19 0.29 -0.68 0.25

RESULTS

Experiment 113 August 2012

18:19

Results Page 23


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96 0.23 0.16 0.17 0.16 0.43 0.22 0.31 0.18 0.29 -0.63 0.25

99 0.30 0.16 0.17 0.15 0.34 0.22 0.31 0.17 0.29 -0.63 0.25

102 0.25 0.16 0.16 0.16 0.34 0.22 0.31 0.17 0.29 -0.50 0.25

105 0.24 0.16 0.15 0.16 0.34 0.22 0.31 0.17 0.28 -0.38 0.25

108 0.21 0.16 0.16 0.16 0.33 0.21 0.31 0.17 0.28 -0.09 0.24

111 0.18 0.15 0.15 0.16 0.29 0.21 0.31 0.16 0.28 0.13 0.23

114 0.15 0.15 0.15 0.16 0.28 0.21 0.31 0.16 0.28 0.20 0.22

117 0.11 0.16 0.15 0.16 0.23 0.20 0.31 0.16 0.28 0.34 0.22

120 0.07 0.16 0.15 0.16 0.21 0.20 0.31 0.17 0.27 0.01 0.21

123 0.03 0.16 0.14 0.16 0.20 0.20 0.31 0.17 0.27 -0.22 0.20

126 0.00 0.16 0.14 0.17 0.20 0.19 0.31 0.17 0.27 -0.82 0.20

129 0.00 0.16 0.14 0.16 0.20 0.18 0.31 0.17 0.27 -1.44 0.20

132 -0.02 0.16 0.14 0.16 0.20 0.18 0.31 0.17 0.26 -1.86 0.20

135 0.06 0.16 0.14 0.14 0.22 0.18 0.31 0.17 0.25 -2.19 0.20

138 0.03 0.16 0.15 0.13 0.21 0.19 0.31 0.17 0.25 -2.57 0.20

141 0.02 0.16 0.14 0.11 0.21 0.19 0.31 0.17 0.25 -2.68 0.22

1440.01 0.16 0.14 0.07 0.21 0.19 0.30 0.17 0.25 -2.79 0.22

147 0.01 0.16 0.14 0.01 0.21 0.19 0.30 0.17 0.25 -2.86 0.22

150 -0.01 0.15 0.13 -0.07 0.20 0.19 0.30 0.16 0.25 -3.11 0.22

153 -0.02 0.16 0.12 -0.09 0.21 0.19 0.30 0.16 0.25 -3.31 0.22

156 -0.10 0.16 0.11 -0.11 0.19 0.19 0.30 0.15 0.25 -3.46 0.23

159 -0.25 0.16 0.10 -0.13 0.18 0.19 0.30 0.15 0.25 -3.62 0.23

162 -0.36 0.16 0.09 -0.16 0.17 0.18 0.30 0.14 0.25 -2.46 0.23

165 -0.50 0.15 0.07 -0.19 0.17 0.16 0.30 0.13 0.25 -1.98 0.23

168 -0.64 0.15 0.05 -0.23 0.15 0.14 0.30 0.13 0.25 -1.78 0.20

171 -0.78 0.14 0.04 -0.25 0.14 0.13 0.30 0.14 0.25 -1.62 0.19

174 -0.92 0.13 0.04 -0.11 0.13 0.11 0.30 0.14 0.24 -1.52 0.18

177 -1.02 0.12 0.02 -0.19 0.13 0.09 0.31 0.14 0.24 -1.45 0.17

180 -0.85 0.10 0.01 -0.23 0.16 0.06 0.30 0.14 0.22 -1.77 0.15

183 -0.51 0.09 0.01 -0.28 0.17 0.02 0.30 0.13 0.22 -2.70 0.13

186 -0.56 0.07 0.00 -0.33 0.17 -0.02 0.30 0.13 0.20 -3.15 0.12

189 -0.62 0.05 -0.02 -0.52 0.17 0.01 0.30 0.13 0.20 -3.53 0.15

192 -0.67 0.05 -0.02 -0.76 0.16 0.03 0.29 0.13 0.20 -3.11 0.17

195 -0.71 0.03 -0.03 -0.97 0.16 0.02 0.28 0.13 0.20 -3.21 0.17

198 -0.57 0.02 -0.04 -1.16 0.16 0.01 0.28 0.13 0.20 -3.56 0.16

201 -0.73 -0.01 -0.06 -1.38 0.16 0.00 0.26 0.12 0.20 -3.87 0.17204 -0.34 -0.03 -0.13 -1.62 0.18 -0.02 0.25 0.10 0.20 -4.04 0.15

207 -1.05 -0.02 -0.20 -1.64 0.16 -0.02 0.23 0.08 0.20 -2.79 0.17

210 -1.61 -0.09 -0.27 -1.52 0.18 -0.03 0.23 0.07 0.21 -1.85 0.15

213 -1.92 -0.10 -0.33 -1.45 0.16 -0.04 0.22 0.06 0.21 -1.26 0.14

216 -2.59 -0.12 -0.39 -1.48 0.14 -0.10 0.22 0.05 0.20 -1.49 0.11

219 -3.07 -0.25 -0.48 -1.52 0.11 -0.25 0.20 0.03 0.19 -1.51 0.06

222 -3.55 -0.42 -0.58 -1.53 0.09 -0.36 0.19 0.02 0.18 -1.41 0.01

225 -4.32 -0.49 -0.58 -1.58 0.07 -0.47 0.18 0.01 0.16 -1.41 -0.12

Results Page 24


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228 -4.67 -0.72 -0.57 -1.62 0.06 -0.58 0.18 0.02 0.15 -1.38 -0.19

231 -4.72 -1.01 -0.58 -1.66 0.06 -0.69 0.17 0.02 0.13 -2.50 -0.27

234 -4.87 -1.16 -0.61 -1.69 0.07 -0.81 0.16 0.01 0.12 -3.15 -0.50

237 -5.24 -1.58 -0.64 -1.68 0.05 -0.95 0.15 0.00 0.12 -3.64 -0.47

240 -5.90 -1.91 -0.67 -1.80 0.08 -1.07 0.09 -0.01 0.12 -3.71 -0.54

243 -6.93 -1.97 -0.71 -2.30 0.07 -0.75 0.01 -0.01 0.14 -4.13 -0.48

246 -7.76 -2.06 -0.76 -3.01 0.05 -0.72 -0.08 -0.03 0.14 -4.39 -0.63

249 -8.40 -1.67 -0.80 -3.78 0.03 -0.72 -0.19 -0.03 0.14 -4.78 -0.87

252 -8.91 -2.45 -0.85 -4.42 0.02 -0.74 -0.28 -0.04 0.14 -4.81 -1.11

255 -9.39 -2.61 -0.90 -5.09 0.02 -0.76 -0.38 -0.05 0.13 -5.26 -1.37

258 -10.20 -2.99 -1.16 -5.95 0.01 -0.77 -0.43 -0.12 0.12 -5.58 -1.58

261 -11.26 -3.28 -1.69 -6.07 -0.05 -0.79 -0.40 -0.22 0.12 -4.48 -1.83

264 -12.42 -3.67 -2.09 -6.30 -0.11 -0.81 -0.37 -0.31 0.12 -4.13 -2.09

267 -13.58 -4.16 -2.27 -6.62 -0.17 -0.82 -0.39 -0.40 0.10 -3.89 -2.37

270 -14.71 -4.93 -2.84 -7.13 -0.18 -0.92 -0.39 -0.52 0.07 -3.86 -3.27

273 -15.76 -6.43 -3.73 -8.03 -0.25 -1.34 -0.40 -0.68 -0.01 -3.86 -4.54

276-16.64 -7.94 -4.58 -8.93 -0.32 -1.67 -0.40 -0.84 -0.25 -3.90 -6.25

279 -17.09 -9.57 -5.39 -9.62 -0.32 -1.98 -0.42 -0.96 -0.31 -3.95 -8.16

282 -17.33 -11.05 -6.29 -10.20 -0.32 -2.24 -0.43 -1.09 -0.42 -4.03 -10.29

285 -17.45 -12.54 -7.58 -10.73 -0.36 -2.50 -0.45 -1.23 -0.54 -4.43 -11.92

288 -17.48 -13.99 -8.78 -11.10 -0.37 -2.73 -0.46 -1.41 -1.32 -5.63 -12.88

291 -17.45 -15.16 -9.40 -11.37 -0.39 -3.01 -0.47 -1.65 -1.63 -6.91 -13.32

294 -17.37 -16.15 -9.95 -11.83 -0.41 -2.84 -0.64 -1.85 -3.58 -8.45 -13.75

297 -17.24 -16.61 -10.55 -12.62 -0.42 -2.57 -0.99 -2.14 -5.33 -10.33 -14.06

300 -17.09 -16.93 -11.02 -13.76 -0.44 -2.48 -1.32 -2.42 -6.98 -12.02 -14.03

Results Page 25


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The formula for the Volume V, of a truncated cone whose height is h, and radius of the base is R and the

radius of the top is r is given by :

V= ph(R^2+Rr+r^2)/3.Proof:

Let the height of the complete cone be H = h+h' where h' is the height of the chopped off part of the

cone at a height h from the base. The frustum's bottom and top radius are R and r.

So the Volume of the Frustum = Volume of the full cone - Volume of the chopped off part which is

another cone with base radius r and height h'

Therefore

V = (1/3)p R^2 (h+h)' - (1/3) pr^2h'.

= (1/3)P (R^2*h+R^2h' -r^2h')..........................(1) But r/R = h'/(h+h') in a cone by similar right angles

triangles whose sides are r and h' and R and h+h'. This gives h' = rh/(R-r). Substituting this value of h' in

(1) , we get:

V = (P/3){ R^2h R^2*rh/(R-r) -r^2*rh/(R-r)}

=(P/3){R^2h+rh(R^2-r^2)/(R-r)}

=(Ph/3){R^2+r(R+r)}, as (R^2-r^2)/(R-r) = (R+r)(R-r)/(R-r) = R+r.

=Ph(R^2+Rr+r^2}/3

Pasted from

Cone15 August 2012

15:09

Results Page 26
http://www.enotes.com/math/q-and-a/what-formular-truncated-cone-143723/http://www.enotes.com/math/q-and-a/what-formular-truncated-cone-143723/http://www.enotes.com/math/q-and-a/what-formular-truncated-cone-143723/


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Conduction in a cone18 August 2012

17:15

Results Page 27


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AVERAGE RESULTSTIME (mins) PLASTI

C CUP

(o

C)

PLASTI

C CUP

+Alumin

ium

Foil

(oC)

STYRO

FOAM

CUP(oC)

STYRO

FOAM

CUP+

Alumin

ium

Foil

(oC)

STAINL

ESS

STEELCUP

(oC)

STAINL

ESS

STEELCUP +

Alumin

ium

Foil

(oC)


0 17.83 85.87 17.67 85.13 17.28 85.91 17.23 85.94 17.88 85.02 17.97

3 16.94 71.51 16.71 72.10 16.81 73.35 16.78 71.92 16.97 61.53 15.51

6 15.61 62.97 14.95 62.55 14.37 63.42 15.84 64.49 15.43 54.18 14.79

9 14.60 54.62 13.46 55.29 12.83 55.63 14.92 57.40 14.84 45.68 14.32

12 13.27 47.76 12.11 49.30 10.02 49.02 13.97 51.46 13.26 38.18 12.96

15 12.06 41.91 10.99 44.27 8.66 43.57 13.26 46.78 11.17 33.15 11.68

18 10.93 36.74 9.91 39.94 7.35 38.96 12.46 42.74 9.95 29.60 10.44

21 9.84 32.22 9.01 36.18 6.09 34.97 11.79 39.33 8.02 26.32 9.40

24 8.46 28.43 8.22 32.86 4.86 31.47 11.07 36.30 7.82 24.25 7.62

27 6.13 25.49 7.25 28.51 3.35 28.54 10.28 33.20 6.11 22.06 6.05

30 5.36 22.96 6.01 24.32 2.96 26.16 9.37 29.98 4.98 20.26 3.96

33 4.57 20.74 4.75 20.42 2.70 23.85 8.36 26.78 3.86 18.28 2.32

36 3.01 18.70 3.60 16.86 2.21 22.03 7.32 24.12 3.10 16.81 1.10

39 2.84 16.85 3.32 13.58 1.72 20.19 6.30 21.29 1.67 14.98 0.51

42 2.12 15.21 2.21 10.57 1.27 18.54 5.42 19.02 0.84 13.66 0.40

45 1.75 13.56 1.17 7.92 1.87 16.78 4.67 16.69 0.55 10.43 0.34

48 0.98 11.72 0.71 3.95 1.50 14.97 2.69 14.63 0.43 7.75 0.30

51 0.44 9.83 0.49 3.21 1.81 13.31 1.73 12.68 0.37 5.82 0.28

54 0.39 7.98 0.38 3.55 1.13 11.49 1.18 10.75 0.32 3.22 0.27

57 0.35 6.29 0.27 3.17 0.91 9.82 0.89 9.13 0.29 0.95 0.26

60 0.32 4.67 0.25 2.20 0.92 8.17 0.63 7.41 0.27 -0.75 0.26

63 0.31 3.25 0.19 1.31 0.82 6.67 0.45 6.00 0.26 -1.63 0.25

66 0.30 1.53 0.21 0.51 0.83 5.14 0.38 4.78 0.26 -2.00 0.24

69 0.29 0.56 0.20 0.24 0.84 3.25 0.35 3.99 0.25 -1.09 0.24

72 0.28 0.20 0.18 0.08 0.84 2.66 0.34 3.31 0.25 -1.03 0.24

75 0.28 0.18 0.17 0.15 0.73 1.90 0.33 2.41 0.25 -0.90 0.23

78 0.28 0.20 0.16 0.16 0.73 1.06 0.33 1.99 0.25 -0.87 0.24

81 0.28 0.18 0.19 0.17 0.67 0.41 0.33 0.95 0.24 -0.81 0.24

84 0.28 0.17 0.18 0.17 0.63 -0.01 0.32 0.51 0.24 -0.87 0.23

87 0.28 0.16 0.17 0.17 0.64 0.07 0.31 0.33 0.23 -0.71 0.24

Experiment 219 August 2012

17:35

Results Page 28


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90 0.29 0.16 0.17 0.17 0.57 0.20 0.31 0.23 0.23 -0.74 0.25

93 0.29 0.16 0.17 0.17 0.44 0.21 0.31 0.19 0.22 -0.68 0.25

96 0.29 0.16 0.17 0.16 0.43 0.22 0.31 0.18 0.22 -0.63 0.25

99 0.29 0.16 0.17 0.15 0.34 0.22 0.31 0.17 0.22 -0.63 0.25

102 0.29 0.16 0.16 0.16 0.34 0.22 0.31 0.17 0.22 -0.50 0.25

105 0.28 0.16 0.15 0.16 0.34 0.22 0.31 0.17 0.22 -0.38 0.25

108 0.28 0.16 0.16 0.16 0.33 0.21 0.31 0.17 0.23 -0.09 0.24

111 0.28 0.15 0.15 0.16 0.29 0.21 0.31 0.16 0.23 0.13 0.23

114 0.28 0.15 0.15 0.16 0.28 0.21 0.31 0.16 0.23 0.20 0.22

117 0.28 0.16 0.15 0.16 0.23 0.20 0.31 0.16 0.23 0.34 0.22

120 0.27 0.16 0.15 0.16 0.21 0.20 0.31 0.17 0.23 0.01 0.21

123 0.27 0.16 0.14 0.16 0.20 0.20 0.31 0.17 0.23 -0.22 0.20

126 0.27 0.16 0.14 0.17 0.20 0.19 0.31 0.17 0.23 -0.82 0.20

129 0.27 0.16 0.14 0.16 0.20 0.18 0.31 0.17 0.23 -1.44 0.20

132 0.26 0.16 0.14 0.16 0.20 0.18 0.31 0.17 0.23 -1.86 0.20

1350.25 0.16 0.14 0.14 0.22 0.18 0.31 0.17 0.22 -2.19 0.20

138 0.25 0.16 0.15 0.13 0.21 0.19 0.31 0.17 0.24 -2.57 0.20

141 0.25 0.16 0.14 0.11 0.21 0.19 0.31 0.17 0.24 -2.68 0.22

144 0.25 0.16 0.14 0.07 0.21 0.19 0.30 0.17 0.24 -2.79 0.22

147 0.25 0.16 0.14 0.01 0.21 0.19 0.30 0.17 0.24 -2.86 0.22

150 0.25 0.15 0.13 -0.07 0.20 0.19 0.30 0.16 0.24 -3.11 0.22

153 0.25 0.16 0.12 -0.09 0.21 0.19 0.30 0.16 0.21 -3.31 0.22

156 0.25 0.16 0.11 -0.11 0.19 0.19 0.30 0.15 0.21 -3.46 0.23

159 0.25 0.16 0.10 -0.13 0.18 0.19 0.30 0.15 0.21 -3.62 0.23

162 0.25 0.16 0.09 -0.16 0.17 0.18 0.30 0.14 0.19 -2.46 0.23165 0.25 0.15 0.07 -0.19 0.17 0.16 0.30 0.13 0.19 -1.98 0.23

168 0.25 0.15 0.05 -0.23 0.15 0.14 0.30 0.13 0.23 -1.78 0.20

171 0.25 0.14 0.04 -0.25 0.14 0.13 0.30 0.14 0.20 -1.62 0.19

174 0.24 0.13 0.04 -0.11 0.13 0.11 0.30 0.14 0.19 -1.52 0.18

177 0.24 0.12 0.02 -0.19 0.13 0.09 0.31 0.14 0.19 -1.45 0.17

180 0.22 0.10 0.01 -0.23 0.16 0.06 0.30 0.14 0.18 -1.77 0.15

183 0.22 0.09 0.01 -0.28 0.17 0.02 0.30 0.13 0.17 -2.70 0.13

186 0.20 0.07 -0.00 -0.33 0.17 -0.02 0.30 0.13 0.17 -3.15 0.12

189 0.20 0.05 -0.02 -0.52 0.17 0.01 0.30 0.13 0.15 -3.53 0.15192 0.20 0.05 -0.02 -0.76 0.16 0.03 0.29 0.13 0.14 -3.11 -0.10

195 0.20 0.03 -0.03 -0.97 0.16 0.02 0.28 0.13 0.13 -3.21 -0.09

198 0.20 0.02 -0.04 -1.16 0.16 0.01 0.28 0.13 0.12 -3.56 -0.10

201 0.20 -0.01 -0.06 -1.38 0.16 0.00 0.26 0.12 0.11 -3.87 -0.01

204 0.20 -0.03 -0.13 -1.62 0.18 -0.02 0.25 0.10 0.06 -4.04 -0.09

207 0.20 -0.02 -0.20 -1.64 0.16 -0.02 0.23 0.08 0.01 -2.79 -0.13

210 0.21 -0.09 -0.27 -1.52 0.18 -0.03 0.23 0.07 -0.02 -1.85 -0.15

213 0.21 -0.10 -0.33 -1.45 0.16 -0.04 0.22 0.06 -0.02 -1.26 -0.14

Results Page 29


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216 0.20 -0.12 -0.39 -1.48 0.14 -0.10 0.22 0.05 -0.03 -1.49 -0.11

219 0.19 -0.25 -0.48 -1.52 0.11 -0.25 0.20 0.03 -0.07 -1.51 -0.06

222 0.18 -0.42 -0.58 -1.53 0.09 -0.36 0.19 0.02 -0.11 -1.41 -0.01

225 0.16 -0.49 -0.58 -1.58 0.07 -0.47 0.18 0.01 -0.12 -1.41 -0.12

228 0.15 -0.72 -0.57 -1.62 0.06 -0.58 0.18 0.02 -0.15 -1.38 -0.19

231 0.13 -1.01 -0.58 -1.66 0.06 -0.69 0.17 0.02 -0.17 -2.50 -0.27

2340.12 -1.16 -0.61 -1.69 0.07 -0.81 0.16 0.01 -0.25 -3.15 -0.50

237 0.12 -1.58 -0.64 -1.68 0.05 -0.95 0.15 0.00 -0.31 -3.64 -0.47

240 0.12 -1.91 -0.67 -1.80 0.08 -1.07 0.09 -0.01 -0.39 -3.71 -0.54

243 0.14 -1.97 -0.71 -2.30 0.07 -0.75 0.01 -0.01 -0.41 -4.13 -0.48

246 0.14 -2.06 -0.76 -3.01 0.05 -0.72 -0.08 -0.03 -0.53 -4.39 -0.63

249 0.14 -1.67 -0.80 -3.78 0.03 -0.72 -0.19 -0.03 -0.62 -4.78 -0.87

252 0.14 -2.45 -0.85 -3.42 0.02 -0.74 -0.28 -0.04 -0.76 -4.81 -1.11

255 0.13 -2.61 -0.90 -4.09 0.02 -0.76 -0.38 -0.05 -0.91 -5.26 -1.37

258 0.12 -2.99 -1.16 -3.95 0.01 -0.77 -0.43 -0.12 -1.00 -5.58 -1.58

261 0.12 -3.28 -1.69 -4.07 -0.05 -0.79 -0.40 -0.22 -1.19 -4.48 -1.83264 0.12 -3.67 -2.09 -4.30 -0.11 -0.81 -0.37 -0.31 -1.45 -4.13 -2.09

267 0.10 -4.16 -2.27 -4.62 -0.17 -0.82 -0.39 -0.40 -1.96 -3.89 -2.37

270 0.07 -3.93 -2.84 -5.13 -0.18 -0.92 -0.39 -0.52 -1.79 -3.86 -3.27

273 -0.01 -4.43 -3.73 -6.03 -0.25 -1.34 -0.40 -0.68 -1.87 -3.86 -4.54

276 -0.25 -4.94 -3.58 -6.93 -0.32 -1.67 -0.45 -0.84 -2.62 -3.90 -6.25

279 -0.31 -4.57 -4.39 -6.62 -0.32 -1.98 -0.78 -0.96 -3.14 -4.95 -8.16

282 -0.42 -5.05 -6.29 -6.68 -0.32 -2.24 -0.81 -1.09 -4.79 -5.03 -9.29

285 -0.54 -5.54 -6.58 -7.73 -0.36 -2.26 -0.92 -1.23 -4.98 -6.43 -9.92

288 -1.32 -5.99 -7.78 -8.10 -0.37 -2.25 -1.04 -1.41 -5.01 -8.63 -10.88

291 -1.63 -6.16 -8.40 -8.37 -0.39 -2.13 -1.47 -1.65 -6.39 -10.9

1

-11.3

2

294 -3.58 -6.15 -8.75 -8.83 -0.41 -2.09 -1.64 -1.85 -7.09 -12.4

5

-11.7

5

297 -5.33 -6.61 -8.94 -9.62 -0.42 -2.19 -1.99 -2.14 -8.21 -13.3

3

-12.0

6

300 -6.13 -6.93 -9.01 -9.76 -0.44 -2.11 -2.32 -2.42 -10.3

2

-13.9

7

-12.4

3

Results Page 30


31/54

AVERAGE RESULTSTIME (mins) PLASTIC

CUP

(oC)

PLASTIC

CUP

+

Aluminiu

m Foil

(oC)

STYROF

OAM

CUP

(oC)

STYROFO

AM CUP

+

Aluminiu

m Foil

(oC)

STAINLE

SS STEEL

CUP (oC)

STAINLES

S STEEL

CUP +

Aluminiu

m Foil

(oC)


0 17.83 85.87 17.67 85.13 17.28 85.91 17.23 85.94 17.88 85.02 17.97

3 16.94 71.51 16.71 72.10 16.81 73.35 16.78 71.92 16.97 61.53 15.51

6 15.61 62.97 14.95 62.55 14.37 63.42 15.84 64.49 15.43 54.18 14.79

9 14.60 54.62 13.46 55.29 12.83 55.63 14.92 57.40 14.84 45.68 14.32

12 13.27 47.76 12.11 49.30 10.02 49.02 13.97 51.46 13.26 38.18 12.96

15 12.06 41.91 10.99 44.27 8.66 43.57 13.26 46.78 11.17 33.15 11.68

18 10.93 36.74 9.91 39.94 7.35 38.96 12.46 42.74 9.95 29.60 10.44

21 9.84 32.22 9.01 36.18 6.09 34.97 11.79 39.33 8.02 26.32 9.40

24 8.46 28.43 8.22 32.86 4.86 31.47 11.07 36.30 7.82 24.25 7.62

27 6.13 25.49 7.25 28.51 3.35 28.54 10.28 33.20 6.11 22.06 6.05

30 5.36 22.96 6.01 24.32 2.96 26.16 9.37 29.98 4.98 20.26 3.96

33 4.57 20.74 4.75 20.42 2.70 23.85 8.36 26.78 3.86 18.28 2.32

36 3.01 18.70 3.60 16.86 2.21 22.03 7.32 24.12 3.10 16.81 1.10

39 2.84 16.85 3.32 13.58 1.72 20.19 6.30 21.29 1.67 14.98 0.51

42 2.12 15.21 2.21 10.57 1.27 18.54 5.42 19.02 0.84 13.66 0.40

45 1.75 13.56 1.17 7.92 1.87 16.78 4.67 16.69 0.55 10.43 0.3448 0.98 11.72 0.71 3.95 1.50 14.97 2.69 14.63 0.43 7.75 0.30

51 0.44 9.83 0.49 3.21 1.81 13.31 1.73 12.68 0.37 5.82 0.28

54 0.39 7.98 0.38 3.55 1.13 11.49 1.18 10.75 0.32 3.22 0.27

57 0.35 6.29 0.27 3.17 0.91 9.82 0.89 9.13 0.29 0.95 0.26

60 0.32 4.67 0.25 2.20 0.92 8.17 0.63 7.41 0.27 -0.75 0.26

63 0.31 3.25 0.19 1.31 0.82 6.67 0.45 6.00 0.26 -1.63 0.25

66 0.30 1.53 0.21 0.51 0.83 5.14 0.38 4.78 0.26 -2.00 0.24

69 0.29 0.56 0.20 0.24 0.84 3.25 0.35 3.99 0.25 -1.09 0.24

720.28 0.20 0.18 0.08 0.84 2.66 0.34 3.31 0.25 -1.03 0.24

75 0.28 0.18 0.17 0.15 0.73 1.90 0.33 2.41 0.25 -0.90 0.23

78 0.28 0.20 0.16 0.16 0.73 1.06 0.33 1.99 0.25 -0.87 0.24

81 0.28 0.18 0.19 0.17 0.67 0.41 0.33 0.95 0.24 -0.81 0.24

84 0.28 0.17 0.18 0.17 0.63 -0.01 0.32 0.51 0.24 -0.87 0.23

87 0.28 0.16 0.17 0.17 0.64 0.07 0.31 0.33 0.23 -0.71 0.24

90 0.29 0.16 0.17 0.17 0.57 0.20 0.31 0.23 0.23 -0.74 0.25

93 0.29 0.16 0.17 0.17 0.44 0.21 0.31 0.19 0.22 -0.68 0.25

96 0.29 0.16 0.17 0.16 0.43 0.22 0.31 0.18 0.22 -0.63 0.25

Final Results25 August 2012

14:11

Results Page 31


32/54

99 0.29 0.16 0.17 0.15 0.34 0.22 0.31 0.17 0.22 -0.63 0.25

102 0.29 0.16 0.16 0.16 0.34 0.22 0.31 0.17 0.22 -0.50 0.25

105 0.28 0.16 0.15 0.16 0.34 0.22 0.31 0.17 0.22 -0.38 0.25

108 0.28 0.16 0.16 0.16 0.33 0.21 0.31 0.17 0.23 -0.09 0.24

111 0.28 0.15 0.15 0.16 0.29 0.21 0.31 0.16 0.23 0.13 0.23

114 0.28 0.15 0.15 0.16 0.28 0.21 0.31 0.16 0.23 0.20 0.22

117 0.28 0.16 0.15 0.16 0.23 0.20 0.31 0.16 0.23 0.34 0.22

120 0.27 0.16 0.15 0.16 0.21 0.20 0.31 0.17 0.23 0.01 0.21

123 0.27 0.16 0.14 0.16 0.20 0.20 0.31 0.17 0.23 -0.22 0.20

126 0.27 0.16 0.14 0.17 0.20 0.19 0.31 0.17 0.23 -0.82 0.20

129 0.27 0.16 0.14 0.16 0.20 0.18 0.31 0.17 0.23 -1.44 0.20

132 0.26 0.16 0.14 0.16 0.20 0.18 0.31 0.17 0.23 -1.86 0.20

135 0.25 0.16 0.14 0.14 0.22 0.18 0.31 0.17 0.22 -2.19 0.20

138 0.25 0.16 0.15 0.13 0.21 0.19 0.31 0.17 0.24 -2.57 0.20

141 0.25 0.16 0.14 0.11 0.21 0.19 0.31 0.17 0.24 -2.68 0.22

144 0.25 0.16 0.14 0.07 0.21 0.19 0.30 0.17 0.24 -2.79 0.22

147 0.25 0.16 0.14 0.01 0.21 0.19 0.30 0.17 0.24 -2.86 0.22

150 0.25 0.15 0.13 -0.07 0.20 0.19 0.30 0.16 0.24 -3.11 0.22

153 0.25 0.16 0.12 -0.09 0.21 0.19 0.30 0.16 0.21 -3.31 0.22

156 0.25 0.16 0.11 -0.11 0.19 0.19 0.30 0.15 0.21 -3.46 0.23

159 0.25 0.16 0.10 -0.13 0.18 0.19 0.30 0.15 0.21 -3.62 0.23

162 0.25 0.16 0.09 -0.16 0.17 0.18 0.30 0.14 0.19 -2.46 0.23

165 0.25 0.15 0.07 -0.19 0.17 0.16 0.30 0.13 0.19 -1.98 0.23

168 0.25 0.15 0.05 -0.23 0.15 0.14 0.30 0.13 0.23 -1.78 0.20

171 0.25 0.14 0.04 -0.25 0.14 0.13 0.30 0.14 0.20 -1.62 0.19

174 0.24 0.13 0.04 -0.11 0.13 0.11 0.30 0.14 0.19 -1.52 0.18177 0.24 0.12 0.02 -0.19 0.13 0.09 0.31 0.14 0.19 -1.45 0.17

180 0.22 0.10 0.01 -0.23 0.16 0.06 0.30 0.14 0.18 -1.77 0.15

183 0.22 0.09 0.01 -0.28 0.17 0.02 0.30 0.13 0.17 -2.70 0.13

186 0.20 0.07 -0.00 -0.33 0.17 -0.02 0.30 0.13 0.17 -3.15 0.12

189 0.20 0.05 -0.02 -0.52 0.17 0.01 0.30 0.13 0.15 -3.53 0.15

192 0.20 0.05 -0.02 -0.76 0.16 0.03 0.29 0.13 0.14 -3.11 -0.10

195 0.20 0.03 -0.03 -0.97 0.16 0.02 0.28 0.13 0.13 -3.21 -0.09

198 0.20 0.02 -0.04 -1.16 0.16 0.01 0.28 0.13 0.12 -3.56 -0.10

201 0.20 -0.01 -0.06 -1.38 0.16 0.00 0.26 0.12 0.11 -3.87 -0.01

204 0.20 -0.03 -0.13 -1.62 0.18 -0.02 0.25 0.10 0.06 -4.04 -0.09

207 0.20 -0.02 -0.20 -1.64 0.16 -0.02 0.23 0.08 0.01 -2.79 -0.13

210 0.21 -0.09 -0.27 -1.52 0.18 -0.03 0.23 0.07 -0.02 -1.85 -0.15

213 0.21 -0.10 -0.33 -1.45 0.16 -0.04 0.22 0.06 -0.02 -1.26 -0.14

216 0.20 -0.12 -0.39 -1.48 0.14 -0.10 0.22 0.05 -0.03 -1.49 -0.11

219 0.19 -0.25 -0.48 -1.52 0.11 -0.25 0.20 0.03 -0.07 -1.51 -0.06

222 0.18 -0.42 -0.58 -1.53 0.09 -0.36 0.19 0.02 -0.11 -1.41 -0.01

225 0.16 -0.49 -0.58 -1.58 0.07 -0.47 0.18 0.01 -0.12 -1.41 -0.12

Results Page 32


33/54

228 0.15 -0.72 -0.57 -1.62 0.06 -0.58 0.18 0.02 -0.15 -1.38 -0.19

231 0.13 -1.01 -0.58 -1.66 0.06 -0.69 0.17 0.02 -0.17 -2.50 -0.27

234 0.12 -1.16 -0.61 -1.69 0.07 -0.81 0.16 0.01 -0.25 -3.15 -0.50

237 0.12 -1.58 -0.64 -1.68 0.05 -0.95 0.15 0.00 -0.31 -3.64 -0.47

240 0.12 -1.91 -0.67 -1.80 0.08 -1.07 0.09 -0.01 -0.39 -3.71 -0.54

243 0.14 -1.97 -0.71 -2.30 0.07 -0.75 0.01 -0.01 -0.41 -4.13 -0.48

246 0.14 -2.06 -0.76 -3.01 0.05 -0.72 -0.08 -0.03 -0.53 -4.39 -0.63

249 0.14 -1.67 -0.80 -3.78 0.03 -0.72 -0.19 -0.03 -0.62 -4.78 -0.87

252 0.14 -2.45 -0.85 -3.42 0.02 -0.74 -0.28 -0.04 -0.76 -4.81 -1.11

255 0.13 -2.61 -0.90 -4.09 0.02 -0.76 -0.38 -0.05 -0.91 -5.26 -1.37

258 0.12 -2.99 -1.16 -3.95 0.01 -0.77 -0.43 -0.12 -1.00 -5.58 -1.58

261 0.12 -3.28 -1.69 -4.07 -0.05 -0.79 -0.40 -0.22 -1.19 -4.48 -1.83

264 0.12 -3.67 -2.09 -4.30 -0.11 -0.81 -0.37 -0.31 -1.45 -4.13 -2.09

267 0.10 -4.16 -2.27 -4.62 -0.17 -0.82 -0.39 -0.40 -1.96 -3.89 -2.37

270 0.07 -3.93 -2.84 -5.13 -0.18 -0.92 -0.39 -0.52 -1.79 -3.86 -3.27

273 -0.01 -4.43 -3.73 -6.03 -0.25 -1.34 -0.40 -0.68 -1.87 -3.86 -4.54

276 -0.25 -4.94 -3.58 -6.93 -0.32 -1.67 -0.45 -0.84 -2.62 -3.90 -6.25

279 -0.31 -4.57 -4.39 -6.62 -0.32 -1.98 -0.78 -0.96 -3.14 -4.95 -8.16

282 -0.42 -5.05 -6.29 -6.68 -0.32 -2.24 -0.81 -1.09 -4.79 -5.03 -9.29

285 -0.54 -5.54 -6.58 -7.73 -0.36 -2.26 -0.92 -1.23 -4.98 -6.43 -9.92

288 -1.32 -5.99 -7.78 -8.10 -0.37 -2.25 -1.04 -1.41 -5.01 -8.63 -10.88

291 -1.63 -6.16 -8.40 -8.37 -0.39 -2.13 -1.47 -1.65 -6.39 -10.91 -11.32

294 -3.58 -6.15 -8.75 -8.83 -0.41 -2.09 -1.64 -1.85 -7.09 -12.45 -11.75

297 -5.33 -6.61 -8.94 -9.62 -0.42 -2.19 -1.99 -2.14 -8.21 -13.33 -12.06

300 -6.13 -6.93 -9.01 -9.76 -0.44 -2.11 -2.32 -2.42 -10.32 -13.97 -12.43

PLASTICCUP

STYROFOAM CUP

STAINLESSSTEEL CUP

Without A.F With

A.F

Without A.F With

A.F

Without A.F With

A.F

Room 85 Room 85 Room 85 Room 85 Room 85 Room

BEFORE 129.49 129.11 132.45 131.98 127.22 127.76 130.48 131.01 162.75 162.34 165.12

AFTER 128.35 124.37 131.58 127.66 125.24 122.64 129.45 126.04 161.91 158.46 164.91

Differenc

e

1.14 4.74 0.87 4.32 1.88 5.12 1.03 4.97 0.84 3.88 0.21

AVERAGE WATER QUALITY

ACIDITY (pH) DISSOLVED OXYGEN (mg/L)

Room Temperature 8.43 12.91

85 oC 9.32 0.62

Results Page 33


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The variable of Surface area was changed to surface roughness because

theoretically both change convection but the surface area also effects the

conduction by air whereas changing to surface roughness only effects convection.

By using foil for changing roughness, it is a better reason to ignore radiation

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When a 100 degree celcius water was taken to the freezer, it was noticed that the

temperature didnt remain constant as it generally decreased when put into the

freezer hence making it an unfair experiment. Also having water boiling caused

water to be lost due to evaporation therefore it was decided to us 85 degree

celcius. So the temperature doesnt drop, the water was heated until 90, covered

with plastic sheet ( no evaporation) and then taken into the freezer. We waited

until the temp dropped to 85

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As many of the cups are small and thin, it was very difficult to measure its thickness

using a normal micrometer. For accuracy, we used a digital micrometer, which was

much more accurate as its results were in three decimal place.

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The experiment with the plastic cup was repeated because it didnt show

expected results. Actually the results made no sense because according to

it, the plastic was the better conductor for heat transfer. Therefore we

though about it. Then we figure that the radiation factor wasnt kept

constant, as the plastic cup was transparent. Therefore the heat could go

straight through. Now we are using white plastic cups, for more fair results.


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MODIFICATIONSAfter conducting the first trial experiment, there were several modifications

made to improve the method:

MODIFICATION JUSTIFICATION

Instead of testing the

effect of surface area, the

variable was changed to

the roughness of the inner

and outer walls of the cup.

This was altered due to two reasons. The first being that

materials such as plates and bowls were hard to find in

consistent and similar shapes. Therefore, if the experiment

were to be continued, then the results would not have been

accurate and reliable as not all factors, such as thickness and

shape, were kept constant.

The second reason being that by changing the surface area,

the conduction and convection rates would have been altered

as the surface area of the outer walls would also change.

However, the purpose of changing this specific variable was to

only test for the convection currents. Therefore, since

convection is reliant on the smoothness of the edges of the

container, the surface area variable was replaced with the

roughness of the walls variable.

Instead of testing for four

different initial water

temperatures (25 oC, 50 oC,

75 oC and 100 oC) only two

initial temperatures were

tested (room temperature

and 85 oC)

This was altered purely because of the fact that testing for

four different temperatures took a significant amount of time.

As this variable tested the impact of different water

temperatures, (hot and cold), it would be fair and reasonable

to test for only room temperature and 85 oC.

The reason for why water at 100 oC was not tested was due to

that fact that by the time the volumes of water was

transferred into a measuring cylinder and then into the cup, a

great amount of heat (approximately 12-15 oC) was lost to the

surrounding environment.

The experiment was

conducted for 5 hours

instead of 3 hours

The time length of this experiment had to be altered as for

this experiment to be fair; all the volumes of water would

have to pass the latent phase. The styrofoam cup (assumed to

take the longest to freeze) took approximately 4 hours 40

mins, therefore the duration of the experiment was changed

to 5 hours.

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IMprovements Page 38


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A digital micrometer was

used to measure the

thickness of the cups

instead of a manual

micrometer

When measuring the cups, it was found that the recordings

were not consistent; therefore to increase the accuracy, a

digital micrometer was used. Also, by using a digital device, it

decreases the chanced of human errors.

IMprovements Page 39


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[Physics FAQ] - [Copyright]Written Nov, 1998 by Monwhea Jeng (Momo),Department of Physics, University of California

Yesa general explanation

History of the Mpemba EffectMore-detailed explanationsReferences

Can hot water freeze faster than cold water?

Yesa general explanationHot water can in fact freeze faster than cold water for a wide range of experimental conditions. This phenomenon is extremely counterintuand surprising even to most scientists, but it is in fact real. It has been seen and studied in numerous experiments. While this phenomenonbeen known for centuries, and was described by Aristotle, Bacon, and Descartes [13], it was not introduced to the modern scientific comuntil 1969, by a Tanzanian high school pupil named Mpemba. Both the early scientific history of this effect, and the story of Mpemba'srediscovery of it, are interesting in their own rightMpemba's story in particular providing a dramatic parable against making snap judgeabout what is impossible. This is described separately below.The phenomenon that hot water may freeze faster than cold is often called the Mpemba effect. Because, no doubt, most readers are extremskeptical at this point, we should begin by stating precisely what we mean by the Mpemba effect. We start with two containers of water, widentical in shape, and which hold identical amounts of water. The only difference between the two is that the water in one is at a higher (temperature than the water in the other. Now we cool both containers, using the exact same cooling process for each container. Under somconditions the initially warmer water will freeze first. If this occurs, we have seen the Mpemba effect. Of course, the initially warmer wat

not freeze before the initially cooler water for all initial conditions. If the hot water starts at 99.9C, and the cold water at 0.01C, then cleunder those circumstances, the initially cooler water will freeze first. However, under some conditions the initially warmer water will freeif that happens, you have seen the Mpemba effect. But you will not see the Mpemba effect for just any initial temperatures, container shapcooling conditions.This seems impossible, right? Many sharp readers may have already come up with a common proof that the Mpemba effect is impossible.proof usually goes something like this. Say that the initially cooler water starts at 30C and takes 10 minutes to freeze, while the initially wwater starts out at 70C. Now the initially warmer water has to spend some time cooling to get to get down to 30C, and after that, it's gointake 10 more minutes to freeze. So since the initially warmer water has to do everything that the initially cooler water has to do, plus a littit will take at least a little longer, right? What can be wrong with this proof?What's wrong with this proof is that it implicitly assumes that the water is characterized solely by a single number its average temperatuif other factors besides the average temperature are important, then when the initially warmer water has cooled to an average temperature oit may look very different than the initially cooler water (at a uniform 30C) did at the start. Why? Because the water may have changed cooled down from a uniform 70C to an average 30C. It could have less mass, less dissolved gas, or convection currents producing a nonuniform temperature distribution. Or it could have changed the environment around the container in the refrigerator. All four of these chaconceivably important, and each will be considered separately below. So the impossibility proof given above doesn't work. And in fact th

Mpemba effect has been observed in a number of controlled experiments [5,714]It is still not known exactly why this happens. A number of possible explanations for the effect have been proposed, but so far the experimnot show clearly which, if any, of the proposed mechanisms is the most important one. While you will often hear confident claims that X cause of the Mpemba effect, such claims are usually based on guesswork, or on looking at the evidence in only a few papers and ignoring trest. Of course, there is nothing wrong with informed theoretical guesswork or being selective in which experimental results you trust; theproblem is that different people make different claims as to what X is.Why hasn't modern science answered this seemingly simple question about cooling water? The main problem is that the time it takes waterfreeze is highly sensitive to a number of details in the experimental setup, such as the shape and size of the container, the shape and size ofrefrigeration unit, the gas and impurity content of the water, how the time of freezing is defined, and so on. Because of this sensitivity, whexperiments have generally agreed that the Mpemba effect occurs, they disagree over the conditions under which it occurs, and thus aboutoccurs. As Firth [7] wrote "There is a wealth of experimental variation in the problem so that any laboratory undertaking such investigatioguaranteed different results from all others."So with the limited number of experiments done, often under very different conditions, none of the proposed mechanisms can be confidentproclaimed as "the" mechanism. Above we described four ways in which the initially warmer water could have changed upon cooling to tinitial temperature of the initially cooler water. What follows below is a short description of the four related mechanisms that have been suto explain the Mpemba effect. More ambitious readers can follow the links to more complete explanations of the mechanisms, as well as c

arguments and experiments that the mechanisms cannot explain. It seems likely that there is no one mechanism that explains the Mpembafor all circumstances, but that different mechanisms are important under different conditions.

Evaporation As the initially warmer water cools to the initial temperature of the initially cooler water, it may lose significant amouwater to evaporation. The reduced mass will make it easier for the water to cool and freeze. Then the initially warmer water can freebefore the initially cooler water, but will make less ice. Theoretical calculations have shown that evaporation can explain the Mpembif you assume that the water loses heat solely through evaporation [11]. This explanation is solid, intuitive, and evaporation is undouimportant in most situations. However, it is not the only mechanism. Evaporation cannot explain experiments that were done in closcontainers, where no mass was lost to evaporation [12]. And many scientists have claimed that evaporation alone is insufficient to extheir results [5,9,12].

1.

Dissolved Gasses Hot water can hold less dissolved gas than cold water, and large amounts of gas escape upon boiling. So the inwarmer water may have less dissolved gas than the initially cooler water. It has been speculated that this changes the properties of thin some way, perhaps making it easier to develop convection currents (and thus making it easier to cool), or decreasing the amount ofrequired to freeze a unit mass of water, or changing the boiling point. There are some experiments that favor this explanation [10,14

2.

Monwhea Jeng, 199815 August 2012

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Research Page 40
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supporting theoretical calculations.Convection As the water cools it will eventually develop convection currents and a non-uniform temperature distribution. At motemperatures, density decreases with increasing temperature, and so the surface of the water will be warmer than the bottom: this hascalled a "hot top." Now if the water loses heat primarily through the surface, then water with a "hot top" will lose heat faster than we expect based on its average temperature. When the initially warmer water has cooled to an average temperature the same as the initiatemperature of the initially cooler water, it will have a "hot top", and thus its rate of cooling will be faster than the rate of cooling of tinitially cooler water at the same average temperature. Got all that? You might want to read this paragraph again, paying careful disto the difference between initial temperature, average temperature, and temperature. While experiments have seen the "hot top", andconvection currents, it is unknown whether convection can by itself explain the Mpemba effect.

3.

SurroundingsA final difference between the cooling of the two containers relates not to the water itself, but to the surroundingenvironment. The initially warmer water may change the environment around it in some complex fashion, and thus affect the cooling

process. For example, if the container is sitting on a layer of frost which conducts heat poorly, the hot water may melt that layer of fthus establish a better cooling system in the long run. Obviously explanations like this are not very general, since most experiments adone with containers sitting on layers of frost.

4.

Finally, supercooling may be important to the effect. Supercooling occurs when the water freezes not at 0C, but at some lower temperatuexperiment [12] found that its initially hot water supercooled less than its initially cold water. This would mean that the initially warmer wmight freeze first because it would freeze at a higher temperature than the initially cooler water. If true, this would not fully explain the Meffect, because we would still need to explain why initially warmer water supercools less than initially cooler water.In short, hot water does freeze sooner than cold water under a wide range of circumstances. It is not impossible, and has been seen to occunumber of experiments. However, despite claims often made by one source or another, there is no well-agreed explanation for how thisphenomenon occurs. Different mechanisms have been proposed, but the experimental evidence is inconclusive. For those wishing to readon the subject, Jearl Walker's article in Scientific American [13] is very readable and has suggestions on how to do home experiments on tMpemba effect, while the articles by Auerbach [12] and Wojciechowski [14] are two of the more modern papers on the effect.

History of the Mpemba EffectThe fact that hot water freezes faster than cold has been known for many centuries. The earliest reference to this phenomenon dates back t

Aristotle in 300 B.C. The phenomenon was later discussed in the medieval era, as European physicists struggled to come up with a theoryheat. But by the 20th century the phenomenon was only known as common folklore, until it was reintroduced to the scientific communityby Mpemba, a Tanzanian high school pupil. Since then, numerous experiments have confirmed the existence of the "Mpemba effect", but not settled on any single explanation.The earliest known reference to this phenomenon is by Aristotle, who wrote:"The fact that water has previously been warmed contributes to its freezing quickly; for so it cools sooner. Hence many people, when they

cool hot water quickly, begin by putting it in the sun. . ."[1,4]

He wrote these words in support of a mistaken idea which he called antiperistasis. Antiperistasis is defined as "the supposed increase in thintensity of a quality as a result of being surrounded by its contrary quality, for instance, the sudden heating of a warm body when surroundcold" [4].Medieval scientists believed in Aristotle's theory of antiperistasis, and also sought to explain it. Not surprisingly, scientists in the 1400s hatrouble explaining how it worked, and could not even decide whether (as Aristotle claimed in support of antiperistasis), human bodies and of water were hotter in the winter than in the summer [4]. Around 1461, the physicist Giovanni Marliani, in a debate over how objects coosaid that he had confirmed that hot water froze faster than cold. He said that he had taken four ounces of boiling water, and four ounces ofheated water, placed them outside in similar containers on a cold winter day, and observed that the boiled water froze first. Marliani was,however, unable to explain this occurrence [4].Later, in the 1600s, it was apparently common knowledge that hot water would freeze faster than cold. In 1620 Bacon wrote "Water slightis more easily frozen than quite cold" [2], while a little later Descartes claimed "Experience shows that water that has been kept for a long tthe fire freezes sooner than other water" [3].In time, a modern theory of heat was developed, and the earlier observations of Aristotle, Marliani, and others were forgotten, perhaps becthey seemed so contradictory to modern concepts of heat. However, it was still known as folklore among many non-scientists in Canada [England [1521], the food processing industry [23], and elsewhere.It was not reintroduced to the scientific community until 1969, 500 years after Marliani's experiment, and more than two millennia after Ar"Meteorologica I" [1]. The story of its rediscovery by a Tanzanian high school pupil named Mpemba is written up in the New Scientist [4story provides a dramatic parable cautioning scientists and teachers against dismissing the observations of non-scientists and against makin

judgements about what is impossible.In 1963, Mpemba was making ice cream at school, which he did by mixing boiling milk with sugar. He was supposed to wait for the milkbefore placing it the refrigerator, but in a rush to get scarce refrigerator space, put his milk in without cooling it. To his surprise, he found hot milk froze into ice cream before that of other pupils. He asked his physics teacher for an explanation, but was told that he must have bconfused, since his observation was impossi

Freezing of Water

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