EGR2500 Lab2 W24 (1)

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INTRODUCTION TO THERMAL ENGINEERING EGR 2500 Winter 2024 Laboratory Assignment #2 Measuring the Energy Content of Food The purpose of this laboratory exercise is to apply the First Law of Thermodynamics to determine the energy content (i.e. food calories) of some simple foods. Lab Procedure 1. Carefully read the operating instructions for the Parr Instruments® model 1341 Oxygen Bomb Calorimeter. Ensure that every group member has thoroughly read the instructions. Discuss the details of the experiment so that you are properly prepared before attempting to conduct the experiment, as you will be given only one food sample. Prepare a data sheet for recording the water-bath temperature rise, as discussed in the operating instructions. 2. Sign-out a food sample from the lab. You should do this just prior to conducting the experiment. Do not open your sample capsule. The capsule and contents have been weighed to the closest 0.1mg. Moisture will damage the gelatin capsule. 3. Prepare the oxygen bomb, using your food sample, and burn the sample within the bomb calorimeter. Record the water-bath temperature as detailed in the handout. If you have any questions about operating the calorimeter, please ask before you attempt the experiment. Report Analysis 1. Plot the water-bath temperature as a function of time, and determine the actual temperature rise. 2. Develop a First Law model of the system that is composed of the water-bath, bomb, fuse wire and food sample. Use your model and the measured temperature rise, to estimate the energy value, e fs , of your food sample 1 in cal/g and “food calories”/g. Note that one ‘food calorie’ is equal to one kilocalorie. 3. Perform an uncertainty analysis on your calculation of e fs , and specify the magnitude of the uncertainty for your experiment. You will need to research, list and reference the uncertainty of the digital thermometer used for temperature measurements. 4. Your sample consists of one of the following:  Domino Premium Sugar Cane Granulated  Honey Maid Graham Crackers  Kirkland organic whole cashews unsalted unroasted  Lay’s Baked Potato Chips Original 1 The derivation in the combustion bomb instruction sheet does not consider a gelatin capsule. You must modify the derivation to account for the capsule by decomposing the total “energy release” from the test sample into 2 terms: one accounting for the food sample itself and the other for the gelatin capsule. The heat of combustion of the gelatin capsule is E equiv/gc and is listed in the preliminary calculations section of the handout.

 Research the calorie information for these foods and tabulate in your report (include # food calories (kcal), serving size (g) and energy value per unit mass (kcal/g)). Clearly indicate and cite your sources of information and comment on the reliability of these sources . Which sample would you guess that you measured? Justify your answer. 5. Research and summarize other uses of a bomb calorimeter, as well as approved methods set by the Food and Drug Administration (FDA) of determining the caloric content listed in nutritional labels of packaged food items. Clearly indicate and cite your sources of information and comment on the reliability of these sources . This summary must be written in your own words and must cite the references according to the guidelines specified in the lab report guidelines document. Laboratory Report Contents: Your lab report should include the following:  Title page with abstract  Theory section which includes the derivation of the equation for the energy value e fs of the food sample (theory section from lab report modified to account for gelatin capsule), the derivation of the uncertainty equation for e fs , as well as any other relevant equations.  Results and Discussion section which should include:  Data table(s) that include your collected and calculated data (time, temperature, masses, fuse length, slopes in pre- and post-periods, temperature rise, etc.)  Graph of temperature versus time  Typed equations used to determine the energy value of your food sample and its uncertainty.  Data table listing caloric information for the possible food samples (make sure you cite sources of information).  Discussion of results: Make sure you discuss the results and indicate what food sample you tested based on your results.  Summary of findings from information search (uses of bomb calorimeters; approved ways set by the Food and Drug Administration (FDA) of determining the caloric content listed in nutritional labels of packaged food items; make sure you cite sources of information)  References (remember to cite these references in your report)  Appendix (Lab handout, original data sheet and sample calculations) pg. 2

OPERATING INSTRUCTIONS For the Parr 1341 Oxygen Bomb Calorimeter These instructions cover the steps to be taken in setting up and operating a Parr 1341 Plain Oxygen Bomb Calorimeter. They are extracted from the manufacturer’s complete manuals, which are available upon request. The user should study these instructions carefully before starting to use the calorimeter so that he/she will fully understand the capabilities of the equipment, and so that he/she will be well aware of the safety precautions to be observed in its operation. OPERATING THE CALORIMETER Place the jacket on a sturdy bench or table in a location that is reasonably free from drafts and is protected from sources of radiant heat, preferably in an air-conditioned room. Temperature changes in the room should be minimal. There should be convenient access to running water, to a drain and to an appropriate grounded electrical outlet. About 8 square feet of workspace will be required. The lab assistant will provide already-weighed test samples. A balance capable of weighing up to 2.0 kg with 0.1 g sensitivity, and a tank of oxygen are available in the lab. All operations required to test an unknown sample or to standardize the 1341 plain calorimeter should proceed step-wise in the following manner: 1. Prepare the sample and charge the oxygen bomb. Precautions. Combustion with oxygen in a sealed bomb is a very effective and reliable method for releasing all heat energy obtainable from a sample and for preparing hydrocarbon compounds and carbonaceous materials for analysis, but there are certain precautions, which must always be observed when using this equipment. In particular:  Do not overcharge the bomb with too much sample or with a sample, which might react with explosive violence.  Do not overcharge the bomb with too much oxygen. The initial charging pressure should not exceed 40 atm (590 psig). About 30 atm is recommended here.  Do not fire the bomb alone on an open bench without providing a protective cooling medium. Usually the bomb should be completely submerged in water during firing.  Do not fire the bomb if gas bubbles are released from any point on the bomb when it is submerged in water.  Do not ignite a volatile sample without using one of the sealed sample holders (which would be provided).  Stand away from the bomb during firing and do not handle the bomb for at least 1 minute after firing.  Keep the bomb in good condition at all times. Any parts that show signs of weakness or deterioration must be replaced promptly. Allowable Sample Size. To stay within safe limits, the bomb should never be charged with a sample, which will release more than 8000 calories when burned in oxygen, and the initial oxygen pressure should never exceed 40 atmospheres (590 psig.). To avoid damage to the bomb and possible injury to the operator, it should be a standing rule in each laboratory that the bomb must never be charged with more than 1 of the samples provided (approx 1 g) of material. Attaching the Fuse. Set the bomb head on the A38A support stand and fasten a 10 cm length of fuse wire between the two electrodes. Parr 45C10 nickel alloy wire, used for most tests, is furnished on cards from which uniform 10 cm lengths can be cut. To attach the fuse to quick-grip electrodes, insert the ends of the wire into the eyelet at the end of each stem and push the cap downward to pinch the wire into place. No further threading or twisting is required. Place the fuel capsule with its weighed sample in the electrode loop and bend the wire downward toward the surface of the charge. It is not necessary to submerge the wire in a powdered sample. In fact, better combustion will usually be obtained if the loop of the fuse is set slightly above the surface. When using pelleted samples, bend the wire so that the loop bears against the top of the pellet firmly enough to keep it from sliding against the side of the capsule. It is also good practice to tilt the capsule slightly to one side so that the flame emerging from it will not impinge directly on the tip of the straight electrode. pg. 3

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Liquids in the Bomb. Most bomb combustion procedures call for a small amount of liquid to be placed in the bottom of the bomb as a sequestering agent and absorbent. If the amount and type of liquid are not otherwise specified, add 1.0 mL of distilled or deionized water from a pipet Closing the Bomb. Care must be taken not to disturb the sample when moving the bomb head from the support stand to the bomb cylinder. Check the sealing ring to be sure that it is in good condition and moisten it with a bit of water so that it will slide freely into the cylinder; then slide the head into the cylinder and push it down as far as it will go. For easy insertion, push the head straight down without twisting and leave the gas release valve open during this operation. Set the screw cap on the cylinder and turn it down firmly by hand to a solid stop. When properly closed, no threads on the cylinder should be exposed. If the screw cap tends to bind to the cylinder at this point, indicating that it might be difficult to open the bomb after it has been fired, turn the screw cap back slightly - but only a few degrees - enough to release the binding, since the bottom thread must remain fully engaged. It is not necessary to use a wrench or spanner on the screw cap. Hand tightening should be sufficient to secure a tight seal. Filling the Bomb. The pressure connection to the bomb is made with a slip connector on the oxygen hose, which slides over the gas inlet fitting on the bomb head. Slide the connector onto the inlet valve body and push it down as far as it will go. If it does not slide easily, a drop of water spread around the inlet valve will lubricate the sealing rings. Close the outlet valve on the bomb head; then open or "crack" the oxygen tank valve not more than one-quarter turn. Open the filling connection control valve slowly and watch the gage as the bomb pressure rises to the desired filling pressure (usually 27 atm., but never more than 40 atm.); then close the control valve. The bomb inlet check valve will close automatically when the oxygen supply is shut off, leaving the bomb filled to the highest pressure indicated on the 0-55 atm. gage. Release the residual pressure in the filling hose by pushing downward on the lever attached to the relief valve. The gage should now return to zero. If the pressure drops slowly and a large amount of gas escapes when the pressure relief valve is opened, the check valve in the bomb head is not operating properly. This trouble will have to be corrected before the bomb can be used. If too much oxygen should accidentally be introduced into the bomb, do not proceed with the combustion. Detach the filling connection; exhaust the bomb; remove the head and reweigh the sample before repeating the filling operation. 2. Fill the calorimeter bucket by first taring the dry bucket on a solution or trip balance; then add 2000 (+/-0.5) grams of water. The water temperature should be approximately 1.5° C below room temperature, but not less than about 19.2 °C. 3. Set the bucket in the calorimeter, noting the three dimples in the bottom of the bucket, which rest on supporting pins in the bottom of the jacket. The single dimple must always face forward when setting the bucket in the jacket. Attach the lifting handle to the two holes in the side of the screw cap and lower the bomb into the water with its feet spanning the circular boss in the bottom of the bucket . Handle the bomb carefully during this operation so that the sample will not be disturbed. Remove the handle and shake any drops of water back into the bucket; then push the two ignition lead wires into the terminal sockets on the bomb head, being careful not to remove any water from the bucket with the fingers. 4. Connect the ignition unit. The Parr 2901 Ignition Unit operates from any standard electrical outlet to provide the proper low voltage firing current, providing also a convenient push switch, indicating lamp and connecting terminals. Connect the two lead wires from the calorimeter jacket, one to the "l0 CM" terminal and the other to the “common” terminal on the ignition unit; then plug the power cord into any appropriate grounded electrical outlet. After the unit has been plugged into an outlet do not press the firing button unless the lead wires inside the jacket are connected to a bomb. If the bare terminals on these wires happen to be in contact with each other or with a metal object when the circuit is closed, the resulting short-circuit may cause serious damage to the ignition system. 5. Set the cover on the jacket with the thermometer facing toward the front. Turn the stirrer by hand to be sure that it runs freely; then slip the drive belt onto the pulleys and start the motor. 6. Let the stirrer run for 5 minutes to reach equilibrium before starting a measured run. At the end of this period record the time or start a timer and read the temperature. 7. Read and record temperatures at one-minute intervals for 6 minutes. Then, at the start of the 6th minute... 8. Stand back from the calorimeter and fire the bomb by pressing the ignition button and holding it down until the indicator light goes out. Normally the light will glow for only about 1/2 second but release the button within 5 seconds pg. 4

regardless of the light. Caution: Do not have the head, hands or any parts of the body over the calorimeter when firing the bomb; and continue to stand clear for 30 seconds after firing. 9. The bucket temperature will start to rise within 20 seconds after firing. This rise will be rapid during the first few minutes; then it will become slower as the temperature approaches a stable maximum as shown by the typical temperature rise curve on page 4. 10. Measure the time required to reach 60 per cent of the total rise. Take temperature readings at 45, 60, 75, 90 and 105 seconds after firing and interpolate between these readings to identify the 60% point after the total rise has been measured. 11. After the rapid rise period (about 4 or 5 minutes after ignition) record temperatures at one-minute intervals until the difference between successive readings has been constant for five minutes. Usually the temperature will reach a maximum; then drop very slowly. But this is not always true since a low starting temperature may result in a slow continuous rise without reaching a maximum. As stated above, the difference between successive readings must be noted and the readings continued at one-minute intervals until the rate of the temperature change becomes constant over a period of 5 minutes. 12. After the last temperature reading, stop the motor, remove the belt and lift the cover from the calorimeter. Wipe the stirrer with a clean cloth and set the cover on the support stand. Lift the bomb out of the bucket; remove the ignition leads and wipe the bomb with a clean towel. 13. Open the knurled knob on the bomb head to release the gas pressure before attempting to remove the cap. This release should proceed slowly over a period of not less than one minute to avoid entrainment losses. After all pressure has been released, unscrew the cap; lift the head out of the cylinder and place it on the support stand. Examine the interior of the bomb for soot or other evidence of incomplete combustion. If such evidence is found, the test will have to be discarded. 14. Wash all interior surfaces of the bomb with water and dry carefully. 15. Remove all unburned pieces of fuse wire from the bomb electrodes; straighten them and measure their combined length in centimeters. Subtract this length from the initial length of 10 centimeters and enter this quantity on the data sheet as the net amount of wire burned, . pg. 5 f L

pg. 6 Note: Digital thermometer used in place of glass thermometer

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CALORIMETER CALCULATIONS The raw data should be plotted , as shown below, and inspected for anomalies. There are a few features worth noting. Firstly, the data should have a very slight positive slope during the Pre-period (if the initial water temperature is about 1.5 °C below room temperature to start). During the Post-period, there should be a very slight negative slope. Calculations are based on identifying the Pre and Post-periods, and on identifying the time to achieve 60% of the total temperature rise. Assembly of Data. The following data should be available at the completion of a test in a 1341 calorimeter: t a = time of firing t b = time when the temperature reaches 60 percent of the total rise t c = time at beginning of period in which the rate of temperature change has become constant T a = temperature at time of firing T c = temperature at time c r l = rate (temperature units per time, °C/sec) at which temperature was rising during the 5-min. period before firing r 2 = rate (temperature units per time, °C/sec) at which the temperature was rising during the 5-min. period after time t c . If the temperature was falling instead of rising after time c, r 2 is negative and the quantity -r 2 (c-b) becomes positive and must be added when computing the corrected temperature rise L f = centimeters of fuse wire consumed in firing = thermal capacitance of the calorimeter, determined under CALIBRATING THE COMBUSTION BOMB M s = mass of test sample in grams M gc = mass of gelatin capsule used to contain fuel sample (if used) Temperature Rise. The net corrected temperature rise,  T, is obtained by substituting in the following equation:  T = (T c -T a ) – r 1 (t b -t a ) – r 2 (t c -t b ) Thermochemical Corrections: The heat of combustion for the fuse wire and gelatin capsule can be determined as: E equiv/f = (L f ) (e equiv/f ) = correction in calories for heat of combustion of fuse wire = (L f in cm) x (2.3 cal/cm) (when using Parr 45C10 nickel chromium fuse wire) E equiv/gc = M gc (e gc ) = correction in calories for the heat of combustion of the gelatin capsule (if used) = (M gc in grams) x (4600 calories/gm) pg. 7 Typical Temperature Rise Curve 19 19.5 20 20.5 21 21.5 22 22.5 0 200 400 600 800 1000 1200 1400 1600 Time (sec) Temperature (°C) Pre-period Rise Period Post-period a b c d ~ 60 % of Total Temp. Rise Slope of this line = r 2 Slope of this line = r 1 Cal th C

Calibrating the Combustion Bomb Calorimeter The constant volume combustion bomb (bomb) has been calibrated using a standard sample of benzoic acid according to the procedure below. Some simplifications have been made, but the resulting accuracy is certainly adequate for the purposes of this laboratory experiment. The calibration is based on a simple First Law analysis of the bomb. Once the bomb has been calibrated, a similar analysis may be used to obtain the energy value of any test sample. Please refer to Figure 1 below. Consider a closed system that consists of the combustion bomb, water, test sample, and fuse wire. For the process of igniting the fuse and the test sample, and the resulting rise in water temperature, the 1 st Law states: E ¿ − E out = Δ E sys = E 2 − E 1 (1) Where E 2 and E 1 refer to final and initial total energy of the system. Rearranging this expression, and substituting the energy flows into and out of the system yields: E 2 − E 1 = E ¿ − E out = W elect − Q B (2) Where W elect is the electrical work input and Q B is the heat loss by the system. Since Energy is extensive, and changes in kinetic and potential energy are negligible, E 2 − E 1 = ΔU 12 = ΔU s + ΔU f + ΔU w + ΔU B (3) Where U refers to internal energy and subscripts, s = test sample f = fuse wire w = water surrounding bomb B = bomb Δ = (final state – initial state) 1 = initial state 2 = final state pg. 8 Q B W elect. CM Bomb Sample Fuse Wire + - Q B W elect. CM Bomb Sample Fuse Wire + - Figure 1 - Schematic of the system used for the First Law analysis

Substituting equation (3) into equation (2), the 1 st Law becomes, ΔU s + ΔU f + ΔU w + ΔU B = W elect − Q B (4) Combining terms associated with combustion on the RHS, and separately those associated with resulting temperature rise on the LHS, ΔU w + ΔU B + Q B =− ΔU s − ΔU f + W elect (5) Reviewing the equation, term by term:  ΔU w = energy rise in the water bath = m w c v ,w ( T 2 − T 1 ) , where c v , w is the specific heat of the water  ΔU B = energy rise in the combustion bomb = m B c v , B ( T 2 − T 1 ) where c v , B is the specific heat of the bomb  Q B = heat transfer out of the bomb. Q B is approximately proportional to the temperature rise, and so the quantity ( Q B ( T 2 − T 1 ) ) is approximately constant.  − ΔU s =− ( U ∏ . − U react . ) = ( U react . − U ∏ . ) s = total “energy release” from the test sample = m s e s where e s = “energy value” per unit mass of the test sample  − ΔU f = ( U react . − U ∏ . ) f = L f [ ( U react . − U ∏ . ) f L f ] = L f e f , where, e f is the “energy value” per unit length of the fuse material, and L f is the actual length of the fuse consumed . ( L f = L f ,initial − L f , final )  W elect = electrical work necessary to ignite the fuse, and is proportional to the length of fuse consumed = L f w f Substituting the above back into the energy equation, [ ( m c v ) w + ( m c v ) B + Q B ( T 2 − T 1 ) ] ( T 2 − T 1 ) = m s e s + L f [ e f + w f ] (6) The first term on the left, in brackets, is composed of terms that are approximately constant and together represent the thermal “inertia” or “thermal capacitance” of the calorimeter, C th, cal . The term in brackets on the right represents the “energy equivalent per length of fuse material” ( e ¿ , f = 2.3 cal/cm). The 1 st Law can then be written as, C th, cal ΔT = m s e s + L f e ¿ , f (7) Solving for the thermal capacitance of the calorimeter, C th, cal = m s e s + L f e ¿ , f ΔT (8) Following replicate calibration tests with a reference benzoic acid test sample, it was found that, = 2430.9 ± 17 calories/°C (unit #1), or . = 2420.9 ± 24 calories/°C (unit #2). This value can now be used in conjunction with the temperature rise to account for the energy increase in the water bath and combustion bomb, as well as the heat transfer from the calorimeter when analyzing other test samples. pg. 9 Cal th C Cal th C

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pg. 10 Sample # = Unit # = Mass of Food Sample = Mass of Gelatin Capsule = Initial Fuse Wire Length = Final Fuse Wire Length = Starting H 2 O Temp. = Time (seconds) Temperature (°C) Comment 0 start timer 60 120 180 240 300 <--start logging temperature 360 pre-period 420 " " 480 " " 540 " " 600 (ignite time) begin rise period 645 660 675 690 705 765 825 885 945 1005 1065 1125 1185 1245 1305 1365 1425 1485 1545 Group Leader: