Expert answer:the change in internal energy for a process is

  

Solved by a verified expert:9Heat of Combustion (LabVIEW)Introduction: In this experiment the standard enthalpy of combustion for an organic compound will be measured by means of a bomb calorimeter. As will beshown below, the enthalpy of combustion can be calculated from the temperaturerise, which results when the combustion reaction occurs under in a calorimeter. Ifis important that the reaction in the calorimeter take place rapidly and completely.To this end, the material is burned in a steel bomb with O2 (g) under a pressure ofabout 25 atm. Combustion of a molecule with a known standard enthalpy of combustion, benzoic acid in this experiment, leads to a measurable temperature rise in thecalorimeter. Knowledge of the heat input in conjunction with the measured temperature rise yields the heat capacity for the calorimeter. Once the heat capacity of thecalorimeter has been determined, it can be used to determine the energy/enthalpy ofcombustion for other combustible compounds (benzil, sucrose, or another moleculeof choice).9.1TheoryFrom the first law of thermodynamics, the change in internal energy for a process is∆U = q + wP V + wnon−P V(9.1)where ∆U is the internal energy change for system, q is energy transfer intosystem by heat flow, wP V is pressure-volume work, and wnon−P V is all other formsof work. For a constant volume process, where no other form of work is allowed,∆U = qV(9.2)The subscript V indicates a constant volume process. Equation 9.2 implies thata measurement of the heat added to, or removed from, a constant-volume system,as it moves from products to reactants, is really a measure of the internal energychange. As it is often more practical to conduct experiments at constant pressure asopposed to constant volume, we will define enthalpy, H, to beH ≡ U + PV(9.3)For a constant pressure process where no other forms of work are allowed, thechange in enthalpy is∆H = qP132(9.4) where the subscript P indicates a constant pressure process.Whether the determination of the change in energy is carried out at constantpressure or at constant volume is largely a matter of convenience. Generally, itis easier to work at constant pressure; however, the determination of the heat ofcombustion is more easily carried out in a bomb calorimeter. In either case, switchingbetween internal energy and enthalpy is straightforward as the definition of H leadsdirectly to∆H = ∆U + ∆(P V )(9.5)Since the standard enthalpy and energy for a real gas are so defined as to be thesame, respectively, as the enthalpy and energy of the gas in the zero-pressure limit,the ideal-gas equation may be used to evaluate the contribution of gases to ∆(P V )in Equation 9.5. The result is∆(P V ) = (n2 − n1 )RT(9.6)where n2 is the number of moles of gaseous products and n1 is the number ofmoles of gaseous reactants. The contribution to ∆(P V ) from the net change in P Vof solids and liquids in going from reactants to products is generally negligible.The standard enthalpy of combustion for a substance is defined as the enthalpychange ∆c H o which accompanies the complete oxidation (reaction with O2 ) of anorganic compound to form specified combustion products: CO2 (g), H2 O(l), N2 (g)SO2 (g). Standard enthalpy of combustion at the given temperature implies that thereactants are pure, unmixed, and in their standard states and that products are pure,separated, and in their standard states. Thus the standard enthalpy of combustionof benzoic acid at 298.15 K is given byC6 H5 CO2 H (s) +15O2 (g)20∆c H298.15 = 3228.2→7CO2 (g) + 3H2 O (l)kJkJ= 26.43moleg(9.7)(9.8)More generically, the reaction of the formA(T0 , P0 ) + B(T0 , P0 )→C(T0 , P0 ) + D(T0 , P0 )133∆c H 0(9.9) It should be recognized that the process that actually takes place in the bombcalorimeter does not correspond exactly to one of the type of Equation 9.9. It shouldbe easily noted that this is a constant volume process, i.e. we are measuring energyrather than enthalpy. In addition, for the actual calorimeter process the reactantsand products are not in their standard states.Figure 9.1: Relationship between pertinent states of the calorimeter system. Isothermal standard state process is boxed and the calorimeter process is circled.The constant volume combustion process within the bomb is more accuratelygiven byA(T1 , P1 ) + B(T1 , P1 )→C(T1 , P3 ) + D(T1 , P3 )∆c U(9.10)Considering that energy/enthalpy changes are state functions and path independent, in calorimetry it is usually more convenient to consider the reaction as the sumof two steps:1. Adiabatic reaction (q = 0):A(T1 , P1 ) + B(T1 , P1 )→C(T2 , P2 ) + D(T2 , P2 )134∆c U1(9.11) 2. Products are returned to the initial temperature by either adding heat to thesystem or removing heat from the system.C(T2 , P2 ) + D(T2 , P2 )→C(T1 , P3 ) + D(T1 , P3 )∆c U2(9.12)Since the change in energy is independent of path the energy of combustion, ∆c U(dashed arrow in Figure 9.1) is the sum of step 1 and step 2. Once the energy ofcombustion is known, ∆c U0 and then ∆H0 can be calculated.Figure 9.1 is a diagram of the relationship of the calorimeter process (circled) to theisothermal standard-state process (boxed). Calorimetry is typically done at or near298 K and in most cases it is reasonable to assume that T0 ≈ T1 . In addition to thissimplification, the reactants and products need to be corrected to the standard state(convert ∆c U to ∆c U0 ); this step is marked with ∆Uw in Figure 9.1. The correctionto standard states, called the Washburn correction, may amount to several tenths of 1percent and is important in work of high accuracy; consequently, we will neglect it forthis experiment. The principal Washburn correction terms allow for the changes in Uassociated with (a) changes in pressure, (b) mixing of reactant gases and separatingproduct gases, and (c) dissolving reactant gases in, and extracting product gasesfrom, the water in the bomb.To find ∆c U we simply need to sum ∆U1 and ∆U2 . Since step 1 was carried outadiabatically, ∆U1 = 0 and, consequently, ∆c U = ∆U2 . To find ∆U2 , we need tomeasure the heat required to bring the combustion products back to the startingtemperature. In practice, it is often unnecessary to actually complete this step.(Although you should think about how this might be done.) If we know, or cancalculate, the heat capacity of the system, the change in temperature associatedwith step 1 can provide the requisite information to find ∆U2 . From the first law,we know thatdq = dU =∂U∂TdT = CV dT(9.13)VAfter integration, the energy change in going from T2 to T1 (step 2) is given byT1∆U =CV dTT2135(9.14) Note that the heat capacity we are interested in is for the system and does notinclude the heat capacity contribution from the products. For small temperaturechanges, the heat capacity is nearly constant and Equation 9.14 can be simplified to∆ = CV (T1 − T2 )(9.15)In the first part of this experiment, we calculate CV with a known ∆U anda measured temperature change. In the second part, we use the calculated heatcapacity to find an unknown ∆U with a measured temperature change.9.2ExperimentalFigure 9.2: Calorimeter cross-sectionAbout the calorimeter: A bomb calorimeter has the metal bomb inside of ametal bucket containing water. That metal bucket sits loosely inside an insulatedjacket. There is a stirrer that sticks into the water in the bucket and is driven bya motor outside of the calorimeter. A thermometer also sticks into the water in thebucket and is the device that will be used to determine the change in temperatureduring the reaction. Two electrical leads connect to the top of the bomb from outsideand they will deliver the current that initiates the reaction.136 The Parr 1108 O2 bomb is a 342 mL pressure vessel with a removable head anda closure that can be sealed by simply turning a knurled cap until it is hand tight.Sealing forces develop internally when the bomb is pressurized, but after the pressurehas been released the cap can be unscrewed and the head lifted from the cylinder.Two valves with replaceable stainless bodies are installed in the bomb head. On theinlet side there is a check valve, which opens when pressure is applied and closesautomatically when the supply is shut off. On the outlet side gases are releasedthrough an adjustable needle valve, passing through a longitudinal hole in the valvestem and discharging from a short hose nipple at the top. Turning a knurled adjustingknob controls gas flow through the outlet valve. A deflector nut on the inlet passagediverts the incoming gas so that it will not disturb the sample. A similar nut onthe outlet side reduces liquid entrainment when gases are released. A special acidresistant alloy is used for the construction of the bomb because water and acids areproduced in the reaction.Under normal usage Parr O2 bombs will give long service if handled with reasonable care. However, the user must remember that theses bombs are continuallysubjected to high temperatures and pressures that apply heavy stresses to the sealingmechanism. The mechanical condition of the bomb must therefore be watched carefully and any parts that show signs of weakness or deterioration should be replacedbefore they fail. Otherwise, a serious accident may occur.The head gasket and the electrode seals are the parts that will require most frequent replacement. Check the head gasket frequently and replace it if there is anyuncertainty as to its age or condition. Also check and replace the sealing rings in thevalves and insulated electrode if there is any evidence of leakage at these points. Donot fire a bomb if gas bubbles are observed. Disassemble the bomb and installnew seals immediately. Also, do not use extreme force when closing a bomb valve.A moderate but firm turn on the valve knob should be sufficient to stop all gas flow.Excessive pressure will deform the valve seat and possibly close the gas passage. Ifthis happens in the 1108 bomb, unscrew the valve body and replace the 20VB valveseat. Always keep the 397A-packing nut in this bomb tightened firmly in order tomaintain a tight seal between the 20VB valve seat and the valve body.Never under any circumstances use oil on valve or fittings that handle compressedO2 . This precaution applies to all of the O2 bomb parts as well as to the O2 fillingconnection.137 Although Parr O2 bombs are made from alloys that will withstand most corrosivegases, these bombs will not resist chlorine, fluorine, or bromine in the presence ofmoisture. If samples yielding appreciable amounts of these elements are burned in aParr bomb, the interior surfaces may become etched or corroded. In such cases, thebomb should be emptied and washed as quickly as possible after each combustion.Figure 9.3: Parr bomb cross-sectionThe metal bomb provides a constant-volume system in which the combustionreaction will take place. The sample pellet is placed in the ignition cup and the fusewire is carefully arranged to touch the pellet but not the cup. The bomb is sealedby screwing the cap on and then filled with a high pressure of pure into the waterbucket.Precautions which must be followed to avoid explosion of Parr bomb1. The amount of sample must not exceed 1 g.2. The oxygen pressure must not exceed 30 atm.138 3. The bomb must not be fired if gas bubbles are leaking from it when submergedin water.4. The operator should stand back for at least 15 seconds after igniting the sampleand should keep clear of the top of the calorimeter. An explosion would bemost likely to drive the top upward.5. Much less than 1 g sample should be used for testing materials of unknowncombustion characteristics.6. The use of high-voltage ignition systems is to be avoided. Arcing betweenelectrodes may cause the electrode seals to fail and permit the escape of hotgases with explosive force.Standardizing the calorimeterStandardization procedure: The term “standardization as used here denotesthe operation of the calorimeter on a standard sample from which the energy equivalent or effective heat capacity of the system can be determined. The energy equivalent, W , of the calorimeter is the energy required to raise the temperature onedegree, expressed as calories per degree Celsius. The procedure for a standardizationtest is exactly the same as for testing a fuel sample. Use a pellet of calorific gradebenzoic acid weighing not less than 0.9 or more than 1.25 g. Determine the correctedtemperature rise, t, from the observed test data, also titrate the bomb washings todetermine the nitric acid correction and measure the unburned fuse wire. Computethe energy equivalent by substituting in the following equation:Hm + e1 + e3tW = energy equivalent of the calorimeter in cal/o CH = heat of combustion of the standard benzoic acid sample in cal/gm = mass of the standard benzoic acid sample in gt = net corrected temperature rise in o Ce1 = correction for heat of formation of nitric acid in cale3 = correction for heat of combustion of the firing wire in calW =139(9.16) Example: Standardization with a 1.11651 g benzoic acid sample (6318 cal/g) produces a net corrected temperature rise of 3.077o C. The acid titration required 11.9ml of standard alkali and 8 cm of fuse wire were consumed in the firing. Substitutingin the standardization equation,H = 6318 cal/gm = 1.1651 ge1 = (11.9 ml) (1 cal/ml) = 11.9 cale3 = (8 cm) (2.3 cal/cm) = 18.4 calt = 3.077 o CTherefore,W =(6318)(1.1651) + 11.9 + 18.4= 2402.1 cal/o C3.077(9.17)Poor Combustion: The difference in combustion characteristics of the wide variety of materials which may be burned in an O2 bomb make it difficult to give specificwhich will assure complete combustions for all samples. However, two fundamentalconditions may be stated. First, some part of the sample must be heated to its ignition temperature to start the combustion and, in burning, it must liberate sufficientheat to support its own combustion regardless of the chilling effect of the adjacentmetal parts. Second, the combustion must produce sufficient turbulence within thebomb to bring O2 into the fuel cup for burning the last traces of the sample.An incomplete combustion in an O2 bomb is nearly always due to one or more ofthe following causes:1. Excessively rapid admission of gas to the bomb during charging, causing partof the sample to be blown out of the cup.2. Loose or powdery condition of the sample that will permit unburned particlesto be ejected during a violent combustion.3. The use of a sample containing coarse particles that will not burn readily.4. The use of a sample pellet that has been made too hard or too soft. Eithercondition sometimes causes spilling and the ejection of unburned fragments.5. The use of an ignition current too low to ignite the charge, or too high, causingthe fuse to break before combustion is under way.140 6. Insertion of the fuse wire loop below the surface of a loose sample. Best resultsare obtained by barely touching the surface or by having the wire slightly abovethe sample.7. The use of insufficient O2 to burn the charge, or conversely, the use of a veryhigh initial gas pressure that may retard the development of sufficient gasturbulence within the bomb.8. Insufficient space between the combustion cup and the bottom of the bomb.The bottom of the cup should always be at least one-half inch above the bottom of the bomb, or above the liquid level in the bomb, to prevent thermalquenching.Magnitude of Errors: The following examples illustrate the magnitude of errorsthat may result from faulty calorimeter operations. They are based upon an assumedtest in which a 1.0000 g sample produced a 2.800o C temperature rise in a calorimeterhaving an energy equivalent of 2400 cal/o C.• An error of 1 ml in making the acid titration will change the thermal value 1.0cal.• An error of 1 cm in measuring the amount of fuse wire burned will change thethermal value 2.3 cal.• An error of 1 g in measuring the 2 kg of water will change the thermal value2.8 cal.• An error of 1 mg in weighing the sample will change the thermal value 6.7 cal.• An error of 0.002o C in measuring the temperature rise will change the thermalvalue 4.8 cal.If all of these errors were in the same direction, the total error would be 17.6 cal.141 9.3LabVIEWTemperature Measurement Using Computer Data Acquisition Systemand LabVIEW Program 11In the tradition of calorimetry experiments, at least the one described in yourlab write-up, temperature is measured by a thermometer and a series of readingsare taken to follow the temperature change over the entire combustion and heattransfer process. In this experiment, besides the conventional calorime6try method,you will learn how to take advantage of the modern computerized data acquisitiontechnique. Instead of a thermometer, you will be using a thermocouple to measurethe temperature and letting the computer read and record the data. At the sametime, you will also have the opportunity to program the analog-to-digital converterboard using LabVIEW software.Before the lab: Read “Getting Started with LabVIEW” and attend one of theprelabs.Procedure:1. Practice programming in LabVIEW(a) After attending the prelab, get a floppy disk from the stockroom. Youare allowed to use this disk on the PC designated for this lab experimentONLY during the lab period you are doing the lab. This means after thelab, take it home and use whatever software you are comfortable with todo the data analysis. NEVER bring it back.(b) Turn on the computer and start Windows XP. Insert you floppy disk tothe drive and format it.Using the mouse, double click on “My Computer,” then right click thefloppy drive icon to bring down the menu. Select ”Format” to format thedisk.On the Desktop background of Windows XP, you should see a file“TCE.vi” (the suffix “vi” is not visible). Copy this file to your floppydisk.11modified by Andrew Duffin, Spring 2007142 Right click the file to open the drop-down menu, then choose “copy.”Double click “My Computer” on the desktop background, then double clickthe floppy drive icon. On top of the new window choose the “edit” dropdown menu and choose “paste.”Close all opened windows on the desktop. From now on, you are allowedto operate files ONLY on this floppy disk.(c) Following the “Getting Started with LabVIEW” build your own RandomNumber Generator and test it. When you succeed in Step 8 save your datafile into your own floppy disk as “data1.txt.” Also save your VI programfile. In the next step, use “Notepad” to open that data file.Click “Start” at the bottom left corner of the computer screen. Move themouse pointer through “program” → “accessories” and click “Notepad.”In Notepad, you should see your data is organized in a long row, separated by a space as follows:0.8750.5780.2340.4780.211 . . .It is not convenient to use this format of data. Common spreadsheetsoftware prefers all data listed in a column, which looks like0.8750.5780.2340.4780.211…(d) To transpose the above data array, do the following: Right below thepicture of the “Write to Spreadsheet File.vi” (figure 9.4), create a Booleanconstant (figure 9.5):Put the cursor over an empty place, right click, and choose “Boolean”and place it right below the “Write to Spreadsheet File.vi” icon.143 Figure 9.4: Write to Spreadsheet File.vi(e) Change your mouse pointer to “operation” (little hand with index fingerpointed out) if you are not yet using it. Left click the “T” letter in the box.Using the “Wiring” tool to connect this constant box with the Booleanconstant (figure 9.5) icon. Make sure you find the correct terminal on theicon to make the connection.Figure 9.5: Boolean constant(f) The correct terminal is a tiny green square at the bottom side of the icon,right under the lower left corner of the small disk picture. When themouse is pointed at it, a yellow box will pop out and show “transpose?(no:F).” When you finish, you should see the picture in figure 9.6.Figure 9.6: Correct wiring to transpose data array(g) Save your program under a different name. Execute it and save the newgenerated file to “data2.txt.” Use Notepad to check if your data array is144 transposed. Close the program and all windows in LabVIEW and go backto the “LabVIEW” dialog page.2. Build your own data acquisition Virtual Instrument(a) Open “TCE.vi” from your disk by selecting “Open VI” in the LabVIEWdialog page. It will be open as a panel. Click “Windows” on the top menubar and choose “Show Diagram.” In a new window, you should see thediagram in figure 9.7.Figure 9.7: Subroutine for sampling thermocouple output by an A-to-D converter board.This is a subroutine for sampling thermocouple output by an Analog-toDigital converter board installed on the PC and converting voltage signalto temperature (in degrees C). You should build a complete programbased on it, without changing it too much:• The whole program is inside a “For loop,” which controls everythinginside to repeat 100 times (preset by the number on the upper leftcorner). The whole loop takes about 1 second to finish. When theloop is running, data can be obtained from outside through tunnels145 •••••(black marks on the right side of the loop box in this handout, orangeboxes on the computer screen).Inside the Loop on the left there are two analog input readout boxesusing channels 0 and 1 on the A-to-D board. Channel 0 reads thethermocouple output and channel 1 reads the board zero offset.After the subtraction of the readouts, the board offset is eliminated(the A-to-D card offset is compensated).Multiplying by 1000 converts the signal unit from volts to millivolts.The signal then flows into the first equation box ”AD card readingcompensation” to correct the nonlinear readout behavior of the voltage readout. The equation box is obtained by calibrating the boardwith a high precision digital voltmeter.The corrected signal is then split. One way goes directly out of thebox, labeled as “TC output (mV).”You do not really need to use this signal in the experiment, but ithelps to check how accurate out data acquisition board is, by hookingthe output to an indicator and comparing the reading with the digitalvoltmeter reading. See 2hThe other goes to the second equation box labeled as “Voltage→ Temperature Conversion,” in which the equation is obtained byfitting data in the 20 to 30 degree C region in the standard typeE thermocouple output chart. Between 17 and 32 degrees C, theaccuracy of the equation is better than 0.01 C. A digital indicatorlabeled as “T sample” and also directed out of the “For Loop,” readyto use, then displays the output of this equation.(b) Outside the “For Loop,” build a mean function and indicator. Usingthe “Wiring” tool, wire the Temperature output (the lower tunnel) tothe X input terminal of the “Mean VI.” Now you can average the 100temperature readouts generated by the “For Loop” and display the meanvalue on a digital indicator.(c) Outside the “For Loop,” create a waveform chart and connect it to the“Mean VI” output. Change the Y scale range to 10-40 temporarily for testpurposes. Later, during the experiment, change it to 15-30 or whateveryou feel better).146 (d) Make a “While Loop” to enclose everything. Change to the “Panel”window. Make a vertical toggle switch. Find the switch terminal in the“Diagram” window and make sure it is outside the “For Loop,” but insidethe “While Loop.” Then wire the switch terminal to the conditionalterminal.(e) Select “Write to Spreadsheet File.vi” and place it outside the “WhileLoop.” Transpose the data array, as described above in 1c. Wire the 1Ddata input terminal of this VI to the “Mean VI” inside the “While Loop”(See Guide 2-16 Steps 8-9). Make sure you enable indexing for the newtunnel on the wall of the “While Loop.”(f)(g)(h)(i)(j)Now you have built the whole program, your own VI to do the temperature measurement and data acquisition.The thermocouple wires should already be connected to a Hewlett-PackardDigital Multimeter and to the National Instruments AD board. Makesure that throughout the entire lab the cold reference junction of thethermocouple is immersed in an ice water bath.Test your program by changing the temperature of the thermocouple sensor (using water with different temperatures or by touching it with yourhand) and see if the digital indicator and wave graph give you the correctresponse. Do not forget to turn on the toggle switch to keep the “WhileLoop” running. When you turn off the toggle switch, a file saving windowwill pop out. If you like, save the data file, then open it by Notepad, andcheck if the data are correctly reco…