SUPPORT MATERIALS

collect and analyze datausing the casio fx-9750 and ea-200

EXPLORIng ScIEncE

CONSTRUCTION OF A THERMOCOUPLE THERMOMETER By

Jim Roberts, Professor of Physics and Material Science The University of North Texas

OBJECTIVE: This experiment is designed to show you how to construct a thermocouple or a device made of two (couple) of dissimilar metals that can produce a voltage when heat is applied, to collect voltage data, to plot the results on a fx-9750G graphing calculator and make a thermometer using the results.

INTRODUCTION

There are two types of effects that arise when two dissimilar metals are brought in contact

with each other and the temperature is changed at the junction. One effect produces an

electrical potential (Seebeck effect) when heat is applied and the other effect is to cool the

junction when a current is passed through the junction in the proper direction (Peltier

effect). These two effects can be very useful. Since the voltage at the junction depends

upon the temperature of the end points, we may generate a voltage by heating one junction

while holding the other constant in temperature, a source of electromotive force. The other

effect is to make a cooling device, a refrigerator, by passing a current through the junction in

the proper direction.

In figure 1 is shown a thermocouple. This is the structure of a commercial thermocouple that

is capable of sensing temperature changes at the junction. A very practical usage of the

thermocouple is to control the safety of gas delivering systems. This is done by allowing the

voltage produced to control the valve that delivers gas to the burners. If the burner goes

out, there is no heat to the thermocouple and the voltage drops to release the valve and

close off the gas flow, thus preventing a potential explosion. All gas systems are now

required, by law, to have such safety valves.

The device shown in figure 1 can be produced by the use of two electrically dissimilar metals

such as copper and iron or copper and constantan. When the device has been constructed,

it can be calibrated to read voltage and convert this into a temperature scale. If the

amplifier gain is high enough the voltage can be read using an EA-200 to collect the data

points. When this has been completed, the data are transferred into the graphing calculator

for processing and testing for linear behavior over the temperature range of interest.

Figure 1. A thermocouple mounted into a finger and the thermocouple wires and junction exposed so it can be seen what is in the sensing probe.

PROCEDURE

Construct your thermal junction by twisting a copper and an iron or constantan wire

together at the ends to form a closed loop. Cut the copper wire in two pieces at the center

and clean the surface to make good electrical contact with the iron. The voltmeter mode of

the EA-200 can now be used to measure any potential difference at the terminals.

Figure 2. Schematic of the thermocouple set up for making a thermometer using the voltage generated by a thermocouple. The signal from the thermocouple was amplified to raise the voltage output and to match impedance to the EA-200 Data Collector/Analyzer.

Place the thermocouple in a small test tube to isolate it from water. If the temperature of air

is to be measured, the isolation test tube is not needed. The tube is to isolate the junction

from electrical interaction with the water. Place the thermocouple in the tube in about 250

ml of water in a beaker and place the beaker on a hot plate. Connect the voltage probe to

the terminals of the thermocouple to warm it over a range of temperatures. You can also

change the temperature by using a hair dryer to blow hot air over the temperature probe

and the thermocouple junction. Put the temperature probe in channel 2 with the voltage

probe in channel 1. You are ready to collect temperature and voltage data so the

thermocouple voltage can be calibrated to become temperature.

-10-8-6-4-20246

10.7

16.8

24.5

33.4

43.1

53.4

63.9

75.3

86.1

TEMPERATURE

VOLT

AG

E

Figure 3. (Left) An Excel plot of voltage versus centigrade temperature for the thermocouple with a reference bath of ice and water to reference to 0 degrees centigrade. (Right) A picture of the fx-9750G calculator display window; the bold line is produced by equation 1 below.

Usually the voltage produced by the thermocouple junction is linear over a reasonable range

of temperatures. When the data has been transferred to the fx-9750G graphing calculator it

is tested for linear behavior. When you finish the plot the statistics for a linear least squares

routine can be analyzed to determine how well the data fit a linear response by the r2 value.

If the data do not fit a linear response, the graphing calculator function for X2 is used. The

number r2 should be very close to 1. The values change from +1..-1. If the number is +1 the

data has a perfectly linear response and the data are well correlated to a linear fit. If the

value is -1 the data and a linear response are dis-correlated and the data have the greatest

departure from a linear response.

The data in figure 1 were fit by equation 1 as given below:

T = -7.0592V + 33.524 (1)

1.51.61.71.81.9

22.12.22.32.4

14.8

19.1

23 28 33.6

39.5

46 52.7

59 64.9

TEMPERATURE (C)

VOLT

AGE

Figure 4. (Left) An Excel plot of the amplified voltage versus centigrade temperature for the thermocouple with a reference bath of ice and water to reference to 0 degrees centigrade. (Right) A picture of the fx-9750G calculator display for the same experiment. Note the curvature is more pronounced and the data fit a quadratic model. This effect is due to the nonlinear property of the amplifier. The pictures were taken with a QV-7000-SX digital camera. T = -104.849V2+331.175V -196.23 (2) The thermocouple can be used to measure temperature by making a voltage measurement

and converting to centigrade temperature by using equation 1. The voltage depends on the

gain of the amplifier so each unit must be calibrated for the amplifier used in the

measurement. The thermocouples used were obtained from a hardware store and produce

up to 30 millivolts when heated with a blue gas flame. They serve as safety devices in

conventional hot water heaters.

SUMMARY

The temperature sensor needs to be calibrated against a reference. This may be ice and

water at standard pressure or by use of a reference voltage against which the instrument is

calibrated. Both procedures were tested in this experiment. The type thermocouple chosen

must be one that will produce sufficient voltage to activate the meter used to measure the

output voltage. Of an amplifier is used, any nonlinear response must be considered for the

instrument to be accurate.

QUESTIONS

1. Can you save money by taking the energy from the Sun and converting it into electricity

by using a thermocouple? Discuss the costs involved in providing such energy, if you

answered yes to the question.

2. In the thermocouple part of this experiment you learned about converting heat to

electricity. Discuss how this may be done efficiently by using the Sun's energy. Recall that

focusing the rays of the Sun will multiply the heat energy falling on a given area.

3. The apparatus shown in figure 1 of this exercise is a pyrometer or a device for

determining temperature. Discuss how you think this thing works.

4. One of the properties of nature is that if one process works, the reverse is true. That is,

the generator of electricity produces electricity when a magnet is moved in a coil of wire.

(The generator rule.) The inverse of this is that a current through a wire will cause a magnet

to move. (The motor rule.) Since heating the thermocouple junction produces a voltage,

might a current through the junction cool it? Look up the Seebeck Effect and the Peltier

Effect on the internet and discuss these in the light of the two faces of scientific processes.

5. How many thermocouples of the composition studied above will need to be placed in

series to light a 120 volt light bulb?

6. Since the energy from the Sun can be used to heat the thermocouple to produce

electricity in the day time, discuss how we can store this electrical energy to be used when

the Sun is not shining.

7. The reference junction of the thermocouple system needs to be kept at a fixed

temperature to provide a reference for the second junction. Describe how the fact that the

temperature of the soil at the surface of the Earth relative to a few feet below the surface is

several degrees higher can be used to provide a temperature change that can drive the

thermocouple system.

8. Based on what you learned about the voltage potential, how much voltage can be

produced by the temperature difference found at a depth of one meter relative to the

surface temperature. Determine the temperature difference by using a temperature probe

and the EA-200 Data Collector/Analyzer.

STUDYING VOLTAGE GENERATION BY THE FORCE OF GRAVITY By

Jim Roberts, Professor of Physics and Material Science The University of North Texas

OBJECTIVE: This activity is designed to see how we can generate electricity using gravity, to collect data with a Data Collector/Analyzer and display the data on a fx-9750G graphing calculator and to quantify the results.

INTRODUCTION

It has been long known that the force of gravity can be used to work for us. The

harnessing of gravity from falling water to first power machines and then to produce

electricity has proven to useful in satisfying some of our energy needs.

This experiment is designed to show how a falling object can drive an electric

generator/motor to produce a voltage output for a mechanical force input. It can be

shown that the acceleration of the mass shown in figure 1 produces a change in the output

voltage generated as the object speeds up in its fall.

By studying the amount of voltage generated a determination can be made of the

potential energy available in waterfalls that can be converted to electrical energy.

Moreover, we can develop a device to measure the speed and acceleration by using the

principle of the conversion of notion to electrical energy by using the electric generator.

PROCEDURE

Set up the motor assembly as shown in figure 1. There are a number of small d. c. electric

motors for sale today at modest prices. Any motor/generator will do. Remember that a

generator takes a mechanical energy input and produces an electrical energy output while

a motor takes an electrical energy input and produces a mechanical energy output. The

process is an electro-mechanical transducer that can be operated either way, mechanical

force in for an electrical output or an electrical force in for a mechanical output. Oersted

discovered the motor rule in 1820 and Faraday discovered the generator rule in 1830.

The processes are reciprocals of each other.

Figure 1 shows schematics of the generator set up.

The shaft of the generator (motor) shown on the left of figure 1 is turned as the mass M is

allowed to fall in the earths gravitational field. The voltage output is proportional to the

speed of turning of the coil of wire, shown on the right of figure 1, as the mass speeds up

in its fall.

In figure 2 is shown pictures of the setup for this experiment. The overall setup is shown

on the left and the small motor with pulley and string is shown on the right side of the

figure.

Figure 1 (Left) A sketch of a motor with a pulley and string to drive it using gravity and the mass M. (Right) A sketch showing the principle that a rotating coil in the field of magnets can produce electricity when motion is produced. A picture of the apparatus for making the measurements is shown in figure 2. On the left

is shown the overall setup that consists of the d. c. generator and the Data Collector for

collecting time and voltage input. On the right is shown the motor with pulley and string

drive to activate it in the gravitational field of the earth.

Program the EA-100 or EA-200 for 10 mSec and 20 readings. The mass M will fall with a

velocity given by:

V(t) = gt. (1) The distance of fall is given by: S = gt2 + vot + So . (2) If the mass is started from rest and the distance of fall begins at zero only one term

remains to study the free fall of the mass. The equation reduces to:

S = gt2 (3)

We can let the data collection begin for the cycle as the mass M is released and begins its

travel downward. The distance of fall is given by:

S = (9.8m/sec2)(0.2sec)2 20 cm. (4)

You can experiment with the number of data points and the time for each as needed by

your specific circumstances. These depend upon the space that you have available to

conduct the experiment.

Transfer the data points from the Data Collector to the graphing calculator for analysis.

The results will appear as shown in figure 3. Make your analysis of the results using a fx-

9750G or equivalent calculator. You may do a more detailed analysis by using a

spreadsheet such as Excel and determine the ratio between the rate of fall and the

voltage generated. The device can act as an accelerometer for moving objects.

Figure 2. (Left) An overview of the data collection and transfer system for taking data from the motor as the mass falls and turns the d. c. motor. (Right) A close-up view of the d. c. motor, with the capstan on the shaft to turn as the string unwinds and changes the speed of the motor. Any suitable mass is OK to serve as a driving force as it falls in the gravitational field.

Figure 3. Left. A display of the data taken with the EA-100 Data Collector/Analyzer. The data were analyzed by using the internal routines of the calculator. Right. An Excel plot of the voltage versus time for a d. c. motor made to spin using a falling mass and a pulley attached to the motor shaft. Note that as the object falls it picks up speed and the voltage generated increases accordingly. The data curve displayed on the graphing calculator is quadratic in form. Analysis of the

plot is achieved with the functions in the calculator. Once the profile and equation of the

curve are known an algorithm can be written to determine the acceleration of the mass or

any other mass for the system.

This experiment has demonstrated the versatility of the EA-100 Data Collector/Analyzer

and the fx-9750G to collect and analyze data. There are a number of applications that

can be made of this result. The Atwood machine can be set up with the rotating pulley

attached to an electric generator and a study made of the motion of the masses in the

system.

QUESTIONS

1. If the system described in figure 1 is set up on the moon and the same experiment

done, what will be the amount of voltage generated for the same distance of travel

of the mass M?

2. A bicycle rider decided that if he/she could pace their rate of travel in making a

journey through the mountains, they would minimize the strain that they were under

by using such a device attached to their bicycle wheel to study its motion. Describe

how this approach may be used to improve the biking strategy.

3. If the generator is loaded with a resistance and the string released to allow the mass

M to spin the generator, what will this do to the acceleration of the falling mass?

Remember Lenzs law in answering this question.

4. If a light bulb is attached to the output terminals of the generator and the mass is

dropped, what will happen to the glow of the light as the mass moves in the field of

gravity?

5. Would different masses for M change the voltage output of the generator?

1

Data Analysis Using a Graphing Calculator and a Simple Harmonic Oscillator

By

Jim Roberts, Professor of Physics and Material Science The University of North Texas

OBJECTIVE: This experiment is designed to use the fx-9750G graphing calculator to analyze data taken on an oscillating mass and spring assembly and to test linear properties of matter.

INTRODUCTION In this experiment we will use a graphing calculator to plot data taken for an oscillating

mass attached to a spring supported in the gravitational field of the earth. The

characteristic property of the stretched spring and the subsequent oscillations set up will

be studied using the properties of the graphing calculator. Specifically, we will determine

the value of g through the use of this experiment.

Newton proposed the universal law of gravity that holds throughout the universe. It is

stated as follows:

F = GmM/r2. (1) Where G is a universal constant, m is the mass of an object in the gravitational field of the

earth, M is the mass of the earth and r is the distance between the centers of mass of the

two objects m and M. This equation held for over 300 years until Einstein showed that it

is a specialized case of relativity. The important thing to remember is that it works and

gives us the correct answer. When we are given certain values and are able to measure

other values, it is possible to make select measurements. In this experiment we intend to

measure the value of g for the earth by using an oscillating mass attached to a spring

whose force constant is determined.

The graphing calculator is a very useful tool to plot data and analyze it. We need to set

up an experiment and calibrate the spring that will serve as our force to drive the

oscillator. This is done by choosing a set of mass increments that allows us to collect data

on the amount of stretch of the spring X and the mass attached to the spring to stretch it.

The masses can be copper pennies that can be counted as they are loaded into a tray

attached to the end of the spring. Washers can be used but consider the fact there is not

uniform mass distribution over a box of washers. You can, however, weigh each washer

and take into consideration that there is a spread in mass for the washers in each box that

may be 10% or more from one washer to another. Usually, copper pennies are reasonably

close to the same values, unless corrosion is on the coin. You can assume the spring

stretch is linear and test the mass distribution of the washers in a given set.

Experimental Setup

Set up the oscillator as shown in figure 1 below. This apparatus is simply a spring with a

mass attached to the end so that the assembly can be attached to a rigid mount and set

in oscillation. The oscillator frequency is determined by the mass m, the mass of the earth

and the force constant K of the spring.

0

2

4

6

8

10

12

25 30 35 40

STRETCH (CM)

MA

SS (G

MS)

Figure 1. (Left) A diagram of a simple harmonic oscillator constructed using a spring and a mass attached to a vertical mount in the gravitational field g for weighing the earth. (Middle) A graph of mass vs displacement for a simple spring to find the force constant of the system. (Right) A graph of a rubber band stretched with masses. Note that the spring shows linear behavior and the rubber band does not over all of its range of stretch.

2

Figure 2. (Left)A calculator display of a graph of mass vs displacement for a simple spring to find the force constant of the system. (Right) A graph of a rubber band stretched with masses. Note that the spring shows linear behavior and the rubber band does not over all of its range of stretch. Pictures taken with the QV-7000SX digital camera. Add units of mass to the spring and measure accurately the amount of stretch for the

given mass. Enter the mass and displacement in table 1.

When the table has been completed, input the data for mass and displacement in the first

two columns of your graphing calculator. The data are then analyzed by using the linear

least square regression of the calculator. The value of K can be obtained from the slope

of the mass vs displacement graph.

The results from table 1 can now be used as part of the next phase of the experiment to

determine the gravity of the earth by assuming some simple values. G is well known and

we can precisely measure the period of oscillation of the mass attached to the end of the

spring. When we solve our equations we can determine the value of earths gravity to a

reasonable degree of accuracy.

Set up a table for calibrating the spring to obtain its spring constant as follows.

3

Table 1. A summary of mass versus displacement data.

DETERMINATION OF THE FORCE CONSTANT K

MASS DISPLACEMENT OF MASS

Discussion of Linear Systems

The stretch of a spring is linear over a reasonable range of stretch. Many materials behave

in this way. There are some materials that are not linear. We can use the graphing

calculator to display the linear and nonlinear properties of matter simply by using stretch

and weights to measure the property of the material.

Equations of Motion for the Oscillator

The simple harmonic oscillator can be solved mathematically in the following way. The

energy of stretch must equal the energy released when the spring recoils. This is a

powerful concept.

When the spring is stretched to a length X and released, the motion of the mass is simple

harmonic motion. The period of oscillation for the motion is given by solutions of the

equation of motion:

This equation can be solved to provide an equation for the frequency of oscillation for the

mass for a spring of constant K and a mass m. The universal law of gravity given by

Newton can be used to provide a relationship between the period of oscillation, mass m

and the constant K.

4

Equation (1) can be rewritten by using the assumption that F = mg for the mass hanging

on the end of the spring. Combining this result with equation (1) gives the result:

F = GmM/r2 = mg = -kX (3) When all of the results are combined the frequency of oscillation of the mass on the end

of the spring can be found from the equation:

f = 2(m/k)2 (4) When you have set up the apparatus, choose units of mass and allow the oscillator to

execute 10 oscillations for which you obtain accurate time and from the oscillation time

calculate the frequency. Use equation (4) to calculate the theoretical oscillation

frequency. Enter these values in table 2. When you have tabulated all of the experimental

data, use your graphing calculator to calculate the difference and percent differences.

Table 2. A summary of the experimental results compared to calculated values for a

oscillating mass and spring assembly.

EXPERIMENTAL FREQUENCY

THEORETICAL FREQUENCY

DIFFERENCE

% DIFFERENCE

Set up the experiment again with a rubber band supporting the masses. Calibrate the

displacement constant. Plot the displacement versus mass to see if it is linear. The first

experiment is one done by Robert Hooke that showed that the displacement (stretch)

versus mass (weight) is linear. Many systems obey Hookes law behavior. An interesting

application of this law is Boyles Law for gasses under pressure.

5

Table 3. A summary of the experimental results compared to calculated values for a oscillating mass and rubber band assembly.

EXPERIMENTAL

FREQUENCY THEORETICAL FREQUENCY

DIFFERENCE

% DIFFERENCE

Questions 1. An oscillator is driven by the force of gravity. Can you devise an experiment in

which the value of gravity can be obtained from your data?

2. If you conduct this same set of experiments on the Moon, what do you expect to

find out about the period of oscillation of the mass?

3. A group of smart kids decided that they could use the oscillator to see how fast

they were climbing a high sloping roadway that went up into the mountains. Can

you critique this experiment and see what may be wrong with it?

4. A pilot decided that he could use the oscillator to determine what his altitude is

when he is flying at 40,000 feet. This requires that he is able to measure the period

of oscillations at ground level and then at 40,000 above the ground. Use your

graphing calculator to calculate the value of g at ground level and then at 40,000

feet. Do you think the pilot was realistic in his/her desire to measure altitude in with

this oscillator?

5. What observations did you make about the stretched, oscillating rubber band as

compared to the coiled spring?

6

7

6. What are some sources of error that may change our results?

7. Explain what is meant by a linear coefficient of expansion.

8. Compare the values of r2 (Chi square fits, not the radii) values that you got from the

calculator for each phase of the experiment for the rubber band and for the spring.

Elaborate on what may cause the difference.

9. Do you think that the amplitude of oscillation will affect the frequency of

oscillation?

10. The energy stored in the spring when it is stretched must be converted to kinetic

energy as the mass is released to oscillate. You should detect a small fixed error in

the equation for change in K. E. = change in P. E. Observe the mass very carefully

and determine if it simply moves up and down or if it twists as is oscillates. Do

you think the energy difference between the experimental energy and the

theoretical energy can be accounted for by rotational energy?

11. A smart physicist was also a fisherman. He/she enjoyed applying physics to all

that was done. During a fishing expedition he/she cast a fishing line in the water

with a cork on it to float the apparatus. The cork bobbled as it went into the

water. The physicist decided to time the oscillations to see if a fish was nibbling on

the bait to make the cork bob or if the initial oscillation was just the buoyant force

of the water causing the oscillation. Is it reasonable to think one could find the

difference in a fish tugging at the bait and a natural oscillation of the cork? Explain.

1

DETERMINATION OF THE HEAT OF FUSION OF ICE By

Jim Roberts, Professor of Physics and Material Science The University of North Texas

OBJECTIVE: This experiment is designed to show you how much thermal energy is needed to melt a specified quantity of ice and to plot the results on a fX-9750G graphing calculator.

INTRODUCTION

When a material changes phase a specific amount of energy is needed to change through

each transition, solid to liquid, liquid to gas. The three phases of matter requires specific

amounts of thermal energy to break the bonds and change the order of each molecular

system as the system is cycled over the three phases, beginning with the solid phase and

changing to liquid and then steam (gas).

Water is one of the most studied molecular systems known as the water is cycled over the

three phases of matter. Indeed, the age of the steam engine was characterized by

harvesting the energy recovered from water as it was cycled from steam at 101 C to water

at 99 C or below to operate steam engines to do the work needed .

One of the most efficient methods of heating buildings was by using steam and utilizing the

energy exchange as the steam cooled from above 100 C to below 100 C. The steam was

transported into each room via a radiation strategically placed in the room. The steam was

cooled by exchanging heat with the air in the room with the result that the air in the room

was heated with the energy extracted from the steam.

This experiment is designed to determine the amount of heat energy needed to melt a

known amount of water ice, the heat of fusion.

A specific amount of ice is placed in an insulated bath of water of specific mass. An

immersion neater with known Wattage is used to heat the mixture of water and ice for

specified time. The specific amounts of water and ice depends upon the Wattage of the

heater. This can all be calculated, but some preliminary results allow the experiment to be

duplicated readily.

PROCEDURE Place a 1000 ml beaker inside a thermal jacket to control the heat flow. The shielding used

in this experiment was ordinary newspaper. Dry newspaper is a very good insulator of heat.

Put 5000 ml of water in the insulated beaker. Put 150 mg of ice in a small beaker, 500 ml

volume, and place the beaker in the larger container so that no water can enter this beaker.

Two temperatures are to be measured, that of the outer beaker as the heater raises the

temperature and that of the inner beaker containing the ice to be melted. It is important

that the temperature in two containers be independently measured. This can be achieved

by shielding the temperature probe, all except the tip, and the top of the 150 ml is closed

with insulating material. When all of the components are assembled the experiment is ready

to be set up and data taken.

In Figure 1 the nature of the energy versus temperature profile expected for the experiment

is shown. On the left is shown the profile of changing from solid to liquid to vapor. The

energy needed to change one gram of ice into water is 80 cal/gm. The energy change in

changing water form water to steam is 540 cal/gm. Measurement of this energy is more

difficult than measuring the phase change from solid to liquid.

Figure 2 (left) show schematically the thermal bath and calorimeter used in this experiment.

A specific amount of ice is placed in the container with water. The volume of the ice is

determined by measuring the amount of water produced when it melts.

2

Figure 1 (left) A schematic profile of the change in energy for a water system as it changes from ice to water to steam. (Right) An experimental result for the system described in this work, the heat of fusion for water is 80cal/gm. The upper curve shows the change in temperature of the heating bath and the lower curve shows the temperature of the ice and the resultant water as the ice melts. The results of the experiment are shown in figure 1. (Right.) The lower curve is the curve for

temperature change as the ice is melted in the inner container. The upper curve is the

temperature change in the outer container holding water to heat the inner container with

the ice to be melted in it.

Figure 2 (left)The experimental setup with the heat chamber, calorimeter, holding the water and ice to be melted. (Right) A picture of the experimental setup. The ice is contained in an inner container to isolate the heater from the thermometer. The entire bath is contained in a thermally insulated container.

The total amount of energy put in the calorimiter bath can be obtained from the power of

the heater and the time of the experiment. The heater used was 300 Watts. Thus, with

the time known for the heat exchange the total energy is given by:

Energy Input = Wattage (Joules/sec)Xtime(sec) = Joules (1) E(J) = 300WX600sec = 180,000 Joules (2)

3

This energy serves to heat the total amount of water and melt the ice contained in the

calorimeter. The standard balance of Heat lost = Heat gained is used in

determining the results.

Figure 3 (left) A plot of the energy versus temperature for 160 gms of ice changing from ice at 0 C to water at 70 C. (right) A plot of the energy versus temperature for 160 gms of ice rising in temperature of 10 C changing from ice at 0 C to water at 70 C. The plateau at 0 C can clearly be seen in the figure to the right. During this transition the heat energy continues to flow into the ice to melt it but the temperature does not rise. Pictures taken with the QV-7000SX digital camera.

Immersion heaters are readily available at 200 Watts and 300 Watts at most hardware

stores. Any unit can be used as long as the wattage is knows for the device. A more

precise measurement can be made by using a set up that measures the voltage and

current for each device to determine the Watts used to heat the system.

The amount of heat energy provided is given by equation 2. This heat energy will serve to

heat the 4000 gms of water, melt the ice and raise the temperature of the entire system

to the final value. Be careful to take into consideration all of the heat losses and heat

gains in the system to obtain the best value of the heat of fusion of the ice.

4

QUESTIONS

1. Use the graphing calculator to solve the following problem. Ten grams of ice is

cooled to a temperature of -10 degrees in a deep freeze and then allowed to rise in

temperature until the water from the melted ice rises to 20 C. Calculate the energy

needed to change the ice from -10 C, melt the ice and then raise the temperature

of the ensuing water to 20 C.

2. How much energy is released when 10 gms of steam are cooled from 101 C (vapor)

to 99 C (liquid)?

3. If the energy released in problem 2 is used to move a piston in a cylinder of and

engine with the following geometry, how much weight can the assembly lift in the

field of gravity over a distance of 1 meter?

4. If the volume V in problem 3 is one m3 and filled with steam at 101 C, what will be

the volume when the steam cools to water at 99 C? Recall that the gas laws use

absolute temperature rather than C.

5. Assume that the change in energy versus temperature curve in figure 1 is linear,

what value can you obtain for the Joule Mechanical Equivalent of Heat?

6. An ice storm hits an area of the country and deposits a sheet of ice one cm thick

over the area. If the Suns energy rate is equivalent to 1400 Watts/m2, (This is

equivalent to two hairdryers running at 750 Watts each.) how long will it take to

melt a sheet of ice one meter square and one cm thick? Use what you have learned

about the amount of heat energy needed to change the phase of ice from ice to

water.

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ELECTROCHEMISTRY: FARADAY'S LAWS AND ELECTROLYSIS

By Jim Roberts, Professor of Physics and Material Sciences

The University of North Texas

OBJECTIVE: This activity is designed to show how a simple experiment with electrical current can be used to count atoms. The data are displayed and analyzed using a graphing calculator such as the fx-9750G. The current is measured using an EA-100 Data Collector/Analyzer.

INTRODUCTION

All chemical reactions can be understood from the point of understanding the way in which

electrons are shared among atoms to form molecules. A study of such electron exchanges

is basic chemistry. The entire field of chemistry may be simplified as an exchange or sharing

of electrons among the atoms to form compounds. It is important that we understand that

this leads to the law of definite and multiple proportions. From this concept we can relate

the number of atoms formed to the number of electrons produced in a current flow.

The first part of the experiment we use the process in chemistry of oxidation-reduction. In a

companion reaction, one of the partners is reduced and the other is oxidized. This exchange

of electrons may lead to a pairing of atoms or chemical fragments to form a complete

molecule or the process may be used to separate components into ions. Some oxidation-

reduction reactions occur spontaneously, others have to be aided. The process can be

accelerated or retarded by the use of electrical charges (currents). The potential difference

across the ions will determine whether the components will be able to produce a reaction.

In an electrolytic cell a difference of potential is impressed across the electrodes in the cell.

These electrodes may supply additional electrons to the electrolyte or they may act as an

agent to remove ions from the solution.

The electrolyte contains both positive and negative charged elements. The positive charged

component will migrate toward the negative electrode and the negative ion will migrate

toward the positive electrode. This flow of ions gives rise to a current in the solution. Those

ions that move toward the positive electrode (anode) are anions and those that move

toward the negative electrode (cathode) are cations. The ions may be collected from the

solution to form complete atoms as in the process of neutralizing the copper ions to

produce pure copper, which is collected on one of the two electrodes in the solution. This

1

process of removing metallic components from solution is a very important industry. The

two processes of oxidation and reduction associate with the electrodes in that at the

positive electrode we say we have "oxidation" in the charge exchange process and at the

cathode we have "reduction" in the charge process.

There are a number of examples of electrolysis in nature. In fact, the process of "corrosion"

in which materials are destroyed or weakened by charge and metal exchange, runs

maintenance costs into billions of dollars each year.

One process, which is useful in industry, is the reclamation of sodium (Na) from its

compound with chlorine (Cl). This process of separation is achieved by heating the NaCl to

a molten state and then placing electrodes in an apparatus similar to that shown in figure 1.

When a current is passed through the electrolyte the Cl- ion is attracted to the positive

electrode, forms a gas and "bubbles" away unless it is trapped. The Na+ ion is attracted to

the negative electrode, becomes sodium metal and is deposited onto the electrode.

The electrolyte of NaCl may be replaced with NaCl and H2O and the reaction is slightly

modified. The electrolyte consists of Na+, Cl-, OH- and (H3O)+ ions. The H+ ion will displace

the Na+ ion at the negative electrode because it has a stronger affinity for the electrode than

does the sodium ion. The sodium gains a "partner" by choosing the OH- ion to produce

NaOH. The by products of the process are H2, NaOH and Cl2. The H2 and Cl2 will escape as

a gas unless trapped. This is one way of producing these components industrially. In fact,

the process of reclaiming metals or reducing corrosion by electrolysis is a very important

industry.

Figure 1. A solution of NaCl in water with electrodes to remove the ions from solution. Note that NaCl is a solid and Na is a solid but Cl is a gas at room temperature. Thus, when the ions are changed to elements, one will bubble away and one will become attached to the other electrode.

2

It should be clear that if the components can be reclaimed from solution, the process has

application in electroplating.

Electroplating can be achieved by choosing the correct ion in solution for plating out of

solution and then pass a current through the solution to remove the metal ions. The ions

need not be metallic for their removal from solution. In fact an experiment that has promise

for future application can be conducted by separating the hydrogen and oxygen ions in

water to form gases. The hydrogen gas can then be burned in the presence of the oxygen

and the waste product is water. One can see the potential of such a procedure for fueling

internal combustion engines.

Figure 2. Basic apparatus for conducting experiments in electrochemistry to reclaim metal ions of copper from a copper sulfate solution. Michael Faraday in the Nineteenth century formulated a set of laws to deal with the

processes of separating ions in solution from one another through the use of electricity.

These laws are referred to as the Faraday Laws of Electrolysis and have broad application.

The laws may be stated as:

1. The total amount of charge Q passed through an electrolytic cell will liberate a

given amount of mass m.

2. The amount of mass m liberated is proportional to the gram equivalent of the

material liberated. The valence of each ion must be considered to establish the ratio

between the gram equivalent and the mass of a given atom. A monovalent ion

requires one electron per atom, a bivalent ion two electrons per atom, etc.

Faraday combined these laws into a form that can be used:

m = QA/(Fn) = ItA/(Fn)

3

Where, A is the gram equivalent of the atom, Q the total charge (determined by Q=It,

with I the current and t the time.), n the valence number and F a Faraday or 96,500

Coulomb/mole.

The laws can now be used to determine the properties of valence and the value of

Avogadro's number.

You might guess that if the electrical current can be used to separate charges is it possible

to use the reverse action of the electrolytic cell. This reverse process relies on the

spontaneous oxidation-reduction process to drive the charges around an external loop to

produce a battery. This cell is a battery or a fuel, cell which relies upon the chemical

reaction in the electrolyte to produce potential energy. In a storage battery, the external

charging source serves to store energy in the electrolyte for future delivery to the external

circuits.

By utilizing the circuit given in figure 1, we can conduct our experiment in electroplating and

in determining the value of Avogadro's number.

PROCEDURE:

The experiment that we will perform is one that can yield Avogadro's number from simple

results and using Faraday's laws of electrolysis.

1. Set up the apparatus as shown in figure 3.

*2. Set the current to pass through the solution at a value of 0.1 Amperes by setting

the voltage control on the power supply shown in figure 3.

3. Start the timer to make a measurement of elapsed time and close the circuit to

start the current flowing in the circuit.

4. We need the total charge Q that is transferred through the loop. This is given by Q

= It. (Note that I is in Coulombs/second so you have to convert your time to seconds

to get the proper units.)

5. Once you have allowed the equipment to run for about 30 minutes, you will have

enough data to complete the data table given below.

*You may need to adjust the current setting to a different value that depends upon the

strength of the copper sulfate solution. If one electrode is turning black you are using too

much current for the strength solution used.

4

Figure 3. The setup for measuring the current passed through the electrolyte solution. The schematic diagram is shown on the left and the actual setup is shown on the right. The current is determined by measuring the voltage dropped across a standard value resistor. If a one-Ohm resistor is chosen, the meter will convert voltage directly into current. The copper sulfate solution is shown as blue in the beaker containing the electrodes to be measured. Data for current and time can be taken either with the EA-100 or the EA-200 Data Collector/analyzer.

Summary Table for the Experimental Data

I t Q

V M1 M2 M No Electrode

E1 E2

EXPERIMENTAL DATA

E1 and E2 are the different electrodes in the solution. Record the mass changes for each

electrode to get two values for Avogadros number. One electrode will lose mass to the

solution and the other will gain mass in the same amount. One electrode returns copper to

the solution as ions and the other captures ions to form copper metal in the process.

The data table provides you with data from which you can calculate Avogadro's number.

Notice that one electrode has its mass reduced while the other electrode has its mass

increased. The two measurements in change in mass M should give you the same answer.

One electrode has been "sacrificed" to the solution and one has metal plated onto it.

5

This process of sacrificing one material to save another is used in the pipeline industry to

retard corrosion, which costs billions of dollars each year. The electrochemical processes of

the soil are retarded by means of this anode, which is often magnesium in composition.

Prevention of corrosion of the space capsules becomes important when they are to be

introduced into some planetary atmospheres.

How much does your answer differ from that of the experts? You can calculate this by the

equation:

Percent error = [(standard reading-your reading)]X100% (standard reading) % error = [(6.0221367X1023 - your reading)/6.0221367X1023]X100 When a current is passed through the solution, the electrons will go into solution at the

negative electrode and "neutralize" the positive ions, whereas, the positive electrode will

offer neutralization at its surface to neutralize the negatively charged ions in solution.

This part of the experiment is now complete. You have counted atoms and should have a

reasonably good number for your efforts.

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QUESTIONS

1. Why are the two volumes of gasses liberated at two platinum electrodes placed in

water and a current passed through the electrolyte produced in the ratio 2:1?

2. Why do you think aluminum cans are recycled but ordinary tin cans are not? 3. Much of the earth is covered by water that contains hydrogen and oxygen. The

experiment that you have conducted shows that we can reclaim hydrogen from water

and burn it in the presence of oxygen by using two electrodes to separate the

hydrogen from the oxygen in the water. Why don't we collect the hydrogen from the

ocean and use it for automotive fuel?

4. What is the waste product of burning hydrogen in the presence of oxygen? 5. The human body burns carbon to produce carbon dioxide as a waste gas from the

lungs. The plants use this waste as their fuel and produce oxygen as their waste

product. What do you think will happen to our atmosphere in the next 100 years if we

keep cutting the trees and covering the grass with blacktop?

6. The byproduct (waste) of plants is oxygen. How can we improve our oxygen content

in the atmosphere using this knowledge about plant life?

7. In producing pure metals from their oxides heat is used to melt the metal and drive

out the impurities. Why cant this process be used for aluminum oxides?

8. If the one-Ohm resistor R in figure 3 is replaced with a 10-Ohm resistor, what will

change in the results?

9. If we assume that Avogadros number is correct, can you describe how we can

calibrate the value of a standard resistor?

10. If we want to calibrate a voltmeter, how can we use the results of question 9 to do so

by using Faradays law and Avogadros number?

Heat Exchange in Cooling by Evaporation

By Jim Roberts, Professor of Physics and Material Science

University of North Texas OBJECTIVE: This activity is designed to show how the basic laws of heat exchange can be used to show that objects wrapped in a wet paper towel cool by evaporation. Data collectors and graphing calculators are used to show how the data can be collected and then displayed for analysis.

Introduction

The basic law of heat exchange is summarized in the figure below. This is an expression

of the exchange of energy law that pervades all of nature. Heat energy may flow into one

object from another with the result that one object cools and the other is heated up. All

of the energy available is conserved for the system. One of the ways to solve problems

scientifically is to view the processes in nature as comprising a system subject to

fundamental laws.

Figure 1. A picture of the burrow of a tarantula spider. The thin web over the holed is designed to reduce the flow of infrared energy entering it.

This figure shown the application of laws of radiation and cooling or heating processes

associated with the exchange of heat energy. The web will both shield out certain

wavelengths and admit other wavelengths. Visible waves are hardly stopped by the web,

allowing light into the hole. The soil surrounding the hole collects heat during the daytime

and radiates it out at night and the area is cooled by radiation.

Interesting effects occur on the earth through the variable exchange of energy between

land mass and water masses. This simple experiment can be used to show how the

thermal energy of the sun can warm land and water bodies at different rates and then

when the sun goes down the bodies cool at different rates causing the winds to blow in

patterns that vary from the evening to morning times. Moreover, the nature of cooling of

the earth can be better understood when we speak of cooling of the earth from night to

day. The flow of heat energy out of the system leads to cooling at night and then

warming during the day as new solar energy flows into the earth. When the rains come

and wet the soil the evaporation of the water will cool the area. In some parts of the

world evaporation coolers are used to cool houses. Air is allowed to slow across an

absorber with water vapor in it. As the water evaporates in the device, the flowing air is

cooled and the houses can be cooled in the process. Some ancient castles in the Mideast

were cooled by allowing water to flow around the castle wall in troughs that overflowed

to provide a mist through which the air blew to cool the castle.

Two different type containers are used in this experiment to study heat energy flowing

out of and into reservoirs of water. The heat energy is exchanged between the volume of

water and the air for a given time. The cooling rate for each container is monitored using

the EA-200 to collect the temperature over time for about one half hour at intervals of 30

seconds.

Figure 2. A schematic diagram showing the basic law for heat exchange. One part of the system loses energy and the other absorbs the energy. This process is fundamental in the behavior of a system.

Procedure

Put about 60 ml (60 cm3) in two containers. One of the containers is wrapped in a cloth

wet with water. The second container is wrapped in dry cloth of the same padding. Both

containers are made identical in every way except for one cloth being wet with water.

This procedure allows only one variable to change at a time. This brings up a basic rule in

science, fix all variables but one and allow only it to change. Everything else must be

kept the same.

Figure 3. A picture of the apparatus needed to study the heat energy exchange in this experiment. These results of the study allow us to understand how heat exchange and cooling by evaporation can be measured. The beaker contains 60 cm3 of water. Set up the temperature probe and the EA-200 with a folded paper towel soaked in the

liquid chosen for evaporation. The experiment is now ready to be conducted.

Set the EA 200 Data Collector up to read a total of 200 readings with one reading at

each1 second interval. This should provide sufficient data to study the heat exchange

associated with the experiment.

The data plot shown in figure 4 demonstrates how the process of evaporation of a liquid

can be used to cool an area.

The apparatus is set up as shown in figure 4 to demonstrate how different liquids will

change the rate of cooling of the area. Two liquids were chosen, water and ethanol. The

temperature probe was placed between two layers of paper towel and the liquids were

allowed to evaporate from the towel. The data show a more rapid rate of cooling for

alcohol than for water.

Different liquids can be chosen with varying intervals of time to show how the process of

heat exchange takes place.

Figure 4. A close up view of the set up to measure the thermal energy exchange between the temperature probe and the air surrounding them. The liquid in the towel is water for the curve shown.

18.519

19.520

20.521

21.522

22.523

23.5

0 10 20 30 40 50 60 70 80 90 100TIME

TEM

PERA

TURE

Figure 5. A plot of the temperature change versus time for two liquids, ethanol and water . Note the more rapid rate of cooling for the ethanol as compared to water.

22.2

22.25

22.3

22.35

22.4

22.45

22.5

22.55

22.6

10 30 50 70 90 110 130 150 170 190 210 230 245

ELAPSED TIME

TEM

PERA

TUR

E C

Figure 6. A picture of the graphing calculator with data for 60 ml of water cooled by wrapping it in a paper towel soaked with water to show cooling by evaporation. The graph shows an exponential decrease in temperature with time. Data were gathered using an EA-200 Data Collector/Analyzer. The curve to the right is an excel plot of the same data with number of points reduced to 25 instead of using all of the points collected by the EA-200. Figure 6 shows the effect of cooling for a larger volume of material than the air

surrounding the temperature probe. This shows that with the proper amount of liquid to

evaporate, a reasonably large volume of material can be cooled.

QUESTIONS

1. If the rate of evaporation changes, how will this affect the temperature of the water

in the container?

2. If the water is replaced with different alcohols, how do you think the cooling will

respond?

3. Think of several liquids to use in the experiment and make a scientific guess the

time needed to produce a specific amount of cooling.

4. The rate of evaporation is determined by the surface area exposed to the

environment. Can you design an experiment to show that the rate of cooling follows

a similar trend and that the rate of cooling is proportional to the area of the surface

exposed to the environment?

5. Compare the coefficients in the quadratic fit of the data with the fx-9750G graphing

calculator and the analysis made using the excel fits.

6. Automobiles have radiators on them to cool the engine so that it will not overheat.

Discuss how the radiator increases the surface area to release more heat from the

engine.

7. Dip the temperature probe into several different liquids and use the EA-200 to

collect time and temperature for about five minutes. Does the rate of cooling

depend upon the different liquids as it did in question 3 above?

HOW GOOD IS THAT BATTERY By

Jim Roberts, Professor of Physics and Material Science The University of North Texas

OBJECTIVE: This experiment is designed to show how to determine the life time of a battery, to plot the results on a fX-9750G graphing calculator, to determine an equation for the change of voltage over time under a specific load and from the results predict failure times for batteries.

INTRODUCTION

All sources of energy have finite lifetimes before they become too exhausted to function

properly. Batteries are in extensive usage to day in many different devices. If the voltage

and current demands for an electrical device are known, the length of time that the battery

can operate the device efficiency can be determined. Many companies produce batteries

with differing quality of manufacture. This activity allows us to test a specific battery to

determine its ability to deliver the energy claimed. It becomes useful to test each battery

product to determine what potential life exists in a given battery. These units can be tested

by using a simple circuit for a fixed load and measure the rate of drain from the battery.

PROCEDURE

Set up the circuit shown in figure 1 so the time and voltage can be measured for a given

interval of time. This set up enables us to determine the change in voltage with time or V(t)

and see how long it takes for the battery to have its voltage reduced by a specified amount.

This might be the value of half of its original value. We can refer to this value as the half-

life of the battery. If the battery cannot operate the device at a value below 80%, for

example, the usage of the battery can be predicted for the time and load at which the

battery is technically dead to operate that device.

1

Figure 1 (Left) A schematic diagram of the circuit needed to test the lifetime of a battery. (Right) A picture of the setup to measure the decay of voltage versus time for select batteries. Either the EA-100 or the EA-200 Data/Collector Analyzer can be used to obtain the voltage over time. The picture was taken using a QV-7000SX Casio digital camera.

A plot of voltage versus time will tell the story of how the ability of the battery to deliver a

certain amount of voltage to the load. The formula that describes the curve of voltage

versus time can be used to predict when the battery will be dead or when it has reached a

terminal value such that it can no longer provide the voltage needed to operate a certain

device.

y = 0.0002x2 - 0.0097x + 1.5188

R2 = 0.9919

1.3

1.35

1.4

1.45

1.5

1.55

1 3 5 7 9 11 13 15 17 19 21 23 25 27TIME (MIN)

VOLT

S

Figure 2 (Left) An Excel plot of the decay curve for a battery. The data from the calculator was reduced by taking only every fourth data entry. (Right) A graphing calculator display of the time dependent voltage curve for a loaded battery. The load was a 10 resistor. Note that the average of the voltage follows a power law shape. The equation for this battery decay is 0.0002X2 - 0.0097X + 1.500. X is the time in seconds. The intercept may change from 1.5 V if the calibration is not correct and if the batterys initial voltage is different. The trend in decay is the same.

2

The voltage of the battery and the resistance of the load will determine how long the

experiment needs to run. The source of voltage chosen in this activity was an AA battery

which delivers 1.5 volts when it is at its maximum value. Two loads were chosen, one of 10

and another of 2.5. This will allow a range of operation to be obtained.

The equation that relates the time of failure of the battery tested with a 10 load is given by

the equation below:

V(t) = 0.0002X2 - 0.0097X + 1.500 (1) A fX-9750G graphing calculator was used to display the data and to obtain the equation

that best fits the data curve. An Excel analysis was used to finalize the equations and to

compare the results with the analysis obtained with the graphing calculator.

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4

QUESTIONS

1. Discuss how this experiment can be used to set up a quality control study to test

lifetimes of batteries produced by a specific manufacturer.

2. How much time will it take for the battery tested in figure 2 to be reduced to one half

of its original voltage when loaded with a ten Ohm resistor?

3. A portable CD player consumes 0.01125 A of current at 3.0 volts to make it operate

properly. If the device fails to operate when the batteries have been reduced in

voltage to 0.8 of the original value, how long will the device operate? Assume the

power dissipated is described by equation 1 and scale the equation from 1.5 volts to 3

volts.

4. You have been hired to test the quality of batteries produced by several

manufacturers of batteries. Describe how you can test the batteries from each source

to show what capabilities each battery has.

5. Some prankish students decided to connect a piece of wire that had a resistance of

1 across a battery like the one tested in tested in this experiment. Assuming the

batteries are identical, calculate with your graphing calculation and using equation 1

the time it will take for the battery to be reduced to of its original voltage.

6. How much power is produced by the wire when the battery is fully active at 1.500

volts?

7. In question 6, how much power does the battery produce across the resistor when the

voltage has been reduced to its original value of 1.5 volts?

Construction of a Chemical Battery Using Lemons and Dissimilar Electrodes

By

Jim Roberts, Professor of Physics and Material Science The University of North Texas

OBJECTIVE: The objective of this activity is to show that an electrical potential can be produced by the use of electrodes and lemons. The voltage can be measured by using the EZ-200 Data Collector/Analyzer.

INTRODUCTION

The construction of a battery requires the basic components, two electrodes (dissimilar

metal) and an electrolyte. Such cells are the result of electrochemical potentials produced

when chemical reactions occur between the members of the cell. By choosing a suitable

electrolyte and different electrodes, select potential differences can be produced.

In this activity various electrodes are selected and placed into a lemon to determine what

the electrochemical potential will be. A series of lemon cells are arranged in series to

produce a battery that can be used to energize electrical devices or to light a light emitting

diode. The potential differences are measured by using a data collector. The voltage

produced by each cell is measured and the data set of voltage versus number of cells is

input into a graphing calculator to show the linear dependence of voltage versus number of

cells in a linear array.

PROCEDURE

The cell is constructed by using alternate layers of lemon slices and two dissimilar metals

such as shown in figure 1.

Figure 1. (Left) A sketch of a single stack of electrodes and an electrolyte (lemon) used to produce an electrical potential. (Right) A stack of cells used to produce a lemon battery. The stack of cells should produce six times the potential of a single cell. Since silver is expensive, the electrodes for this experiment were zinc plated iron and copper. There is some ambiguity in describing the difference between a cell and a battery. Cells

come in increments of 1.5 volts for carbon and zinc electrodes with ammonia paste as the

electrolyte. A stack of these in series of six produces a 9-volt battery and four of these in

series will produce six volts.

Figure 2. (Left) A picture of simple lemon battery constructed by using six lemons and two metal electrodes, copper and zinc plated iron and the EA 200 Data collector used to gather the data and the fx-9750G used to graph the data. (Right) A picture of the graphing calculator screen plot showing how the voltage changes each lemon is added in series with the others. The pictures were taken with the QV-7000 SX digital camera. The data were taken with the EA-200 set for one second intervals and the probe was

moved from each cell to the next until all cell voltages had been tested. The data were then

adjusted to retain four data points for each voltage setting. A linear Least Square regression

was made of the data using the graphing calculator. The data for the electrode set and the

lemon electrolyte give a linear equation of:

Y = 0.628X (1) The result from the graphing calculators show that the r2 fit is 0.96, indicating a good linear

fit for the voltage versus number of cells result. X is the number of cells and Y is the voltage

produced by the assembly.

Construct a data table of the total voltage versus the number of cells in the stack. Enter the

data into the graphing calculator and study the plot of voltage versus number of cells. Is the

plot linear? Use the statistical analysis for a linear least squares regression and determine

the level of fit for the data. Use the equation of the plot to answer question 1 at the end of

this activity.

QUESTIONS

1, How many cells such as shown in figure 1 will be needed to light a 120 volt light bulb? Use

equation 1 to predict this result.

2. The electric eel can produce several hundred volts of potential capable of causing a

severe shock for anyone in the water nearby. Describe how you think the eel can produce

such large potentials along its body.

3. Try the set up described in figure 1 by using a sliced Irish potato for the electrolyte. What

voltage do you read for six cells constructed with the sliced potato and copper and silver for

electrodes?

4. If the electrodes in figure 1 are replaced with iron and copper what potential do you read

with the data collector?

5. Examine the table of electrochemical potentials provided in the list and find the two

electrodes that will produce the maximum potential for a single cell.

6. Replace the electrolyte (lemon) with salt water. What potential do you find for a single

cell of copper, silver and salt water?

7. Chemical batteries fail after a period of time. Describe the life cycle of a carbon, zinc and

ammonia paste battery. Will it fail suddenly or will it slowly die over time?

8. A nickel and cadmium (NiCd) battery has special characteristics for its life span. This is

shown in the plot of voltage versus time provided above. Describe the difference between

the two types of batteries, carbon cells and NiCd composition batteries in their nature of

failure.

9. Study the following table and determine the electrode combination that will produce the

maximum theoretical potential difference.

10. Metal tanks, gas transmission lines and water pipes corrode in the soil in which they are

buried. Discuss how this process works in the light of what you have learned in this exercise.

Figure 3. A close up view of the zinc, Copper and Lemon battery composed of six cells in it. The surface area of each plate (electrode) is 2.5 cm by 2.5 cm.

Light Output Experiment and Current Relationships in a Light Bulb Using Technology and Probes

By Jim Roberts, Professor of Physics and Material Science, The University of North Texas

OBJECTIVE: This experiment is designed to establish the validity of intensity of light versus current square law using probes and data analyzers (EA-200) and graphing calculators like the fx-9750G.

INTRODUCTION

This experiment uses Ohms Law, which is one of the most fundamental laws of electric

circuits. The light circuit is analyzed using this law. The law of electricity that showed the

relationship for voltage, current and resistance was first worked out by G. S. Ohm and is

now called Ohms Law. It shows how the three quantities relate. All circuit analysis rests

upon the mutual dependency of these three quantities, voltage V, current I and resistance

R.

The circuit below is set up using the data collector/analyzer (EA-200) with two voltage

probes attached. One probe is used to measure voltage and the second probe is used to

measure current in the following way.

One voltage probe is placed across a one-Ohm resistor. When the voltage is measured

across this resistance, the measurement is scaled to change the unit of voltage into

current by the ratio of Ohms law. I = V/R.

Figure 1. A set up to test the validity of the light intensity law by using the EA-200 data collector to obtain current and voltage. The voltage probe (current) is inserted in channel 1. A one-Ohm resistor R1 serves to convert the voltage reading into current. A pictorial set up is shown in the right of the figure. The light intensity is measured using the light probe provided with the EA-200. The graphing calculator is ready to receive the data

1

2

from the EA-200 after it has been collected. Note the opaque tube surrounding the light source to shield the probe from stray light. The voltage from a variable power supply (shown with an arrow across it to indicate a

variable source) is varied in increments that will provide current and voltage variations in

the closed circuit. The intensity of the light is measured using a light probe coupled to the

EA-200 Data Collector/Analyzer. (See figure 1, right.)

When the circuit has been set up, each setting of the voltage is made at increments of one

volt to set the independent variable and the current (voltage across R1) is measured

(dependent variable). The two values are tabulated in a data table to measure the pattern

of voltage versus current. The data can be transferred from the EA-2oo to the fx-9750G

(See figure 1.) Further analysis can be made by transferring the data sheet into a spread

sheet such as Excel.

Table I. Data table to record data taken for a resistor using the EA-200 modified to make

current and voltage measurements and light intensity for a light bulb.

VOTAGE CURRENT INTENSITY

Table I shows the (x,y) pairs of voltage (V1) and current (V2/1) and to records the intensity of the light. The one Ohm resistor converts the units from voltage to current as per the scheme shown in figure 2 (left). When the data have been collected by the EA-200 it is input into the CFX 9850GB plus

graphing calculator for observation and analysis. The students should be required to plot

the data in a standard way using graph paper and suitable axes. This procedure will

demonstrate the power of technology in the classroom. One of the requirements for

students is to gain experience in graphing as part of the TEKS.

Figure 2. (Left) A sketch of the symbol of the IEEE used to show how voltage can be converted to current by using a scaling resistor. (Right) A picture of the screen of the fx-9750G graphing calculator showing the intensity versus current for a light bulb. The voltage was changed and the current read for fixed increments of the voltage. Note the glitch in the curve. This is due to the interference of the room light as the brightness of the light changes relative to the room.

01234567

0 0.95 1.95 2.95 3.95 4.95 5.95 6.95 7.95 8.95 9.95 11 12

CURRENT (ma)

LIG

HT

AR

B U

NIT

S

Figure 3. An Excel plot of the data taking every fifth point from the graphing calculator to show the trend in the data for the light versus current pattern. The light intensity varies as the square of the input current to the filament. The equation for the data fit is y = aX2 + b. This trend can be checked with the graphing calculator.

3

4

QUESTIONS

1. Discuss what happens in a circuit when current flows through a resistance to produce light.

2. How does the light intensity vary with current?

3. How does the light intensity vary with voltage?

4. Why does the light bulb show a change in voltage and current when it begins to

glow as the voltage is raised to its rated value?

5. Would the same method work for a. c. current to produce light output from the

bulb?

6. If two bulbs are placed in parallel for the same voltage, what will be the intensity of

the light output?

7. If two identical bulbs are placed in series for the same voltage as for

one bulb, what will be the intensity of the lights?

8. Using what you have learned about the way current heats the filament in

a light bulb, show the expected intensity can be calculated using the equation

Watts = I2 R.

STUDYING POLARIZED LIGHT

By

Jim Roberts, Professor of Physics and Material Science

The University of North Texas

OBJECTIVE: This experiment is designed to show how light polarized by one lens of Polaroid sun glasses can be studied by using the second lens to analyze the light as the lenses are rotated relative to each other with the light intensity measured using a light probe. The ensuing light change with relative angle of rotation is plotted on one of the family of fX-9750G graphing calculators.

INTRODUCTION

Ordinary light coming from most sources is vibrating with equal probability through

an angle of 360relative to the direction of propagation. When this non-polarized light is

subjected to special media, reflected or selectively refracted, it will become polarized.

Francois Arago observed that as light passes through certain liquids with suspended

materials in them the light vector leaving the solution is polarized in accordance with the

nature and amount of the suspended materials in solution. This discovery has provided a

powerful tool of analysis for studying solutions. It has been observed that some solutions

rotate the light vectors clockwise and some rotate the light vector counter clockwise. The

angle of rotation is dependent upon the concentration of the solution for a given solute. It

has also been noted that certain materials such as dichroic crystals will produce the same

effect. Polaroid sunglasses with these selectively absorbing materials will produce

polarized light.

In this activity we show how the polarized glasses can be used to polarize light with

one lens acting as the polarizer and the second acting as the analyzer. The light intensity is

measured with a light probe as one lens is held stationary and the second rotated about its

axis in fixed increments of angle.

1

PROCEDURE

Obtain some sunglasses that have the ability to polarize light and not just dark

glasses. Usually, the identifying label of Polaroid will indicate this property. The lenses can

be separated so that one can be rotated with respect to the other one and the light output

measured as the angle or rotation is changed. One lens is fixed in rotation while the other is

rotated in increments of about 10. The light should vary in intensity as the rotation takes

place if the glasses chosen have polarizing capability.

1. Obtain two lenses from discarded Polaroid sun glasses.

2. Fashion an arrow along the edge of each lens so the relative orientation can be

measured. Just cut an arrow shape from sticky labels and paste the labels onto the

edge of each lens. One lens becomes the analyzer and the second the polarizer.

Either lens will serve to act as a polarizer or an analyzer since the light vector position

is relative. This procedure can be improved by gluing the lenses to two cylinders that

fit inside each other. The tubes can then be rotated easily, after the glasses have been

trimmed to fit the ends of the tubes.

3. Turn on the light source and rotate the lens about its axis in increments of 10 as the

light output is measured with the light probe. Use a 180 protractor to measure the

angle of rotation of one lens as it is rotated about its axis.

4. Record the angle of rotation and the light intensity that goes with each angle in a data

table for future input to the fX-9850G graphing calculator for analysis.

5. Use the EA-100 Data Collector/Analyzer to read the light intensity for each angle.

6. Plot the data for X and Y with X the angle of rotation and Y the light intensity.

2

Figure 1. (Left) A schematic setup of the experiment with the two lenses in place and the incident light polarized by one lens and analyzed by the other lens. The light probe is placed in the exit beam of the light. (Right) A picture of the setup with the light source, light tube with polarizer and analyzer attached so one tube can be rotated as the light is measured for each angle. The relative rotation of the lenses can be achieved by use of two tubes that fit inside

each other. This assembly is shown in Figure 1 on the right side of the figure. The plastic

lenses are cut to fit the ends of each tube and then glued in place so they can be rotated

relative to each other. The angle of rotation is determined by use of a pointer attached to

the rotating tube. The data can now be obtained by fixing the tube assembly so that the

bright light shines into the tube at the front end of the assembly.

When the light intensity versus angle of rotation has been measured and tabulated,

the data are input into the graphing calculator for analysis to determine the nature of the

light behavior as the analyzer is rotated relative to the polarizer. These data are tabulated

below for one experiment. Figure 2 shows the plot of a sine wave, an exponential plot and

the experimental data for comparison.

3

Table I. Experimental data and trial fitting results for polarized light using Polaroid sunglasses lens to polarize and analyze the light.

ANGLE INTENSITY 950Sin[2(+10)/360] 950Exp[2(-84)/360]

0 104 168 111 10 179 212 179 20 248 306 273 30 372 437 391 40 492 584 527 50 656 725 668 60 791 840 797 70 859 911 895 80 917 927 945 90 938 886 940 100 824 794 879 110 776 665 773 120 565 518 640 130 440 376 499 140 299 259 366 150 228 186 252 160 202 167 164 170 211 205 135

0

200

400

600

800

1000

0 20 40 60 80 100 120 140 160RELATIVE ANGLE (DEG)

INTE

NSIT

Y

4

Figure 2. An Excel plot of the raw data , a Gaussian fit of the data X and a Sine wave plot of the data . The best fit for the data is given by the Sine wave. ___________________________________________________________

Figure 3. A plot of the experimental data with a Sine curve passing through the points. The FX-9750G Plus graphing calculator determines the best fit sine curve for the data. This is achieved easily by choosing the sin plot in the menu shown on the picture above. The cursor needs to be moved one setting to the right to find the sine function to fit the data, The data fit the curve y = 381 Sin(0.039X-1.684)+547.

Once all of the data have been collected, the data analysis can be made using the

appropriate functions in the graphing calculator. Many applications can be made using the

properties of polarization of light.

5

6

QUESTIONS

1. Find a digital watch and analyze the light coming from the dial by rotating one of the

Polaroid sun glass lenses around its axis as you view the numbers on the dial.

Describe what you see.

2. Repeat the activity in problem #1 by looking through one of the Polaroid sun glasses

and rotating it as you view the digital display on the gas station pumps. Describe

what you see as the lens is rotated about its axis.

3. Try the same activity in question #2 as you view an ordinary light bulb. Describe what

you see.

4. What property do you think makes the difference in what you view in questions 1 and

2 that are different in problem 3?

5. Go to the web site and learn what you can about a Polarimeter.

6. Allow a beam of light from a flashlight to be reflected from a plane mirror with the exit

ray leaving the surface at about 45. Take one of the lenses and rotate it about its axis

while viewing the reflected beam of light. Describe what you see.

7. Late in the evening when the sun is red looking and setting or in the morning when a

similar effect is observed, observe the sun through the lenses of the sunglasses.

Describe what the light does as the lens is rotated as in the experiment above.

8. What is happening to the light from the sun?

Using a Data Collector-Analyzer and Graphing Calculator to Show How the Suns Energy can be Concentrated

By

Jim Roberts Professor of Physics and Material Science

University of North Texas OBJECTIVE: This activity is designed to show how solar energy can be focused to produce highly concentrated energy flux using a data collector/analyzer and a graphing calculator.

INTRODUCTION

It is well known that light waves travel in straight lines. Any wave can be changed in

direction by reflection and by using the lens effect to make the rays that represent the

wave converge or diverge from the source. In this activity it is demonstrated that energy

from the sun can be brought to focus and high temperatures can be produced. Test

tubes of water are used to determine the amount of heat energy gain produced by

focusing the rays of heat coming from the sun. Both test tubes are the same volume and

composition to simplify the comparison for the temperature changes.

EXPERIMENTAL ARRANGEMENT

The EA-200 is programmed for the time and number of points to be gathered in the

experiment. Two temperature probes are used so the experiment can be conducted more

rapidly. Also, by taking data for both the focused and non-focused energy at the same

time all other variables are fixed and a simple comparison of the data can be made.

Figure 1. (Left) A drawing of the lay out of the experiment. Two types of rays are shown, one focused (top) and the other not focused (bottom). (Right) A picture of the experiment in operation. Aluminum foil is used to make the flat reflector (left side of the box) and curved surface (right side of the box). The bottom of the curved surface should be at the same distance from the test tubes of water ad the flat surface. The picture was taken using the QV7000 Casio digital camera. Figure 1 is shows the experimental set up with both a drawing of the focusing apparatus and a picture of the actual experimental set up. The experiment was run for 15 minutes. In figure 1, the rays coming from the sun, left represented by the arrows, will land on the

curved surface and will be focused at A to increase the concentration of energy. The case

for a non-curved surface will not concentrate the energy but will reflect it off the surface.

Thus, the area at A in the curved surface case will have a greater temperature for the

same time exposure. This experiment is to show that the concentration of energy can be

used to significantly raise the temperature at A. The test tubes filled with water are

placed at A, the focal distance of the curved surface. The flat reflector is placed the same

distance from the second test tube.

2 2 .4 8

2 2 .9 8

2 3 .4 8

2 3 .9 8

1 13 25 37 49 61 73 85 97 109

121

T IM E

TEM

PER

ATU

RE

(C)

Figure 2. (Bottom) An Excel plot of the temperature rise with time for the flat reflector (lower curve) and the curved, focused, reflector (top curve). Note that the two curves appear to level off after a time t. This appears to be due to the fact that the wind was blowing across the apparatus and the heat was being carried away by the airflow. The Excel plot shows only125 of the 255 points taken with the fx-9750G graphing calculator. The top view of the figure shows a picture of the display for all of the data points for the two temperature channels. (Left top) Unfocused light. Note that the data are not continuing to rise as rapidly as the focused energy shown at the top right. The picture was taken using the QV7000 Casio digital camera. When the data are collected by the EA-200 they are transferred into the CFX-9850GC

Plus calculator for display and analysis. These data curves for the flat reflector and the

curved reflector are given in figure 2. Data were also input into an excel spreadsheet for

further analysis.

The experiment can be varied by changing the curvature of the reflecting surface.

Changing the composition and reflective properties of the surface will also change the

outcome of the experiment. Try different types of set ups to find the best conditions for

reflecting the hear energy (infrared energy) from the sun onto the test tube. William

Herschel, an astronomer discovered this range of energy from the sun by accident in the

19th century.

QUESTIONS

1. Can you estimate how hot the area in A will get if you know the time of the

experiment? Discuss how you could devise a hot dog cooker that would cook wieners

rapidly and yet not burn them.

2. How much difference in temperature was found for the two containers of water

located at A for the curved surface and for the flat surface?

3. If you reverse the curvature of the surface and compare the temperature produced at

A for the flat surface and the curved surface, how much do you expect the

temperature to change?