Optimization of Thermally Regenerative Electrochemical Cycles in
Galvanic Cells
Zachary Barringer
Alexander Feleo
Macomb Mathematics Science and Technology Center
AP Physics-12A
Mr. Acre, Mrs. Gravel, Mr. McMillan, Mrs. Tallman
17 December 2014
Optimization of Thermally Regenerative Electrochemical Cycles in Galvanic Cells
Industrial and residential processes create large amounts of waste heat, and
harnessing this waste is an appealing way to improve sustainability in manufacturing
processes. This experiment examined a method for recuperating wasted thermal energy to
make usable electrical energy by taking advantage of the difference in cell potentials at
different temperatures. The examined process was a cycle of heating galvanic cells,
charging them, and cooling them. This process is called a thermally regenerative
electrochemical cycle (TREC) and can be used to harness low-temperature waste heat.
This experiment examined the effects that the charging temperature, the concentration of
the electrolytes used in the galvanic cells, and the cooling rate after charging had on the
voltage returned during one cycle. These are all factors in either the cells or the cycle that
could affect performance and may be altered by the implementation or construction of
cells used in TRECs. The effects and interaction effects of the variables were determined
and analyzed with a three-factor Design of Experiment. Of the tested variables, only
maximum temperature had a significant effect on the amount of voltage gained by a
TREC. Therefore, when attempting to maximize the energy recaptured by TRECs, only
the temperature to which the cells were heated for charging increased the energy
recuperated by the cycle; none of the other variables had a significant effect.
Table of Contents
Introduction ....................................................................................................................1
Review of Literature ......................................................................................................3
Problem Statement .......................................................................................................14
Experimental Design ....................................................................................................15
Data and Observations .................................................................................................19
Data Analysis and Interpretation .................................................................................25
Conclusion ...................................................................................................................42
Appendix A: Randomization .......................................................................................51
Appendix B: Creation of the Solutions ........................................................................52
Appendix C: Creation of the Galvanic Cell .................................................................53
Appendix D: Sample Calculation ................................................................................55
Works Cited .................................................................................................................56
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Introduction
How many people ever stop to consider how much energy is thrown away on a
daily basis with barely a thought? Energy is an ever-present concern in modern society,
one that captures attention in every part of contemporary life. Vast amounts of research
and resources go toward making and optimizing low energy processes. One possible
solution to the growing energy problem is the recuperation of the energy lost as heat,
primarily in industrial process. Industrial processes, such as steel processing or goods
manufacturing, create large amounts of heat, and this heat almost always released to the
surroundings. This waste heat is an appealing method of powering the infrastructure of
the modern world, improving the efficiency with which society as uses energy.
Almost one third of the energy used in the United States is used in industrial
processes, and of that energy as much as fifty percent of it is lost as waste heat (US.
Department of Energy) (“Pollution? Think Again.”). This energy is discarded primarily
due to the difficulty in transforming low-grade waste heat into usable energy. Heat
generated by manufacturing processes is primarily at low temperatures, so the process to
transform the wasted thermal energy into a form of usable energy is difficult (“Pollution?
Think Again.”). All these facts lead to the logical conclusion that one of the best ways to
improve energy efficiency in the manufacturing process is to determine a method of
reclaiming low temperature heat to be reused.
An experiment was performed to determine what aspects of one such method
could be optimized; the chosen method is known as a thermally regenerative
electrochemical cycle (TREC) (Lee). This cycle involves heating, charging, and cooling a
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battery. A TREC causes a difference in cell potential in batteries when the batteries are
subjugated to different temperatures. In other words, a TREC is a system that can be used
to recover heat at low temperature levels, making a TREC an appealing way to
implement waste heat recuperating technologies in a wide variety of areas. The heat can
be essentially “stored” or transferred in batteries as electrochemical energy by using the
applying the thermal energy while the battery charges. However, this will only happen if
TRECs develop into a practical technology. To develop this relatively new process,
further experimentation with the TREC needs to be conducted. To this end, an
experiment was conducted to determine what effect several factors had on the
performance of TRECs. These factors include the temperature the battery is heated to, the
concentration of the electrolytes in the battery, and the rate at which the battery is cooled.
These factors’ effects were observed by executing several TRECs and examining
the results under the different conditions that controlled the factors stated above. The
observation of the effects and the interaction effects of these factors help society move a
step forward on the path to making heat recuperation a viable energy source for use in the
future. If further research in this area is successful, energy wasted in manufacturing could
continue to fulfill further manufacturing or residential energy needs. This utilization of
waste energy could reduce the overall cost of goods and energy, while at the same time
fulfilling a need for increasingly efficient uses of energy. The examination of the effects
of heating temperature, electrolyte molarity, and cooling rate, is another step toward
satisfying the need for sustainable energy that could be implemented to improve society
as a whole
.
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Review of Literature
Recently, a lot of attention has been given to renewable energy and saving the
Earth. Hundreds of experiments have been conducted to attempt to harness new forms of
power; however, this experiment differs from many others because instead of trying to
discover new ways of producing energy, it attempts to harness energy that has already
been used. The energy attempting to be harnessed, waste heat, would either be lost or
discarded (US. Department of Energy). The harnessing of the waste heat is accomplished
through a cycle of heating, charging, cooling, and discharging batteries. This process is
called a thermally regenerative electrochemical cycle (TREC) (Lee). The TREC results in
a net gain in the charge of the battery: some of the thermal energy present when the
battery is charged is stored as chemical energy, which can then be converted into
electrical energy. After the battery cools, the battery will then release more energy than
was used to charge it initially. To examine the efficiency of this process, certain concepts
must be understood including the electrochemistry of a basic galvanic cell, the
thermogalvanic effect, thermal energy, and the First Law of Thermodynamics.
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Figure 1. Diagram of a TREC
Figure 1 shows a representation of the steps of a TREC. The first step is to heat
the battery to a higher temperature which is generally under 100°C. Once the battery has
reached this desired temperature the battery is charged. After charging is complete, the
batteries are cooled down to a lower temperature, and the battery can be discharged at a
higher voltage since it is at a lower temperature. This energy stored in the battery at the
low temperature is greater than the amount of energy that was stored in the battery prior
to cooling (Chandler).
As the name would suggest, electrochemistry is the study of how chemical
reactions interact with electric current. This field of study often has to do with batteries
and metal oxidation. This experiment will focus on the application of electrochemistry in
batteries. One common type of battery is a galvanic cell. In a galvanic cell, two electrodes
are partially submersed in a solution, and a wire connects the two electrodes. The final
component of a functional galvanic cell is some means for the charge in the entire cell to
remain balanced; this allows the electrons to continue to flow from one electrode to
another, creating an electric current. This is normally accomplished with either a porous
disk that allows ions to flow between the two solutions, or a salt bridge containing a
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different material that will provide the charges need to balance the overall charge in the
cell. The final product is an apparatus that has an electric potential, which can then be
used to do work. The electric potential of any galvanic cell depends upon the material of
the electrodes and can be calculated based off those materials (Zumdahl). However, since
this experiment will not be changing the materials of either electrode, there should not be
any difference between trials of the expected potential for the galvanic cell.
The chemical reaction of a galvanic cell is a finite process: the current will only
flow so long as there electrons present in the solution that is providing them. However, if
a voltage greater than that produced by the galvanic cell is applied opposite the direction
of the spontaneous current, the reaction will happen in reverse. This process will result in
electrons being returned to the solution that would normally provide them (Zumdahl).
This type of electrochemical reaction is known as electrolysis, and is the principle behind
rechargeable batteries. Since the electrons can be returned to the solution that results in
an electric potential, the battery can be made to hold a charge after it has been depleted
one or more times. However, since the process is not entirely reversible, there is some
degradation in the battery as the electrodes corrode. This is the reason rechargeable
batteries eventually lose their ability to hold a charge (Singamsetti).
The chemical reactions that cause the flow of electrons in a galvanic cell are
known as oxidation and reduction reactions. One of the electrodes, the cathode, is the
oxidizing agent, while the other, the anode, is the reduction agent. The overall redox
equation can be split into half reactions for both the oxidation and reduction reactions.
The oxidizing agent undergoes a chemical reaction that causes the electrode to ionize in
the solution and have electrons be removed from the agent. The electrons that are lost
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from the oxidation reaction flow through the wire connecting the two electrodes. The
reduction reaction then gains the electrons that the cathode lost. This reaction would
otherwise occur briefly and be over due to the imbalance of charges if not for the polar
salt bridge that creates electrical neutrality in the cell by providing anions to the anode
and cations to the cathode. The likelihood something would be reduced is given by its
reduction potential (E0), the larger the reduction potential, the more likely that the
substance will be reduced. The reduction potential equation can be reversed and the
reduction potential’s sign reversed in order to get the oxidation potentials. The measure
of the electric potential of a cell can be calculated by taking the sum of the reduction and
oxidation potentials of the electrodes being used in the electrochemical cell (Zumdahl).
The two electrodes that were used in the experiment are Zinc and Copper (II)
strips. These two electrodes were chosen because they are commonly used in the battery
industry (Zumdahl). In addition, the metals are safe enough to use in a laboratory
environment. The Zinc is the reducing agent because it loses electrons through oxidation.
The half-cell reaction of Zinc is
𝑍𝑛 → 𝑍𝑛2− + 2𝑒 −
𝐸 0 = 0.76𝑉
The half reaction of the Copper is
𝐶𝑢2+ + 2𝑒 − → 𝐶𝑢
𝐸 0 = 0.34𝑉
This means that the expected cell potential for this galvanic cell is 0.76 volts plus 0.34
volts, which is a total 1.1 volts. The electrolytes used with these two electrodes are
Copper Sulfate and Zinc Sulfate, but this has no effect on the cell potential.
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Figure 2. Constructed Galvanic Cell
Figure 2 displays a sample galvanic cell such as those that were constructed. In
this cell, the two different electrodes were Copper and Zinc as the cathode and anode
respectively. The bridge connecting the two electrolytes, Copper (II) Sulfate and Zinc
Sulfate, is also labeled. With the correct components for the cell, a voltage can be
achieved by connecting the two electrodes, which completes the circuit. The voltmeter
also in the image reads that the voltage across the cell is 1.10 volts. This reading is in
accordance with what can be expected with having Copper and Zinc electrodes (Averill).
This experiment will measure the electric potential of a galvanic cell before,
during, and after the TREC. Understanding standard electric potential requires an
understanding of electric current. Electric current is created when there is a flow of
charges through a conductor. In the case of batteries, the current is created by the flow of
the electrons between the two electrodes (Singamsetti). Though current is measured as
flowing from the positive terminal (positive electrode) to the negative terminal (negative
electrode), the electrons actually move in the opposite direction. The units for electric
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current are coulombs per second, or an ampere. A coulomb is merely the measure of the
charge of electrical charge something possesses. A joule (J) is the amount of energy
transferred when exerting one newton of force over one meter. Electric potential, or
voltage, is measured in volts (V), or the measure of the potential energy per unit charge;
consequently, one volt equals 1 joule per coulomb (Young). The greater the amount of
voltage a battery has the greater amount of work that can be done by that battery. This is
why different methods of increasing the voltage efficiency are studied extensively.
Discovering and improving ways of producing more voltage would essentially make
more energy, and move towards potentially solving the world’s energy crisis.
Thermal energy is the movement of molecules on an atomic level: the more the
molecules move, the more thermal energy the object has. Warmer objects have more
thermal energy, and cooler objects have less. The temperature of an object is a measure
of the average movement of the particles, or a measure of the average thermal energy of
an object. Heat and temperature are commonly mistaken for being tantamount. However,
temperature is different than heat because the temperature is the measure of the thermal
energy of an object, while heat is the transfer of thermal energy. They are related
concepts, they are not exactly the same (Hilliard). The primary significance of this
distinction is that energy is transferable between states due to the Law of Conservation of
Energy. The Law of Conservation of Energy, or the First Law of Thermodynamics, states
that energy can be neither created nor destroyed; it can only be transferred between forms
(Chemical Thermodynamics). This means that thermal energy can be changed to
electrical or chemical energy, but temperature cannot be changed into other energies
since it is only a measure of energy. However, since heat is an attribute of an object with
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thermal energy, heat can translate to a different type of energy. Temperature is measured
in degrees Celsius (°C) while heat is measured in joules. Since, energy is measured in
joules, it is apparent that temperature is not actually energy while heat is. In summary,
temperature and heat are related, but they also differ; temperature is a measure of thermal
energy, but is not equivalent to thermal energy. The actual transfer of thermal energy
between objects is called heat. When an object loses thermal energy, the energy cannot be
destroyed so it becomes another form of energy, or is released to either another object or
the environment.
One way to produce additional current, and thus more voltage, is to utilize the
phenomena known as the thermogalvanic effect. A difference in temperature between the
electrodes in a galvanic cell produces the thermogalvanic effect. This temperature
difference produces additional current as extra energy is added to the electrons as they
flow between the electrodes. The temperature difference could be created using what
would otherwise be known as waste heat. The heat that would have been lost could be
applied to the galvanic cell creating the temperature difference. Thus, waste heat could be
used to create additional current (Liebhafsky). This follows the principle of the First Law
of Thermodynamics. Since energy is always conserved and never lost, the thermal energy
is transferred into electrochemical energy. This means that the extra electrochemical
energy is created from nothing, since that would be impossible (Chemical
Thermodynamics). The added energy comes from the applied thermal energy which takes
on a new form in the storage process. While this is not what this experiment tests, it does
demonstrate another method waste heat can be used to generate electricity.
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The underlying principle of why there is a gain in electrochemical energy from
the application of heat in a TREC is Gibbs free energy. Gibbs free energy is an extension
of The Second Law of Thermodynamics which states that in an isolated system, an
increase in enthalpy occurs to spontaneous reactions. These spontaneous reactions are
natural processes, thus the universe has constant increase of enthalpy due to nature
(“Chemical Thermodynamics”). Gibbs free energy can be used to determine whether or
not a reaction is spontaneous. This can be done since Gibbs free energy is the amount of
energy that can be used for work by a chemical reaction (“Gibbs Free Energy”).
Furthermore, the change in voltage of a cell is directly proportional to the amount of
Gibbs free energy in the system. When Gibbs free energy decreases so does the change in
the electrical potential of the cell (“Chapter 10 Notes”). The converse is also true; as
Gibbs free energy increases so does the voltage. Temperature causes Gibbs free energy to
inversely change; when temperature increases, Gibbs free energy decreases, and when
temperature decreases, Gibbs free energy increases. Thus, there is a small change in
voltage at a high temperature and a larger change in a voltage at a low temperature.
Therefore, there is a voltage gain while the batteries cool since the Gibbs free energy is
increasing as the temperature is decreasing. This raises the voltage difference between the
half reactions which results in additional voltage in the cell. The added thermal energy
was stored as electrochemical energy since with more energy the electrons can move
more freely in the cells. Since the voltage requires electron transfer between cells,
additional voltage is achieved with an increased transfer of the electrons from the
oxidizing electrode to the reducing electrode (Bandhauer).
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ΔV
ΔT
Figure 3. Temperature vs. Voltage Graph (Cooper)
Figure 3 shows a graph of temperature vs. electric potential. While it is not the
exact graph of how voltage decreases with the increase of temperature of the particular
galvanic cell used in the experiment, it illustrates the effect that temperature has. It can be
seen the voltage steadily decreases as temperature increases. The opposite is also true: if
the temperature decreases the voltage would increase. This can be seen with the arrows
on the graph. The change in temperature (ΔT) results in a gain in voltage (ΔV) so long as
the change of temperature is negative. In other words, when the temperature decreases
instead of increases, the change in voltage would be positive. This is in accordance with
the concept of Gibbs free energy.
The specific heat of a substance is defined as the amount of energy required to
raise the temperature of one gram a substance one degree Celsius. It is measured in joules
per kilogram degree Celsius. Specific heat is an intensive property, meaning that it is
independent of the sample size of the substance. In other words, the specific heat of a
substance remains the same regardless of the mass or volume of the substance (Nave).
This makes a controlled change of the specific heat of a substance impractical without
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actually changing the substance for a different substance, which then changes other
properties. This means that while controlling the specific heat of a cell is impractical, the
cell’s temperature can easily be raised by a uniform amount, reducing possible
discrepancies in the experiment.
One property that can be altered while keeping the same materials is the molarity
of the electrolytes used in the battery. Molarity (M), or concentration, is the number of
moles of a substance per unit volume; it is commonly measured in moles per liter. Since
molarity commonly differs depending on the specific battery, molarity of the solutions is
a common factor that changes in batteries. Having different molarities in different
batteries leads to the possibility that the concentration of the solutions could affect the
performance of a TREC. Changing the molarity of the batteries would not change the
electric potential of the cell so long as the ratio between the two electrolytes is still 1:1
(Friebe). This mean that the molarity could be 3M for both the electrolytes and the
standard electric potential will be the same as the voltage received from electrolytes with
a molarity of 1M. However, once the ratio between electrolytes changes, the voltage that
can be expected from that cell will be different than the standard electric potential. Due to
this, the electrolyte molarity ratio between the Copper (II) Sulfate and Zinc Sulfate in the
constructed galvanic cells will be kept consistent at 1:1.
Concentration has no effect on the specific heat of the solutions since the
solutions are primarily composed of water (Blauch). Therefore, it would have no effect
on the amount of heat required to raise the cells to the desired temperature. However,
heat does affect the solubility of a solution (“Temperature/Pressure”). At higher
temperature, a solution becomes more soluble and the amount of solute that will dissolve
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in the solution increases. This would be a factor if the concentration that is desired is
higher than or near the limits of the solubility of that solution. The addition of heat would
allow the molecules in the electrolytes to dissolve more easily causing the concentration
to increase to a higher level. While a higher level concentration has no effect on the
voltage of the cell, differences in concentrations between the two electrolytes would have
an effect (Zumdahl). Potentially, the addition of heat to the system would alter the
solubility rules of the two solutions causing the molarity ratio to be altered from the
desired 1:1 ratio.
Previous works that explore exploiting waste heat as a means to increase the
efficiency of rechargeable batteries include an article published by researchers from
Massachusetts Institute of Technology and Stanford University. The research examines
the efficiency of TRECs. Using Copper and Copper Hexacyanoferrate electrodes the
experimenters were able to achieve an efficiency of 5.7%. The reason for the use of these
specific materials is that they have “low polarization, high charge capacity, moderate
temperature coefficients, and low specific heat” (Lee). This experiment did not to use
Copper Hexacyanoferrate because it is potentially toxic and difficult to synthesize
(Gheorghiu). While the efficiency is not great, it paves the way for a different way to
utilize waste heat. That article will be expanded upon the work of this experiment by
examining the effects of several variables upon the efficiency of TREC.
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Problem Statement
Problem Statement:
Does change of temperature, rate of cooling, or concentration of the electrolyte
affect the amount of voltage created by TRECs?
Hypothesis:
If a galvanic cell has the greatest change of temperature, the slowest rate of
cooling, and the high concentration, then it will have the largest change in voltage during
a TREC.
Data Measured:
The dependent variable of this experiment is the voltage measured in the cell after
the TREC. This voltage directly corresponds to the amount of power a battery has stored
in it. To find the change in voltage, the voltage will be recorded at two points during the
TREC: immediately before and after the cell is cooled. The independent variables will be
the combination of change in temperature, the speed with which the cell is cooled, and
the concentration of the electrolyte. The change in temperature refers to the change in
temperature of the cell which will be controlled by changing the temperature of the
surroundings to an extreme until the desire temperature is observed. The speed with
which the cell is cooled by controlling the extreme used to cool the battery. The results
will be examined with a three factor design of experiment (DOE). This should reveal
which of the dependent variables affected the outcome and how they interacted.
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Experimental Design
Materials:
2 M Copper Sulfate
(4) 6.5 cm x 18 cm x 8 cm Loaf Pans
2 M Zinc Sulfate
13.8V Lab Power Source
Constructed Galvanic Cells
(8) Alligator Clips
(3) 5 mL Syringes
Multimeter (0.01V)
100 mL Graduated Cylinder
(2) Thermometers (0.1°C)
600mL Beaker
Hotplate
(3) 100 mL Beakers
Water
Procedure:
Safety Note: Be sure to wear goggles and a lab coat and avoid contact with the
chemicals and hot materials
1. Randomize the temperature difference and rate of change of temperature to be used in
each trial (see Appendix A for randomization).
2. Prepare the solutions of Copper Sulfate, Zinc Sulfate, and Potassium Nitrate (see
Appendix B for the creation of the solutions).
3. Set up the galvanic cell, using 2mL of the solutions of Copper Sulfate and Zinc
Sulfate as the electrolyte for the high concentration, 1mL of each solution and 1mL of
water for the medium concentration, and use .5mL of each solution and 1.5mL of
water for the low concentration (see Appendix C for the preparation of the galvanic
cell).
4. Put 2 mL of water in a different cell with a separate syringe. It will be used to
measure the temperature of the cell throughout the trial.
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5. Heat approximately 500 mL water in the 600 mL beaker on the hotplate to
approximately 70°C for the high temperature, 60°C for the moderate temperature, or
50°C for the low temperature, as determined by the randomization.
6. Pour hot water into the loaf pan, filling it so the water level is about 15 mm, and
move the loaf pan to the hotplate. Put the microplate into the water.
7. Put one of the thermometers in the water inside the loaf pan and the other
thermometer in the water placed in the cell to measure the temperature of the cell.
Adjust the temperature of the hotplate to manipulate the temperature of the loaf pan
water to the desired temperature.
8. Once the desired charging high temperature is reached in the galvanic cell, begin to
charge the galvanic cell by using the alligator clips to connect the Copper (II)
electrode to the negative outlet of the lab power source and the Zinc electrode to the
positive side of the lab power source.
9. Charge the cells for 5 minutes. During this time, monitor the temperature of the water
in the cell using the thermometer. Adjust the temperature of the hotplate to maintain
the desired temperature.
10. Disconnect the alligator clips from the galvanic cell after the 5 minutes and measure
the electric potential of the cell by connecting the voltmeter to the two electrodes
while the microplate is still heated.
11. Fill the second loaf pan with water of the temperature appropriate for the trial, as
shown in Table 1 and determined by randomization, and the maximum temperature.
When it has reached the temperature of the surrounding water, move to water in
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another loaf pan of the second temperature if applicable. Once it has reached that
temperature, move it to water of the third and final temperature, if applicable.
Table 1
Cooling Temperatures for the Different Cooling Processes
Max Temperature
70°C
60°C
50°C
High
20°C
20°C
Temperature 1 20°C
Normal
40°C
35°C
Temperature 1 45°C
20°C
20°C
20°C
Temperature 2
Low
47°C
40°C
Temperature 1 53°C
33°C
30°C
Temperature 2 37°C
20°C
20°C
Temperature 3 20°C
12. Record the voltage of the fully cooled galvanic cell using the voltmeter.
13. Disassemble the galvanic cell.
14. Repeat step 2-13 until the remaining trials involving the other concentrations of the
electrolyte, the other temperature differences, and the other cooling rates of the
galvanic cell.
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Diagram:
Lab Power Source
Copper (II) Sulfate
Zinc Sulfate
Voltmeter
Galvanic Cells
Figure 4. Constructed Galvanic Cell in a TREC
Figure 4 shows the cell as its voltage is about to be measured for the after cooling
step. While the electrodes are too small to be seen in this picture, the wells filled with the
Copper (II) can be clearly seen. The Zinc Sulfate is clear like water making it hard to see,
but it is in the adjacent wells to the Copper (II) Sulfate as shown. To measure the voltage
in one of the cells, the probes on the voltmeter would be touched to the two electrodes.
The cells are in the coolest water when the voltage is measured. For this particular trial,
two separate water baths were used to cool the cell making this a standard trial. The
voltage achieved after the cooling process is complete is the final voltage for that trial.
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Data and Observations
Table 2
First Standard Trial Data
Standard
Concentration
1M
Voltage
Before
Cooling (V)
1.16
Voltage After
Cooling (V)
1.172
Difference
in Voltage
(V)
0.012
Table 2 shows the before and after cooling temperature, and the difference
between the two, of the first trial conducted with standard values.
Table 3
High Temperature and Fast Rate of Cooling Data
High Temperature, Fast
Cooling
Difference
Concentration
in Voltage
Voltage
Voltage After
(V)
Before
Cooling (V)
Cooling (V)
2M
1.225
1.253
0.028
2M
1.228
1.262
0.034
.5 M
1.228
1.255
0.027
.5 M
1.238
1.262
0.024
Average
Voltage
(V)
0.031
0.026
Table 3 shows the data collected for the microplate treated at the high temperature
of 70°C and at the fastest cooling rate. It also shows the difference between the measured
values and the average of the differences for each molarity.
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Table 4
High Temperature and Slow Rate of Cooling Data
High Temperature, Slow
Cooling
Difference
Concentration
in Voltage
Voltage
Voltage After
(V)
Before
Cooling (V)
Cooling (V)
2M
1.286
1.319
0.033
2M
1.295
1.32
0.025
.5 M
1.254
1.3
0.046
.5 M
1.22
1.278
0.058
Average
Voltage
(V)
0.029
0.052
Table 4 shows the data collected when the microplate was treated at the high
temperature and the slow cooling rate. This table also shows the difference in the two
values and the average of the two differences.
Table 5
Second Standard Trial Data
Standard
Concentration
1M
1M
Voltage
Before
Cooling (V)
1.295
1.259
Voltage After
Cooling (V)
1.297
1.265
Difference
in Voltage
(V)
Average
Voltage
(V)
0.002
0.006
0.004
Table 5 shows the voltage and the difference in voltage for the second trial run
with standard values. It also shows the average of the two differences.
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Table 6
Low Temperature and Fast Rate of Cooling Data
Low Temperature, Fast Cooling
Voltage
Concentration
Voltage After
Before
Cooling (V)
Cooling (V)
2M
1.286
1.305
2M
1.279
1.296
.5 M
1.26
1.285
.5 M
1.256
1.265
Difference
in Voltage
(V)
0.019
0.017
0.025
0.009
Average
Voltage
(V)
0.018
0.017
Table 6 shows the results of the trial treated with the low temperature and fast
cooling. It also shows the difference in the voltage before and after cooling along with the
average of the two differences.
Table 7
Low Temperature and Slow Rate of Cooling Data
Low Temperature, Slow
Cooling
Difference
Concentration
in Voltage
Voltage
Voltage After
(V)
Before
Cooling (V)
Cooling (V)
2M
1.275
1.288
0.013
2M
1.262
1.303
0.041
.5 M
1.262
1.249
-0.013
.5 M
1.247
1.225
-0.022
Average
Voltage
(V)
0.027
-0.018
Table 7 shows the results from the microplate treated with a low temperature and
a slow rate of cooling, along with the differences between after cooling and before
cooling, and the average of the differences.
21
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Table 8
Third Standard Trial Data
Standard
Concentration
1M
1M
Voltage
Before
Cooling (V)
1.345
1.321
Voltage After
Cooling (V)
1.353
1.325
Difference
in Voltage
(V)
0.008
0.004
Average
Voltage
(V)
0.006
Table 8 shows the before and after cooling temperature, and the difference
between the two, of the third and final trial conducted with standard values.
The difference in voltage for each trial was calculated as shown below
∆𝑉 = 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝐴𝑓𝑡𝑒𝑟 𝐶𝑜𝑜𝑙𝑖𝑛𝑔 − 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝐵𝑒𝑓𝑜𝑟𝑒 𝐶𝑜𝑜𝑙𝑖𝑛𝑔
The voltage before and after cooling is measured with a voltmeter. A sample
calculation for change in voltage can be found in Appendix D.
Figure 5. Cell during Charging with Heat
Figure 5 shows a microplate containing multiple galvanic cells being heated
through the use of a water bath on the hot plate. In this instance, the heat is turned down
22
Barringer-Feleo
on the hot plate in order for constant temperature to be maintained at which the cells were
charged at. The alligator clips in the picture were connected to the lab power source.
Thus, the cells seen in the picture were in the midst of the five minute charging period.
The temperature at which the cells charged at varied depending on the particular trial.
Once the five minutes for charging had passed, the voltage for each individual cell was
measured.
Figure 6. Cell during Cooling Process
Figure 6 shows a picture of the galvanic cell being cooled down to the final
temperature. The microplate was transferred between the separate water baths through the
use of aluminum foil. Each water bath had a different temperature, allowing for the
cooling of the cells to be done in a few steps. In this trial the cells were cooled in two
steps. The final water bath, the one that the microplate was in, contained the colder water
that brought the temperature of the cells to the desired minimum temperature of 20°C.
The temperature was monitored through the use of an electronic thermometer that was
placed in one of the extra wells that contained water in order to determine the
temperature of the solutions in the wells of the microplate without having to disrupt the
23
Barringer-Feleo
electrolytes in the cells. Once the temperature across the microplate was 20°C, the
voltage of all the cells was taken.
Table 9
Average Change in Voltage for Each Combination of Variables
High
Trial Concentration
Rate of Cooling
Temperature
1
Standard
Standard
Standard
7
+
+
+
9
+
+
2
+
+
4
+
6
Standard
Standard
Standard
8
+
+
10
+
3
+
5
11
Standard
Standard
Standard
Average Change in Voltage
(V)
0.012
0.031
0.018
0.029
0.027
0.004
0.026
0.017
0.052
-0.018
0.006
Table 9 shows the average difference in voltage for each set of variables, and the
order the trials were conducted in. Trials two and three were conducted together, as were
four and five, seven and eight, and nine and ten. This was because the only different
variable was concentration so the trial could be conducted on the same microplate with
the same heating and cooling process.
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Table 10
Observations Made During the Experiment
Trial Observations
Had one slightly warped microplate. Used flat one for standard trial,
1
but it heated too high and had to be cooled with water. One of the
wells was swamped and we only got one data point from those trials.
Moved solutions to the middle cells of the microplate to avoid
2,3
swamping. Planned to use the warped plate for the high heat trials.
Electrodes added after the plate was put into the water.
Mixed new solutions to use as electrolytes in subsequent trials. Used a
4,5
different sheet of Copper to make the Copper electrodes. The new
Copper was slightly thicker.
The cell cooled slightly during charging and was reheated to its goal
6
temperature during the charging process. The Copper electrodes were
changed back to the original Copper used.
This plate was left to sit overnight after it was prepared the day
before. The solutions in the microplates were stirred before the trial
7,8
was conducted. The salt bridges were added after the plate started
heating.
The wells seemed to be filled different amounts despite re-measuring;
9,10
attributed to the warping of the plastic. No effect on capacity. Some of
the electrodes were slightly longer due to availability.
This plate seemed to take longer to heat up and cool down. Noticed a
11
small amount of black precipitate on the Zinc electrode that came into
contact with the salt bridge.
Table 10 show observations made by the researchers during the course of the
trials. They are grouped by microplate, so the trials that were conducted together are
listed together.
25
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Data Analysis and Interpretation
Since this experiment is attempting to discern the effect that several variables
have on voltage, a Design of Experiment (DOE) was used to analyze the data. A DOE
highlights both the effect that the individual variables and the interactions between the
tested variables had on the results of the trials. This experiment examined the effect that
maximum temperature, rate of cooling, and the concentration of the solution had on the
amount of voltage gained by a battery in a TREC. This was examined by finding the
difference in voltage at two points in a TREC: before and after cooling. To ensure that
this data was valid, the order of the trials was randomized (see Appendix A). This helped
to ensure that any gradual change in how the experiment was conducted throughout the
trial had as little impact as possible. Additionally, the difference in voltage was measured
in two separate cells treated at the same time and the two values were averaged together
to be analyzed. This helped ensure that the results were based on the tested attributes, not
the small differences in individual cells. With these protocols it can be assured that a
statistical analysis can be performed on the data with reasonable results.
In order to examine the effect the variables had, high, low, and standard values for
each of the variables had to be set. The values used in this experiment are shown in Table
11 below;
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Table 11
The Values of the Variables
Concentration (M)
Rate of Cooling
2
1
.5
One Step
Two Steps
Three Steps
High(+)
Standard
Low(-)
High
Temperature (°C)
70
60
50
Table 11 displays the different variables that were tested in the experiment and
each of the values that the variables were tested at. The concentration is the concentration
of solution used for each electrolyte. The high temperature is the temperature to which
the cell was heated and then charged at. The rate of cooling was controlled by cooling the
cell in a series of warm water baths. Using more baths resulted in a slower cooling time
and using fewer resulted in faster cooling time, allowing rate of cooling to be easily
controlled. The temperature for each hot water bath varied with the maximum
temperature of the water, as shown in Table 12 below.
Table 12
Cooling Rate Temperatures Relative to Maximum Temperature
Max Temperature (°C)
70
60
50
High
Temperature 1 (°C)
Normal
Temperature 1 (°C)
Temperature 2 (°C)
Low
Temperature 1 (°C)
Temperature 2 (°C)
Temperature 3 (°C)
20
20
20
45
20
40
20
35
20
53
37
20
47
33
20
40
30
20
Table 12 shows the values used to cool the cell based on the rate of cooling and
the maximum temperature. For example, if a trial uses 50°C as the maximum temperature
27
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and three step cooling then it uses three water baths set at 40°C, 30°C, and 20°C to cool
the cell to the final temperature which was always 20°C.
0.04
0.035
Δ in Voltage (V)
0.03
0.025
0.02
0.015
0.01
0.005
0
0
1
2
3
Trials
Figure 7. Dot Plot of Standards
Figure 7 shows the difference in voltage measured for each of the standard trials.
The results from the standard trials are relatively linear meaning that the data that was
collected in the experiment was consistent and therefore valid. If the standards were not
close together in the values that were produced, the data would not have been precise.
Therefore, the data would not be valid as the range of standards, which serve as controls,
would be too large. A large range of standards would illustrate that the results from the
trials were not consistent; thus, there would be a trend over time that would cause the
data to be skewed. This is not case as the standard trials have a small range, 0.008 volts.
There is a data point that stands out from the others, and that was the first standard trial.
For that particular trial, there was no second cell to average the first with, leaving the
possibility that difference in that particular individual cell could have affected the result
of the trial. Without a second cell to average, the possibility of the error in the cell cannot
28
Barringer-Feleo
be ignored. However, since the data still appears to have a small range, it can be assumed
that the data that was collected still is precise and valid, even with the possibility that the
first trial could have been affected by lurking variables. Though the range of standards is
relatively small, a certain amount of variability is expected due to only three standard
trials being performed. Without a large number of trails to ensure that the data would
become normal over time, variability can be expected in the data. This variability could
account for the larger change in voltage that was achieved in the first standard trial.
While the data can be assumed to be valid and precise, caution has to be exercised with
interpreting the data since there is not a large amount of trials that were performed.
Table 13
Effect of Cooling Rate
Cooling Rate
(+)
(-)
0.031
0.018
0.029
0.027
0.026
0.017
0.052
-0.018
Average:
0.023 Average: 0.0225
Table 13 shows the results of the trials in which the high and low values of
cooling rate were used. The results are given in the change of voltage from before the
cooling treatment was applied to after the cooling treatment was applied. For each trial,
there were two cells that were constructed and tested upon. The table shows the average
of the two readings per trial. The effect cooling rate has on the voltage gain of the cell
can be calculated by subtracting the average of the trials in which the low cooling rate
was used from the average of the trials in which the high cooling rate was used. Once this
is performed, the effect of cooling rate is found to be 0.0005 voltage gain. In other words,
on average as the cooling rate of the galvanic cell increases (speeds up) the voltage gain
from the thermogalvanic effect increases by 0.0005 volts. This effect is incredibly small
29
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and is essentially 0. When rounded to the three decimal point significant figures, the
effect is 0.001 volts.
0.04
0.035
Δ in Voltage (V)
0.03
0.023
0.025
0.0225
0.02
0.015
0.01
0.005
0
-1
1
Cooling Rate
Figure 8. Effect of Cooling Rate Graph
Figure 8 shows the graph of the effect of cooling rate on voltage difference. The
two data points that are connected are the averages of the high and low values of cooling
treatment. The average of the low values is graphed as -1 on the x-axis and thee average
of the high values is graphed as 1 on the x-axis. This is done because the low values are
assigned the value of -1 while the high values are assigned a value of 1 in the experiment.
The slope of the line segment in the graph shows the effect of cooling rate. As it can be
seen by the near horizontal line, the cooling rate of the trial had a very small effect on the
change in voltage. As cooling goes from slow cooling to rapid cooling, the voltage
difference from after the cooling treatment increased by 0.0005 volts.
30
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Table 14
Effect of Molarity
Molarity
(+)
(-)
0.029
0.027
0.052
-0.018
0.031
0.018
0.026
0.017
Average: 0.02625 Average: 0.01925
Table 14 displays the difference in voltage that was achieved in the trials when
the molarity of the electrolytes was at either the high or low values. As was the case with
Table 13, the averages of the two readings per trial are displayed in the table. In order to
find the effect of molarity, the difference between the average of the trials that included
the high values of molarity and the trials that included the low values of molarity. The
effect of the molarity of the electrolytes is then calculated to be a 0.007 voltage
difference. This means that on average, as the molarity of both the Copper (II) Sulfate
and the Zinc Sulfate increased, the added voltage gain from the heating, charging, and
finally cooling of the cells was 0.007 volts.
31
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0.04
0.035
Δ in Volatge (V)
0.03
0.02625
0.025
0.02
0.01925
0.015
0.01
0.005
0
-1
1
Molarity
Figure 9. Effect of Molarity Graph
Figure 9 is the graph of the effect of the molarity of the solutions on the change in
voltage achieved after the cooling treatment. Again, the average of the low values is
graphed as having an x-value of -1 and the average of the high values is graphed as
having an x-value of 1. The positive slope of the graph indicates that as the molarity
increased, so did the change in voltage of the galvanic cells. However, the slope is not
steep illustrating that the effect molarity has is not large. Both of these facts are proved
by the actual calculated effect which is 0.007 volts.
Table 15
Effect of Temperature
Temperature
(+)
(-)
0.031
0.029
0.027
0.026
0.052
-0.018
Average: 0.0345 Average:
0.018
0.017
0.011
Table 15 displays the change in voltage after the cooling treatment was applied in
the cells with both the high value of temperature and the low value of temperature. The
temperature in this instance is the temperature that the cells were heated to before
32
Barringer-Feleo
charging began. Two cells were constructed in the microplate wells, allowing for two
cells to be heated to the same temperature at the same time. The average change in
voltage of the two is shown in Table 15. The calculation that can be used to find the
effect of the high temperature is to merely subtract the average of the low values from the
average of the high values. After this calculation is performed the effect that the different
temperatures had on the gain of voltage is 0.0235 volts.
0.04
0.0345
0.035
Δ in Voltage (V)
0.03
0.025
0.02
0.015
0.011
0.01
0.005
0
-1
1
Temperature
Figure 10. Effect of Temperature Graph
Figure 10 shows the line segment that models the effect of temperature on the
voltage difference. In this graph, the steep, positive slope from the average of the low
values of temperature to the average of the high temperature indicates that temperature
had a strong positive effect on the gain in voltage. This is reinforced by the calculated
effect temperature has of a 0.0235 difference in voltage. On average as the value of
temperature the cells are increased, the amount of voltage gain through the
thermogalvanic effect is also increased by 0.0235 volts.
33
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Table 16
Interaction of Cooling Rate and Molarity
(+) Cooling Rate
(+) Solid
Line
0.031 0.018 Average:
0.0245 0.029
(-) Dashed
Line
0.026 0.017 Average: 0.02125 0.052
(-) Cooling Rate
0.027 Average:
0.028
-0.018 Average:
0.017
Table 16 shows the interaction between the cooling rate of the cells and the
molarity of the electrolytes of the cells. The data that is shown is based on the values of
cooling rate and the molarity of the trails. For instance, 0.031 is the average of the
voltage difference that was received from the two cells when both the cooling rate and
the molarity were high. The average of the combination of the two values of cooling rate
and molarity are also shown in the table as these will be used to calculate the interaction
effect between these two variables.
34
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0.04
0.035
Δ in Voltage (V)
0.028
0.017
0.03
0.025
0.0245
0.02
0.0215
0.015
0.01
0.005
0
-1
1
Molarity
Figure 11. Interaction of Cooling Rate and Molarity Graph
Figure 11 shows the graph of the interaction between the cooling rate and the
molarity used in the trials. The slopes of the two line segments are nearly parallel
implying that there is a small chance of an interaction between the two variables. To have
a possible interaction between cooling rate and molarity, the differences in the slopes
would be much greater. The small chance of an interaction effect is proved by the
interaction effect between cooling rate and molarity which is found to be -0.004 volts.
This effect is found by subtracting the slope of the low values of cooling rate (the dashed
line segment) from the slope of the high values of cooling rate (the solid line segment).
Even though only small voltage gains were measured in the experiment, this interaction is
still miniscule.
35
Barringer-Feleo
Table 17
Interaction of Molarity and Temperature
(+) Molarity
(+) Solid
Line
0.031 0.029 Average:
(-) Dashed
Line
0.027 0.018 Average:
(-) Molarity
0.03
0.026 0.052 Average:
0.039
0.0225
-0.018 0.017 Average:
-0.0005
Table 17 shows the interaction of molarity and temperature on the change in
voltage from the TREC. The data shown in the table is the average of the trials of the
different combinations of the molarity and temperature values. The solid and dashed line
in the table is the high and low values of temperature. The data in this table can be used
to find the interaction effect of the two variables by calculating the slope of the line
segments that would appear if the averages were graphed. To calculate the slope using
this table, subtract the average of when molarity is low from the average of when
molarity is high and then divide that difference by two. This can be done for both the
solid and dashed line segments. Finally, the difference between the slope of the solid line
(or when temperature is high) and the slope of the dashed line (when temperature is low)
can be taken to find the interaction effect of temperature and molarity on the difference in
voltage. When all of this is done, the effect is found to be -0.016 volts.
36
Barringer-Feleo
0.039
0.04
0.035
0.030
0.03
Δ in Voltage (V)
0.025
0.0225
0.02
0.015
0.01
0.005
-0.0005
-1
0
-0.005
Temperature
1
Figure 12. Interaction of Molarity and Temperature Graph
Figure 12 shows the graphed line segments of the interaction between the
molarities of the solutions and the charging temperature of the cells. The difference in the
slopes is much greater than the difference in slopes for the interaction effect of cooling
rate and molarity. Since one of the slopes is positive and one of the slopes is negative, the
resulting interaction effect will be negative due to the fact that the negative slope is
smaller than the positive slope. It is inferred from the graph that the interaction effect is a
larger negative slope. This is confirmed when the interaction effect is found by
subtracting the slope of the dashed line (which is positive) from the slope from the slope
of the solid line (which is negative). Thus, the interaction of the values of molarity and
temperature on the voltage gain from subjecting the cells to the procedure is found to be 0.016 volts. This effect along with the graph showing line segments that are not parallel,
suggests that there is a possible interaction between these two variables.
37
Barringer-Feleo
Table 18
Interaction of Cooling Rate and Temperature
(+) Cooling Rate
(+) Solid
Line
0.031
0.026 Average:
(-) Dashed
Line
0.018
0.017 Average:
(-) Cooling Rate
0.0285 0.029
0.052 Average:
0.0405
0.0175 0.027
-0.018 Average:
0.0045
Table 18 shows the trials in which certain combinations of cooling rate and
temperature and the voltage difference caused by the heating and subsequent cooling of
the galvanic cells. In this table, the solid and dashed lines represent the variable
temperature and the different values that were used. The averages of the interactions are
also shown in the table. For example, when both temperature and cooling rate were low,
the average of the two trials (because two different molarities were used) was 0.0045
volts. These averages are used as the end points of the segments whose slopes allow for
the calculation of the interaction effect of the two variables.
38
Barringer-Feleo
0.0405
0.04
0.035
Δ in Voltage (V)
0.03
0.0285
0.025
0.02
0.0175
0.015
0.01
0.0045
0.005
0
-1
1
Temperature
Figure 13. Interaction Cooling Rate and Temperature Graph
Figure 13 shows the graph of the interaction of the rate of cooling and the
temperature on the voltage gain from the process of implementing a TREC on the
galvanic cells. The graph portrays that there is a good chance of the possibility of an
interaction between cooling rate and temperature because the lines are not parallel. The
dashed line segment’s slope is larger than the solid line segment’s slope, thus it can be
deduced that the interaction will be negative since the slope method of calculating the
effect is by subtracting the slope of the dashed line segment from the slope of the solid
line segment. The interaction effect between the cooling rate that was used in the TREC
and the temperature that the cells were charged at was -0.0125 volts.
A prediction of what the theoretical voltage difference before and after the
cooling treatment can be made by using a prediction equation. A prediction equation uses
the effects of all the variables and the interactions between those variable to produce an
unbiased estimation of a regression line that would fit the data. This provides the means
to make predictions on what the voltage gain would be from the thermogalvanic effect
39
Barringer-Feleo
when using certain values of the cooling rate, molarity of the electrolytes, and high
temperature. The prediction equation that can be formed reads that ŷ (the unbiased
estimator) is equal to the grand average of all the trials plus one half of effects of the
variables and their interactions. Therefore, the equation reads one half of the effect of
cooling rate multiplied by the variable “c” for cooling rate, plus the effect of molarity
multiplied by the variable “m” for molarity, plus the effect of temperature multiplied by
the variable “t” for temperature, plus the interaction effect of cooling rate and molarity
multiplied by the variable “cm” which is the values of both cooling rate and molarity,
plus the interaction effect of molarity and temperature multiplied by the variable “mt”
which is the values of both molarity and temperature, and plus the interaction effect of
cooling rate and temperature multiplied by the variable “ct” which is both the values of
cooling rate and temperature. In addition to the grand average and effects, noise is added
to the prediction equation to take into account lurking variables.
The resulting prediction equation is shown below;
ŷ = 0.019 + 1/2(0.0005 ∗ 𝑐 + 0.007 ∗ 𝑚 + 0.02325 ∗ 𝑡 − 0.004 ∗ 𝑐𝑚 − 0.016 ∗ 𝑚𝑡
− 0.0125 ∗ 𝑐𝑡) + 𝑛𝑜𝑖𝑠𝑒
Although the prediction equation takes every effect into account while making
predictions, not all the effects are significant and needed while making predictions. A
more concise prediction equation would only include the few effects that caused a
significant change in the voltage difference; this type of prediction equation is called the
parsimonious prediction equation. In order to decide what effects can be deemed
significant in terms of the voltage difference they cause, a significance test can be
performed. The test of significance is calculated by finding the range of the standards and
40
Barringer-Feleo
multiplying it by two. Anything larger than twice the range of standards is large enough
to be considered significance. A visual of this is provided by the dot plot of all the effects
-0.02
-0.01
0
Temperature
Cooling Rate
Molarity
Cooling Rate and Molarity
Cooling Rate and Temperature
Molarity and Temperature
which can be seen in Figure 14 below.
0.01
0.02
0.03
Effects
Figure 14. Dot Plot of Effects
Figure 14 is the dot plot with all the individual effects of the variables along with
their interaction effects. The black lines are graphed at twice the range of standards, thus
it marks the significance test of the effects. The range of standards was found to be 0.008;
therefore, the line is plotted at the value of 0.016 along with the value of -0.016. Any
effect outside the line with a larger absolute value would be significant; conversely,
anything inside the black lines would be insignificant due to the fact that the effect would
be too small. By looking at the plot of the effects it can be seen that there is only one
effect whose effect on the voltage gain from the thermogalvanic cell is large enough to be
considered significant. This effect is the effect of temperature. The rest of the effects are
too small to be included in the parsimonious equation. The interaction effect between
molarity and temperature was on borderline to being significant since it has an effect of -
41
Barringer-Feleo
0.016 volts which is the exact same as the test of significance. It was determined that
while the interaction effect played the second largest role and was the same as the
significance test, the interaction effect was ultimately insignificant due to rounding.
When the unrounded interaction effect was found, it was found that the interaction effect
was -0.01575. This number is smaller than the significance test; therefore, while the
effect was on borderline being significant, the interaction between molarity and
temperature was deemed to be insignificant.
Now that the test of significance has filtered out the significant effects from the
insignificant effects, a parsimonious prediction equation can be formed using only the
remaining effects. The estimator, ŷ, is now equal to the grand average plus one half the
effect of temperature which is multiplied by the variable “t” again for the value of the
temperature that is being used. As with the regular prediction equation, the variable noise
is added to the overall parsimonious prediction equation to account for any outside,
lurking variables. The new parsimonious prediction equation is shown below;
ŷ = 0.018545 + 1/2(0.02325 ∗ 𝑡) + 𝑛𝑜𝑖𝑠𝑒
42
Barringer-Feleo
Conclusion
This experiment examined the effect that traits of galvanic cells used in Thermally
Regenerative Electrochemical Cycles (TRECs) could have on the efficiency of TRECs as
a method of recuperating thermal energy. The experiment examined the effect change in
temperature, concentration of the electrolytes used in the galvanic cell, and the rate at
which the cell was cooled had on the change in the electrical potential of a cell during a
TREC. This was done by running several TRECs, varying the tested factors each time,
and comparing the change in the electric potential of the cell before and after cooling.
Since this was done, a Design of Experiment (DOE) was setup and performed in order to
analyze the data to see what variables had significant effects and if any of the interactions
between the variables were significant.
It was hypothesized that a large temperature change, slow change in temperature,
and high concentration would have the largest change in potential of the cell. This
hypothesis was rejected due to the fact that the actual largest change in voltage that was
achieved in trials came from the trials in which a large change in temperature, slow
change in temperature, and low concentration was used. This change in the voltage across
the cell was 0.052 volts, much larger than the change that the trials that the hypothesis
predicted would be the most significant which was a mere 0.029 volts. Thus, there is no
evidence to support that a TREC using a cell with high concentrations, and using a slow
rate of cooling and high maximum temperature would consistently produce the largest
change in electric potential. The hypothesized largest gain in voltage was neither the
maximum nor the minimum voltage gain achieved since it was the third highest value
achieved by the TREC. The second highest value was 0.031 volts which was when
43
Barringer-Feleo
cooling rate, temperature, and molarity were all at their high values. The minimum
voltage gain that was recorded was -0.018 volts, and this occurred when the molarity,
cooling rate, and temperature were all low. Since a TREC is supposed to give a positive
voltage increase, achieving a negative increase would indicate that those specific trials
were performed incorrectly. It is impractical that instead of gaining additional voltage
from heating the batteries, voltage was actually lost during the process; thus, the question
of the legitimacy of those trials is raised. However, the other trial being performed
simultaneously inside the same microplate yielded a positive net voltage gain, so the
cycle which worked on half the cells failed to work on the other half of the cells. It was
concluded that the measuring process was flawed since the conditions could be at fault
since the other cells had an increase.
Through the use of the DOE and the significance test, it was found that only the
high temperature that the cells were charged at had a significant effect. Neither the rate at
which the temperature changed to cool the cell nor the concentration of the electrolytes
had significant effects on the change in potential of the cell. All of the interactions
between the three variables were also found to be insignificant on the voltage gain from a
TREC. However, there was a slight interaction effect between temperature and
concentration. Even though it was not deemed significant through the use of the
significance test, it was very close to being significant when rounded for significant
figures. In fact, when rounded, the interaction effect was exactly the same as the test of
significance, -0.016 volts. However, when unrounded numbers were used to calculate the
interaction effect, it was found that it was 0.00025 volts from being significant, an
incredibly small margin, but a margin nevertheless. Because of the margin, it was deemed
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insignificant, but the interaction being so close to becoming significant raises the
question on whether or not that the effect could be proven significant with further
experimentation.
This result is compatible with accepted science for several reasons. First, one of
the two principles that drive TRECs, the Law of Conservation of Energy, says that the
change in electric potential during TRECs comes from energy in the form of heat in the
surrounding environment. It therefore makes sense that a greater change in electrical
energy would be observed if there is a larger amount of thermal energy in the
surroundings. The greater energy in the surroundings translates to a greater change in the
energy of the system, but due to the process of charging, the energy is in the form of
electric potential rather than heat energy.
The second principle that drives TRECs is the extension of the Second Law of
thermodynamics, Gibbs free energy. The Second Law of Thermodynamics states that in
an isolated system, the natural order of a process is spontaneous when it leads to in an
increase in disorder. In other words, all natural processes lead to an increase of entropy
("Chemical Thermodynamics"). To calculate if a reaction is spontaneous or
nonspontaneous, the Gibbs free energy of the system can be found. This is because the
Gibbs free energy is the measure of energy associated with a chemical reaction that can
be used for work ("Gibbs Free Energy"). Gibbs free energy is directly proportional to the
change of voltage in a cell. As temperature increases, the amount of Gibbs Free Energy
decreases which in turn decreases the change in the electric potential ("Chapter 10
Notes"). As the temperature of the galvanic cells decreases, the change in voltage
increases because the amount of Gibbs free energy increases. This is what results in the
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voltage gain after the cooling off the cells. The larger the temperature changes the more
the Gibbs free energy changes, which in turn changes the voltage by a larger amount. The
thermal energy is absorbed by the cell and stored as electrochemical energy. The added
energy from the thermal energy makes it easier for the electrons to separate from the
oxidizing agent, the Zinc, and move towards the reducing agent, the Copper. This
additional transfer of electrons is responsible for the increased voltage since the voltage
in an electrochemical cell comes from the transfer of electrons between the two
electrodes. This is again, in accordance with the Law of Conservation of Energy as the
thermal energy is transformed into additional electrical energy.
Additionally, the rate at which the cells cooled did not have a large effect since
the change in energy is the same between any two heats regardless of how rapidly the
energy changes between observations, so long as it changes the same amount each time.
Alternatively, it could be that the electrical energy a TREC gains is gained during the
charging process, when the temperature is constant. If this is the case, then there is no
way the rate of change of temperature could affect the voltage of the cell, since it occurs
after the charging process has ended. To ascertain which of the reasons is the true reason
rate of change of change of temperature has little effect on the change in potential of
galvanic cells during TRECS would require further experimentation. Further experiments
can focus on the interaction between temperature and concentration. One such
experiment could have smaller increments at which the molarity increase per trial to
observe that the large jumps in molarity had no part in the voltage gain. In addition to
subjugating these different molarities of the same two electrolytes to different levels of
thermal energy, different substances with different molarities could be used for the
46
Barringer-Feleo
electrolytes. Furthermore, research into the solubility of the electrolytes could explain
whether changing the solubility of the solutions, and therefore the amount dissolved, has
an actual effect on the results of a TREC. Even different molarity ratios could be
experimented with to see how a skewed ratio would affect the net voltage gain.
Finally, concentration does not change the potential of galvanic cells, the specific
heat of most solutions, or the ability of a galvanic cell to be charged. Since the
concentration of the solution has so little effect on the cell, it is reasonable to conclude
that it does not significantly affect TRECs. Despite this, there was a slight interaction
effect between temperature and concentration. There are several potential reasons for
this. Foremost among these reasons is that there is that the solubility of a material
changes with heat (“Temperature/Pressure”). The concentrations chosen for this
experiment were too high for the solute to completely dissolve in the water. This error
was deemed insignificant, as explained below, but since more solute was dissolved at
higher temperatures, it could have shown more of the effect of concentration when it was
at a higher temperature.
As mentioned above, the concentrations chosen for the extremes of concentration
were too large, resulting in solutions that were not the desired concentrations that should
have been used for the trials. This problem mainly occurred with the Copper (II) Sulfate.
However, since the solutions were created from dilutions from one central solution of a
consistent concentration, the concentrations were consistent, and the same proportions
relative to each other. Additionally, there was a very noticeable difference in the hue of
the different concentrations of Copper (II) Sulfate. The solution with the greater molarity
was a much darker blue than the solution with the lower molarity. These reasons indicate
47
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that there was still a significant enough difference in the concentrations of the solutions to
conduct the analysis. The slight interaction between temperature and concentration is
likely due to the change in the amount of solute dissolved in the electrolyte at different
temperatures. This could indicate two things: either there is some effect due to
concentration, or the potential of the cells changed for some reason unrelated to TRECs
due to the change in temperature. While the concentration of the electrolytes does not
affect the cell potential of galvanic cells, differences in concentration between the two
electrolytes in the cell does affect the cell potential (Zumdahl). Therefore, if the change in
solubility of one solution at a higher temperature is greater than the change in solubility
of the other, then the interaction effect is a result of that outside variable, not due to
effects on TRECs. Based on observations made during the experiment, this is the case:
the Copper (II) Sulfate did not dissolve very well at room temperature, but Zinc Sulfate
dissolved almost completely. As the Copper (II) Sulfate was heated to higher
temperatures, it would dissolve more, creating a larger cell potential at a higher
temperature than it would at a lower temperature. It can be therefore concluded that the
slight interaction effect between temperature and concentration is the result of a flaw in
the experimental design, not an indication that there is a flaw in the conclusions of the
experiment.
Other possible errors of this experiment include slightly different high
temperatures, slightly different concentrations, slightly different charging times, and
other flaws in the execution of the experiment. The method devised for this experiment to
heat the galvanic cells was imprecise and inconsistent. Heating the cells through the use
of a hot water bath succeeded in raising the temperature of the galvanic cell to
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approximately the temperature desired, it was difficult for a consistent temperature to be
obtained using the hot plate. Either the temperature would steadily decrease since the hot
plate was not on a high enough setting and heat was lost to the surrounding environment,
or the temperature would continue to climb at a slow rate as the hot plate was on a setting
that was too high. The temperature was closely monitored in order to account for the
changes in temperature, but the temperature still fluctuated with a range near the desired
temperature. The possible error in different concentrations came from the Copper (II)
Sulfate not dissolving completely in the desired amounts as was previously stated.
Furthermore, the tools used to transfer the electrolytes to the micro plate and dilute the
concentrations had a very limited precision. Human error could have caused the
measurements of the dilution of the electrolytes to be off. The differences would have
been too miniscule to have an important effect on the TREC. The time that the cells were
charging also was not consistent at the time that the cells were supposed to charge at. The
amount of time that the cells were charged at was occasionally slightly too long by a few
seconds as the researchers were attempting to set up the second micro plate. In addition,
by the time all of the alligator clips were disconnected from all of the electrodes, some of
the cells were charged longer than other. This additional charge only came from a few
seconds more charge which was deemed small enough to have a negligible effect on the
charge of the cells. A few seconds in comparison to 5 minutes is a small amount. All of
these flaws are likely not significant because they affect each trial relatively equally,
including the standard trials, and the trials were randomized so errors would not form
trends in the data that did not exist.
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There are ample opportunities for further research in this area. Examples of
further research include examining methods for recuperating heat for use in TRECs,
examining different variables within the system or it surroundings, and examining the
efficiency of TRECs on a larger scale. Additional research could also focus on mitigating
the errors of this experiment, such as that of the concentration of Copper (II) Sulfate. The
Copper (II) Sulfate was unable to properly dissolve in the high molarity that was
required, so having a smaller molarity would allow for more valid results since it would
avoid the complications of having a solution that was settling. A smaller high molarity
may also prove or disprove the significance of the interaction between molarity and
temperature. Future research could even discover a way to industrialize the TRECs to
recuperate heat to produce usable energy on industrial scale on which it would have the
largest effect. A TREC would have to be performed on the industrial batteries to
determine how the cycle would perform on a scale that is not miniaturized in a
laboratory. Implementing a TREC in several factories and observing the performance
would reveal the current efficiency of the cycle and what factors would need to be
researched more extensively. In addition, a process that takes the heat that the cooling
batteries loses and uses that lost heat to begin heating the next battery, creating a heat
engine, could be devised to further recycle the heat improving the efficiency of the
process of the actual heating of the cells. Any of these are feasible ways to further
humanity’s knowledge of heat recuperation.
These results that were achieved could be applied to the creation of batteries for
the use of a TREC by knowing that the molarity of the electrolytes of the batteries would
not matter on the resulting gain. To achieve the best results by altering the attributes of
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the cycle, a high temperature is the most significant. The speed at which the batteries cool
can be largely ignored as it has little or no effect on the voltage gain. This means that the
batteries can be left to cool slowly without any extra applied treatment. Without the need
for a cooling treatment, the energy that would have otherwise been used to cool the
batteries rapidly could be saved and used for other applications. All of this information
can be used by the manufacturing companies that would be the most likely to implement
a system in which to utilize the waste heat that is continuously produced by their own
factories. By using the ambient thermal energy pouring out of buildings such as power
plants or factories, heating the batteries to as high as a temperature as possible, the
biggest gain in voltage can be achieved. The molarity of the batteries does not matter, so
the concentrations of the electrolytes in the batteries does not need to be extremely high
allowing for more options and variability in the batteries. Once the batteries are charged
at the high temperature they could be left to cool slowly in order to conserve energy. By
doing so, additional electrical energy can be obtained simply by using the heat that would
have been lost to the surroundings. While the voltage gain is not huge, with only a few
hundredths of volts being gained, it still is source of additional energy that merely
requires the heat that would have been wasted regardless. Gathered over an extended
period of time and with a great number of batteries, this small amount of voltage can
quickly turn into a huge amount. All that needs to be done is to begin implementing this
process in industry while continued research on the optimization of the TREC is
performed to improve the efficiency. By doing so, the energy crisis currently plaguing the
world can be cut back and potentially solved.
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Appendix A: Randomization
This appendix shows the procedure for randomization used in this experiment.
Materials:
TI Nspire CX Graphing Calculator
Procedure:
1. Group the trials according to molarity. This gives three standard trials and four
trials with varying values for high temperature and rate of cooling.
2. Using the random integer function of the TI Nspire to assign numbers to the four
non-standard trials.
3. Execute the trials in the following order: Standard, Randomized 1, Randomized 2,
Standard, Randomized 3, Randomized 4, and Standard.
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Appendix B: Creation of Solutions
This appendix shows the procedure to create the solutions required for the galvanic cells.
Materials:
(100g) Copper (II) Sulfate
Scoopula
(100g) Zinc Sulfate
100mL Graduated Cylinder
(100g) Potassium Nitrate
(3) 250mL Beakers
Scale (0.01g)
Water
(3) Plastic Weight Boats
(3) Glass Stir Rods
Procedure:
Safety Note: Be sure to wear goggles and a lab coat and avoid contact with the
chemicals
1. Place one of the weight boats on the scale and tare the scale.
2. Measure out 25.0 g of the Copper (II) Sulfate using the scoopula by placing it in
the weight boat on the scale.
3. Measure out 50 mL of water using the graduated cylinder and pour it in one of the
beakers.
4. Pour the 25.0 g of the Copper (II) Sulfate into the 50 mL of water in the beaker
and stir using one of the glass stir rods until all of the solution has completely
dissolved.
5. Place the next weight boat on the scale and make sure that the scale is still tared to
the weight of the boat.
6. Scoop 28.8 g of Zinc Sulfate with the scoopula into the weight boat on the scale.
7. Using the graduated cylinder, measure out another 50 mL of water pouring the
water into the next beaker.
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8. Mix the Zinc Sulfate into the water by dumping the Zinc Sulfate into the beaker
of water and using the second glass stir rod to ensure that the entire solution has
dissolved.
9. Using the final weight boat on the tared scale and the scoopula, measure out 10.1
g of Potassium Nitrate.
10. Measure and pour 100 mL of water into the final beaker.
11. Place the Potassium Nitrate into the final beaker and stir using the third glass stir
rod.
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Appendix C: Creation of the Galvanic Cell
Materials:
(1) 2mL Well Microplate
2M Copper (II) Sulfate
(3) 5mL Syringes
2M Zinc Sulfate
(2) Tweezers
Water
12.5mm x 25mm Zinc Electrode
Chromatography Paper
12mm x 25mm Copper Electrode
1M Potassium Nitrate
Procedure:
1. Put 2mL of the electrolyte of the randomized concentration into two adjacent
wells on the microplate using the syringes. A different syringe should be used
each chemical to avoid unwanted mixing of the chemicals. Use the amount of
each sulfate and the amount of water specified in the experimental design.
2. Soak a 5 mm strip of chromatography paper in the Potassium Nitrate solution for
1 minute in order to create the salt bridge.
3. Using the two tweezers, remove the salt bridge and place one end of the strip into
each of the electrolytes connecting the two.
4. Place the Copper electrode into the Copper Sulfate electrolyte.
5. Put the Zinc electrode into the Zinc Sulfate electrolyte.
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Appendix D: Sample Calculations
This appendix will show examples of the calculation performed during the data analysis.
The difference in voltage is found be using the formula
∆𝑉 = 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝐴𝑓𝑡𝑒𝑟 𝐶𝑜𝑜𝑙𝑖𝑛𝑔 − 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝐵𝑒𝑓𝑜𝑟𝑒 𝐶𝑜𝑜𝑙𝑖𝑛𝑔
Where ΔV is the change in voltage. Figure 13 shows a sample calculation of the change
in voltage.
∆𝑉 = 1.319 𝑉 − 1.286 𝑉
∆𝑉 = 0.033 𝑉
Figure 15. Sample Calculation of Change in Voltage.
Figure 15 shows a sample calculation of the change in voltage is measured. The
measured voltage before cooling is subtracted from the voltage that was measured after
the cooling of the cell. In this case, the voltage after cooling was 1.319 volts and the
voltage before cooling is 1.286 volts. Thus, when the difference is found between the two
voltages, the change in voltage was found to be 0.033 volts.
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