PROJECT FINAL REPORT COVER PAGE
GROUP NUMBER R4
PROJECT TITLE Definitive Upgrading of Parr Bomb Calorimeter
DATE SUBMITTED April 29, 2002
ROLE ASSIGNMENTS
ROLE GROUP MEMBER
FACILITATOR……………………….. Neeta Shah
TIME & TASK KEEPER……………… André Ilbawi
SCRIBE………………………………..
Tracy Yuen
PRESENTER…………………………. Joshua Doloff
SUMMARY OF PROJECT
The main objective of this experiment was to quantitatively determine which temperature device among a manually-read mercury thermometer, electronic Labview I
(DMM) thermometer, or Labview II (“Bomb2”) thermometer was most precise and accurate in finding the gross heat of combustion of high purity benzoic acid using the
1341 Parr bomb calorimeter. This was achieved through extensive calibration, statistical analysis of past lab reports, and determination of the heat of combustion values of benzoic acid and the W factor for each calorimeter. Although all the devices yielded results with confidence intervals that included the accepted literature value of 6318 ± 1.0 cal/g, the manually-read mercury thermometer was found to be the most accurate and precise as seen by the -0.153 % percent error and a precision of ± 26. cal/g (0.41 % error), respectively. It was followed by the Labview II thermometer, which had a 0.885
% error with a precision of ± 57 cal/g (0.90% error), and lastly the Labview I with a percent error of 1.651 % and precision of ±118 cal/g (1.83 % error). The W factors found for the mercury thermometer, Labview I, and Labview II were 2430. cal/ o C ± 10 % (95%
Confidence Interval), 2405. cal/ o C ± 25%, and 2387. cal/ o C ± 44%, respectively. These findings were confirmed using the experimentally determined W factors and recalculating the precision of the thermometers. Although the mercury thermometer was found to be the most precise and accurate, considering ease of function, the Labview II is the most efficient yet still within the range of allowable accuracy and precision.

OBJECTIVES:
The primary objective of this experiment was to compare a manually-read mercury thermometer and two electronic thermometers (using Labview I – DMM and
Labview II – “Bomb2” computer programs) and statistically determine which device is most accurate in finding the gross heat of combustion of high purity benzoic acid. In order to accomplish this primary objective, three specific aims were achieved. Our first specific aim was to analyze all raw data obtained in 2001/2002 to statistically determine which device was most accurate (between the electronic Labview II and mercury thermometers). Our second aim was to measure the heat of combustion of high purity benzoic acid using all temperature measuring devices, in order to compare values obtained to the accepted literature value. Finally, our third specific aim was to obtain and compare the W factors (energy equivalent factor) of the Parr bomb calorimeters using the three temperature measuring devices. These values would then be used to re-determine the relative accuracy and precision of the temperature-measuring devices and compared to the initial experimental values.
BACKGROUND :
Benzoic acid (C
6
H
5
COOH), the compound used in the experimental trials, is a white, crystalline, organic compound with a molecular weight of 122.12 g/mol.
1
Classified as a carboxylic acid, benzoic acid is often used as a food preservative, as well as in the manufacture of cosmetics, plastics, dyes, and insect repellent.
2 It is also naturally found in cranberries.
The standard heat of combustion is a precisely defined thermodynamic quantity that represents the amount of energy released when burning the compound completely in
25.0 atmospheres of oxygen at 25˚C (and at 1 atmosphere of pressure- this was the surrounding).
3
The accepted literature value of the standard heat of combustion of high purity benzoic acid is –3228.0 ± 0.5 kJ/mol or –6318 ± 1.0 cal/g.
1
The W factor (energy equivalent factor) given from the Parr Bomb Calorimeter product description 4 was 2426 cal/˚C when used with the corresponding mercury thermometer. No W factors for the two electronic thermometers were given.
APPARATUS AND MATERIALS:
The materials used in this experiment are listed in the BE 210 Spring 2002 lab manual (Experiment 6). In addition to these materials, a negative temperature coefficient thermistor and two LM135 series precision temperature sensors were used with the virtual bench analysis software, Labview I (DMM program) and Labview II (“Bomb2” program). Sucrose pellets were used for calibration trials in order to minimize costs, and later replaced with calorific grade benzoic acid pellets for use in the experimental trials.

METHODS:
Calibration Methods:
CALIBRATION OF TEMPERATURE SENSORS
The four temperature sensors were bound together with duct tape and staggered to ensure that nothing was blocking the mercury bulb of the thermometer and that water was flowing all around the four sensors. Three different types of calibration trials were conducted: steady state, gradual change, and temperature shock.
For the steady-state calibration, all devices were immersed into 5 beakers of water ranging from 22˚C to 27˚C and the temperature-voltage data recorded for 1 minute after equilibrium was reached. The difference in temperature readings was corrected for, using the manually-read mercury thermometer as the primary standard. The temperature read by the electronic program in Celsius was translated from the equation: temperature [ o
C] = slope * voltage output – intercept (see Appendix Figure A3).
For the gradual change calibration, the four temperature sensors were immersed in a beaker of water at equilibrium. The beaker was then placed on a heating plate and the temperature change observed on all devices as it gradually increased. The graph of temperature vs. time was used to determine if there was a lag time in temperature readings.
The temperature shock calibration was used to determine the time constant for each temperature sensor. Two beakers containing water of different temperatures
(temperature difference of ~3.0°C) were prepared. All thermometers were immersed in one beaker and data recorded for one minute (10 readings/sec). After two minutes, the thermometers were quickly transferred to the other beaker of a higher temperature, and data immediately recorded as the temperature rose.
CALORIMETRY
The calorimetry process is essentially the same as that described in the Parr instrument manual. A pressurized oxygen cylinder containing the pure benzoic acid pellets was submerged in a bucket of 2000 grams of water. The bomb was then fired at six minutes and the energy released from the combustion heated the surrounding water.
The virtual bench analysis software was used to continuously record the temperature values for both the thermistor and the two chip sensors. The W factor was then determined using equation: H g
= (tW-e
1
-e
2
-e
3
)/m.
Six trials were performed with an initial temperature near room temperature (20 to
25 degrees). The 95% confidence limits of the W values obtained were then compared to the value given in the product description
4
to see if the W factor given matched the value obtained experimentally using the three temperature measuring devices.

RESULTS:
Mercury
Labview II
Labview I
Summary of Gross Heat of Combustion, H g
: Benzoic Acid
Bomb
Calorimeter
I
II
I
II
I
II
H g
[cal/g]
6308.
6280.
6374.
6381.
6422.
6320.
95 % Confidence
Interval [± cal/g]
Precision
(%)
± 26.
± 52.
0.41
0.82
Accuracy (Percent
Error [%])
-0.153
-0.603
± 57.
± 35.
0.90
0.55
0.885
0.996
± 118.
± 96.
1.83
1.52
1.651
0.027
Average of 3
Thermometers
I
II
6368.
6320.
± 56.
± 47.
0.89
0.75
0.786
0.034
Figure 1 : Summary of average gross heat of combustion, H g
, for all benzoic acid trials using each calorimeter and the mercury thermometer, Labview I, or Labview II software. The data assumes the W factor, the specific heat for the calorimeter, to be 2426 cal/ o C. The 95 % confidence interval for all but one combination included the expected literature value of 6318 cal/g 1 . The precision values were calculated as the range of the confidence interval from the averaged gross heat of combustion for each trial. The accuracy values represent the percent error between the average calculated value and the expected literature value of 6318 cal/g 1 .
Data from 2001/2002 BE 210 Lab Reports:
Hg [cal/g]
Standard Deviation
[cal/g]
95 % Confidence
Interval [cal/g]
Labview II
Mercury
Labview II
Mercury
3949. 53.
3835. 95.
Ratio to Given Value: Hg = 3940.4 cal/g
1.002 0.014
0.973 0.024
27.
40.
0.0069
0.0103
Figure 2 : Summary of gross heat of combustion values of sucrose from 2001 and 2002 BE 210
Lab reports for the electronic Labview II software and the mercury thermometer. The ratio of the average gross heat of combustion to the excepted value yields a value with a confidence interval for the electronic thermometer that includes 1. On the other hand, the confidence interval of the mercury thermometer does not include 1.
Mercury
Labview II
Labview I
Average of 3
Thermometer
Summary of W Factor: Benzoic Acid
Calorimeter
I
II
I
II
I
II
I
II
W (t corr
)
[cal/ o C]
2430
2441
2405
2439
2387
2464
2389
2434
95 % Confidence
Interval [cal/ o C]
± 10.
± 20.
± 25.
± 57.
± 44.
± 120.
± 21.
± 31.
Precision
[%]
0.41
0.82
1.04
2.34
1.84
4.86
0.88
1.27
Accuracy (Percent
Error [%])
-0.16
-0.62
0.87
-0.54
1.61
-1.57
1.53
-0.33
Figure 3 : Summary of W factor for each bomb calorimeter calculated using the expected heat of combustion value (benzoic acid) of 6318 cal/g 1 as the gross heat of combustion for each

calorimeter and the corrected temperature value of t corr
. The mercury thermometer and the two electronic thermometers for both calorimeters have a confidence interval that includes the expected W factor from the product description 4 , 2426 cal / o C. The average of each thermometer
/calorimeter pairing yielded a W factor specified for that apparatus that can be used to recalculate the gross heat of combustion. The precision values were then calculated from the percent of the confidence interval divided by the given average W factor for each set of trials. The accuracy was the percent error from the expected value of 2426 cal / o C 4 .
Recalculated Gross Heat of Combustion based on Specific W Factor for Each
Thermometer/Calorimeter Pairing for Benzoic Acid:
Mercury
Labview II
Labview I
Bomb
Calorimeter H g
[cal/g]
I 6318
II
I
II
I
II
6318
6318
6319
6320
6322
Standard Deviation 95 % Confidence
[cal/g]
± 26
± 46
Interval [cal/g]
± 26
± 52
± 58
± 106
± 118
± 222
± 57
± 120
± 116
± 252
Precision
[%]
0.41
0.82
0.90
1.91
1.83
3.98
Figure 4 : Summary of recalculated gross heat of combustion values of benzoic acid based on corrected W factor. Using the averaged W factor and the corrected temperature change, the gross heat of combustion was calculated assuming that the experimental W factor for each pairing of one thermometer in one calorimeter was the most accurate. In turn, the average gross heat of combustion was reconfigured to be about the given expected value, H g
= 6318 cal/g. The confidence interval was then analyzed for precision. In the end, the mercury thermometer was found to be the most precise, based on the percentage of the calculated value of the confidence interval divided by the gross heat of combustion.
Summary of W factor: SUCROSE
Mercury
H g
[cal/g]
3925.
Labview II 4053.
95%
Confidence
Interval [cal/g]
± 51.
± 195.
± 251.
Accuracy
(Percent
Error [%])
-0.4
2.9
W (t corr
)
[cal/°C]
2417.
2333.
95%
Confidence
Interval [cal/g]
Recalculated
95 % Confidence
Interval [cal/g]
± 72.
± 122.
± 141.
± 121 .
± 208.
± 253. Labview I 4094. 3.9 2313.
Figure 5 : Summary of 5 sucrose trials using bomb calorimeter I. The gross heat of combustion was initially calculated using the given W factor of 2426 cal/ o C. The corresponding 95 % confidence interval and accuracy, calculated by the percent error from the expected value of
3940.4 cal/g 7 , are also tabulated. Using the average W factor for each thermometer in calorimeter I and the corrected temperature change, the gross heat of combustion was recalculated using the experimentally determined W factor. In turn, the average gross heat of combustion was reconfigured to be about the given expected value, H g
= 3940.4cal/g 7 . The confidence interval was then analyzed for precision. Similar to benzoic acid, the mercury thermometer is the most precise, based on the recalculated value of the confidence interval.

Effect of Time Lag on Gross Heat of Combustion
Mercury:
Hypothetical
Labview II:
Experimental Average
Mercury: Labview II: b b b + t k
7.448 7.784 c r
1 r
2 t [ o C]
H g
[cal/g] c r
1 r
2 t
H g c + a* t k r
1 r
2
+ d t + r
1
* t k
+ r
2
* t k
*(a-1)
H g
+ W/m*( t + r
1
* t k
+ r
2
* t k
*(a-1))
12.5
0.0111
0.00556
2.57
6296.
13.09
0.0104
0.00944
2.575
6309.
Predicted Effect on Final Heat of Combustion Due to t k
: 13.0 cal/g
Figure 6 : A thermal time constant for each thermometer was calculated (see Appendix), and the table above summarizes the effect of that lag. The values of b, c, r
1
, and r
2
, are based on the experimental averages of the mercury thermometer and the Labview II. The t (highlighted blue) for the latter is based on the compounded effect of a thermal time constant on the electronic apparatus. In turn, the lag observed during the rise period increases the gross heat of combustion by an average of 13.0 cal/g or about 0.21 % of the expected value.
ANALYSIS:
Thermometer
Reference Chart for Caliormeter I
Accuracy of H g
(Percent error [%])
Precision of H
[%] g
W Factor ± 95%Confidence
Interval [cal/ºC]
Mercury
Labview II
Labview I
-0.153
0.885
1.651
0.41
0.90
1.83
2430. ± 10.
2405. ± 25.
2387. ± 44.
Figure 7: Reference chart for Calorimeter I giving average accuracy, precision, and W factor values for the mercury, Labview I, and Labview II thermometers.
Our initial hypothesis, based on analysis of past lab data, expected that the electronic thermometer would be more precise than the mercury thermometer. However, this was not the case. Current findings (Figure 7) demonstrate that the mercury thermometer is the most accurate and precise, though all the devices still yielded results within the confidence intervals in comparison to the accepted literature value of 6318 ±
1.0 cal/g. The thermal time constant was determined to be statistically insignificant in comparison to the excepted gross heat of combustion of benzoic acid (see Figure 6).
Finally, depending on the total allotted time for watching over the experiment and for recording data, one of two devices may be used over each other. If one has more time and desires the highest accuracy and precision possible, it is recommended that one should use the mercury thermometer. However, if reliable data is solely desired, and not the most accurate data possible, one may use the Labview II electronic thermometer to save time and for simplicity without sacrificing much of either accuracy or precision. In fact, the data obtained, would be expected to lie within the 95% confidence intervals of the accepted literature value. It is important to find the best instrument depending on the experimental circumstances in order to refine the applicable uses of a Parr bomb calorimeter, such as with combusting food products in order to figure out calorie content.

The data from each trial using the two electronic thermometers (Labview I and
Labview II) and the manually-read mercury thermometer were statistically compared in order to determine which device was more accurate for finding the heat of combustion of high purity benzoic acid. The Labview II electronic thermometer and mercury thermometer were also compared using previous experimental data (see Figure 2). The data analysis of past experimental data suggested that the Labview II electronic device was found to be more precise and accurate than the mercury thermometer for measuring the gross heat of combustion of sucrose. The average experimental heat of combustion value obtained using the electronic device was 3949 cal/g versus the expected value of
3940.4 cal/g (see Figure 2).
Initial sucrose trials suggested that the mercury thermometer was the most precise and accurate temperature-recording device. This conclusion disagrees with past data, due to the different experimental techniques and various methods of analysis used by the different groups performing the trials. Different techniques were used to record the temperature of the mercury thermometer as well as determining the experimental values of b, c, T b
, T c
, among others. Furthermore, the relative positioning of the thermometers may alter the reproducibility of the results. For this experiment, the temperature devices were all bound closely together yet positioned carefully to avoid directly touching the base of the mercury thermometer. This was the only way to use all the temperaturerecording devices and still keep the lid on the Parr bomb calorimeters. Although the lid is not critical in maintaining an adiabatic system, it is essential for the motorized metal stirrer attached to it. If it were possible to introduce a magnetic stirrer or another means of stirring the water, then this alternative is suggested in order to determine if a noncontact positioning of the thermometers is significantly different.
After experimentation using benzoic acid pellets, the mercury thermometer was found to be the most precise and accurate device, shown by the values in Figure 1, similar to the data obtained from trials run using sucrose pellets. The gross heat of combustion determined by the mercury thermometer had the smallest 95% confidence intervals of ±
26. cal/g for calorimeter 1 and ± 52. cal/g for calorimeter 2. In statistically comparing the three devices, it was found that the mercury thermometer had the highest precision
(lowest percent error amongst trials) with values of 0.41% error for calorimeter 1 and
0.82% error for calorimeter 2. Furthermore, the mercury thermometer had the highest accuracy (lowest percent error in comparison to the literature value) with a -0.153% error for calorimeter 1 and a -0.603% error for calorimeter 2. When considering the corrected
W factors for both bombs, the mercury thermometer again displayed the highest precision of 0.41% error for calorimeter 1 and 0.82% error for Bomb calorimeter 2.
For calorimeter 1, the Labview II electronic thermometer yielded a higher accuracy, 0.885% error from the expected value, and a higher precision of 0.90% in comparing the two electronic thermometers. This was compared to an accuracy of
1.651% error and a precision of 1.83% in the Labview I device. When considering both corrected W factors as well as the gross heat of combustion values (calculated from the corrected W factors), Labview II was found to be the more precise electronic device due to its lower percent error of 1.04% as opposed to 1.84% for the Labview I program.
For calorimeter 2, the Labview I electronic thermometer was found to be more accurate than Labview II, with a percent error of only 0.027% compared to 0.996% for
Labview I. Yet, when considering the W factors for calorimeter 2, the Labview II

electronic chip thermometer again has a lower percent error (higher precision) of 1.91% in comparison to the 3.98% precision of the Labview I device. Despite these findings, it was difficult to conclude that the precision was higher for the Labview II electronic thermometer for bomb calorimeter 2 due to the limited trials performed. In addition, these numbers were solely based off of the benzoic acid trials, thereby decreasing the degrees of freedom even further.
Another aim was to obtain and compare the W factors of the two Parr bomb calorimeters, using pure benzoic acid. The mercury thermometer was in the confidence interval specified by the Parr calorimeter specifications; therefore, it is both a precise and accurate thermometer even according to the published data accompanying the Parr bombs. After doing so, these W factors were later corrected and used to calculate new gross heat of combustion values based on the new corrected W factor values. The corrected W factor values, seen in Figure 3, for both calorimeters 1 and 2 were used to generate these new values, seen in Figure 4. Again, the mercury thermometer yielded the most precise data as reflected by the small standard deviation, confidence interval, and high precision (see Figure 4). The Labview II electronic thermometer yielded the next most precise data with a relatively small confidence interval and standard deviation for both calorimeters 1 and 2. Finally, while the regenerated values for the Labview I
(DMM) thermometer were not statistical deviant from expected values, they were the least precise and least accurate and had the largest 95% confidence intervals and standard deviations of the three devices.
For further evaluation, thermal time constants for each device were determined experimentally and then statistically compared. These values for the mercury, Labview I, and Labview II were 2.7 ± 1.0 seconds, 3.2 ± 0.9 seconds, and 8.2 ± 1.5 seconds, respectively (see Appendix A1). The thermal time constant reflects the time it takes between the temperature recognition and the recording of that temperature for each device. Each of the electronic thermometers had noise filters, which minimized the noise in the data. Furthermore, the electronic devices were protected with a polymer and an epoxy coating. The mercury thermometer lag may be attributed to the specific heat of mercury and the reading/recording response of the experimenters. As a result, the actual temperatures were recorded later than they were actually read by the device. Although these time constants may be responsible for the decreased precision and accuracy of the electronic devices, further data analysis, as shown in (see Figure 6), demonstrates that this effect is relatively insignificant. It is only responsible for an uncertainty of ± 13.0 cal/g out of 6318 cal/g or about 0.21 %. The thermal time constant may be misleading; although it causes a noticeable shift in the temperature versus time graph, it is not statistically significant.
Although the thermal time constant was determined to be statistically insignificant
(Figure 6), a new experiment solely focused on the effect of the thermal time constant might be explored. Also, more trials may be done at different temperature intervals in order to see if one of the temperature devices performs better in one of the specific ranges.

CONCLUSIONS:
1.
The mercury thermometer yielded the most accurate and precise H g
values, followed by the Labview II (Bomb 2 software) electronic thermometer, and lastly by the Labview I (DMM) electronic device, for the bomb calorimeters in addition to the smallest 95% confidence intervals, standard deviation, and percent error.
2.
The effect of the thermal time constants of the temperature devices was found to be insignificant as are only responsible for an uncertainty of ± 13.0 cal/g out of
6318 cal/g. Although it causes a noticeable shift in the temperature vs. time graph, it is not statistically significant.
3.
The W factors found for the mercury thermometer, Labview I, and Labview II were 2340. cal/ o C ± 10 % (95% Confidence Interval), 2405. cal/ o C ± 25%, and
2387. cal/ o C ± 44%, respectively. Using these W values in calculating H g
, the precision values for each thermometer were recalculated, determined from the confidence interval, and found to be ± 26 cal/g for the mercury thermometer, ± 58 cal/g for Labview II, and ± 118 cal/g for Labview I.
REFERENCES:
1.
NIST Webbook. “Benzoic Acid.” Online: http://webbook.nist.gov/cgi/cbook.cgi?ID=C65850&Type=HCOMB&Units=SI&
Mask=8
2.
Encyclopedia Britannica Online. “Benzoic Acid.” http://www.britannica.com/eb/article?eu=80802.
3.
Campbell, Reece and Mitchell, 1999. Biology, 5th Edition
4.
Operating Instructions for 1108 Oxygen Combustion Bomb (205M), Oxygen
Bomb Calorimeter (204M), Pellet Press, and Mercurial Thermometer (211M).
Parr Instrument Co., Moline, IL 61265.
5.
“Thermometer Correction Table.” Parr Instrument Company. 17 Jan. 1996.
Catalog No. 1603. Serial No. 2H2321.
6.
Experiment 6 Lab reports, Spring 2001, Spring 2002. http://www.courseweb.upenn.edu
7.
NIST Webbook. “Sucrose.” Online: http://webbook.nist.gov/cgi/cbook.cgi?Name=sucrose&Units=SIhttp://webbook.n
ist.gov/cgi/cbook.cgi?ID=C65850&Type=HCOMB&Units=SI&Mask=8

APPENDIX:
Thermal Time Constant [sec.]
95 % Confidence
Mercury
Labview I
Labview II
Average [sec]
2.7
3.2
8.2
Interval [sec]
± 1.0
± 0.9
± 1.5
Thermistor 6.8 -
Figure A1: Data obtained from the temperature shock calibration were modeled to fit an exponential curve. From the curve, a thermal time constant was determined as the time at which
63.2 % of the temperature rise occurred. The thermistor, Labview II, and Labview I were recording 10 logs per second.
Average Values for Benzoic Acid Trials b [min] c [min] r
1 r
2
Mercury 7.45 12.43 0.0111 0.00556
Labview II 7.78 12.83 0.0104 0.00887
Labview I 7.59 12.53 0.0114 0.02118
Figure A2: The effect of a thermal time constant can also be observed in the average value of b, c, and r
2
in each temperature rise curve for the benzoic acid trials. Since combustion occurred at the same time, t = 6.0 min, any difference in b, or the time at 60% the total temperature rise, may be attributed to the thermal time constant. The mercury thermometer has the most rapid response to a temperature change, while Labview I had the slowest response. This matches the data from the temperature shock calibration.
Calibration Data:
Labview I
Slope [K/mV]
Lower 95%
99.967
Intercept 274.98
Labview II
Upper 95% Average: Correction:
100.017 99.995 100
273.73 274.35 274.35
Slope [K/mV]
Lower 95%
99.986
Upper 95% Average: Correction:
100.004 99.995 100
Intercept 273.79 273.35 273.70 273.70
Figure A3: Summary of calibration data for the combination of one electronic against the mercury thermometer, which was the primary standard. The calibration equations were temperature (read by software) = slope* voltage output – intercept. Both programs had settings with two entries for slope and intercept. These values were determined to accurately match the mercury thermometer readings over a temperature range of 22 o C to 27 o C. The slope correction factor used was 100 K/mV. The linear correction factor, or the intercept, had no effect on the final gross heat of combustion but was changed in the program settings for other statistical analysis.