the change in internal energy for a process is

26 Jun the change in internal energy for a process is

Question
9

Heat 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 be
shown below, the enthalpy of combustion can be calculated from the temperature
rise, which results when the combustion reaction occurs under in a calorimeter. If
is 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 of
about 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 the
calorimeter. Knowledge of the heat input in conjunction with the measured temperature rise yields the heat capacity for the calorimeter. Once the heat capacity of the
calorimeter has been determined, it can be used to determine the energy/enthalpy of
combustion for other combustible compounds (benzil, sucrose, or another molecule
of choice).

9.1

Theory

From 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 into
system by heat flow, wP V is pressure-volume work, and wnon−P V is all other forms
of 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 that
a 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 energy
change. As it is often more practical to conduct experiments at constant pressure as
opposed to constant volume, we will define enthalpy, H, to be
H ≡ U + PV

(9.3)

For a constant pressure process where no other forms of work are allowed, the
change in enthalpy is
∆H = qP
132

(9.4)

where the subscript P indicates a constant pressure process.
Whether the determination of the change in energy is carried out at constant
pressure or at constant volume is largely a matter of convenience. Generally, it
is easier to work at constant pressure; however, the determination of the heat of
combustion is more easily carried out in a bomb calorimeter. In either case, switching
between internal energy and enthalpy is straightforward as the definition of H leads
directly to
∆H = ∆U + ∆(P V )

(9.5)

Since the standard enthalpy and energy for a real gas are so defined as to be the
same, 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 of
moles of gaseous reactants. The contribution to ∆(P V ) from the net change in P V
of solids and liquids in going from reactants to products is generally negligible.
The standard enthalpy of combustion for a substance is defined as the enthalpy
change ∆c H o which accompanies the complete oxidation (reaction with O2 ) of an
organic 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 the
reactants are pure, unmixed, and in their standard states and that products are pure,
separated, and in their standard states. Thus the standard enthalpy of combustion
of benzoic acid at 298.15 K is given by
C6 H5 CO2 H (s) +

15
O2 (g)
2

0
∆c H298.15 = 3228.2

→

7CO2 (g) + 3H2 O (l)

kJ
kJ
= 26.43
mole
g

(9.7)
(9.8)

More generically, the reaction of the form
A(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 bomb
calorimeter does not correspond exactly to one of the type of Equation 9.9. It should
be easily noted that this is a constant volume process, i.e. we are measuring energy
rather than enthalpy. In addition, for the actual calorimeter process the reactants
and 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 accurately
given by
A(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 sum
of two steps:
1. Adiabatic reaction (q = 0):
A(T1 , P1 ) + B(T1 , P1 )

→

C(T2 , P2 ) + D(T2 , P2 )
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∆c U1

(9.11)

2. Products are returned to the initial temperature by either adding heat to the
system 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 of
combustion 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 the
isothermal standard-state process (boxed). Calorimetry is typically done at or near
298 K and in most cases it is reasonable to assume that T0 ≈ T1 . In addition to this
simplification, 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 correction
to standard states, called the Washburn correction, may amount to several tenths of 1
percent and is important in work of high accuracy; consequently, we will neglect it for
this experiment. The principal Washburn correction terms allow for the changes in U
associated with (a) changes in pressure, (b) mixing of reactant gases and separating
product gases, and (c) dissolving reactant gases in, and extracting product gases
from, the water in the bomb.
To find ∆c U we simply need to sum ∆U1 and ∆U2 . Since step 1 was carried out
adiabatically, ∆U1 = 0 and, consequently, ∆c U = ∆U2 . To find ∆U2 , we need to
measure the heat required to bring the combustion products back to the starting
temperature. 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 can
calculate, the heat capacity of the system, the change in temperature associated
with step 1 can provide the requisite information to find ∆U2 . From the first law,
we know that
dq = dU =

∂U
∂T

dT = CV dT

(9.13)

V

After integration, the energy change in going from T2 to T1 (step 2) is given by
T1

∆U =

CV dT
T2

135

(9.14)

Note that the heat capacity we are interested in is for the system and does not
include the heat capacity contribution from the products. For small temperature
changes, 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 and
a measured temperature change. In the second part, we use the calculated heat
capacity to find an unknown ∆U with a measured temperature change.

9.2

Experimental

Figure 9.2: Calorimeter cross-section

About the calorimeter: A bomb calorimeter has the metal bomb inside of a
metal bucket containing water. That metal bucket sits loosely inside an insulated
jacket. There is a stirrer that sticks into the water in the bucket and is driven by
a motor outside of the calorimeter. A thermometer also sticks into the water in the
bucket and is the device that will be used to determine the change in temperature
during the reaction. Two electrical leads connect to the top of the bomb from outside
and 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 and
a 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 pressure
has 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 the
inlet side there is a check valve, which opens when pressure is applied and closes
automatically when the supply is shut off. On the outlet side gases are released
through an adjustable needle valve, passing through a longitudinal hole in the valve
stem and discharging from a short hose nipple at the top. Turning a knurled adjusting
knob controls gas flow through the outlet valve. A deflector nut on the inlet passage
diverts the incoming gas so that it will not disturb the sample. A similar nut on
the 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 are
produced 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 continually
subjected to high temperatures and pressures that apply heavy stresses to the sealing
mechanism. The mechanical condition of the bomb must therefore be watched carefully and any parts that show signs of weakness or deterioration should be replaced
before 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 any
uncertainty as to its age or condition. Also check and replace the sealing rings in the
valves and insulated electrode if there is any evidence of leakage at these points. Do
not fire a bomb if gas bubbles are observed. Disassemble the bomb and install
new 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. If
this happens in the 1108 bomb, unscrew the valve body and replace the 20VB valve
seat. Always keep the 397A-packing nut in this bomb tightened firmly in order to
maintain a tight seal between the 20VB valve seat and the valve body.
Never under any circumstances use oil on valve or fittings that handle compressed
O2 . This precaution applies to all of the O2 bomb parts as well as to the O2 filling
connection.

137

Although Parr O2 bombs are made from alloys that will withstand most corrosive
gases, these bombs will not resist chlorine, fluorine, or bromine in the presence of
moisture. If samples yielding appreciable amounts of these elements are burned in a
Parr bomb, the interior surfaces may become etched or corroded. In such cases, the
bomb should be emptied and washed as quickly as possible after each combustion.

Figure 9.3: Parr bomb cross-section

The metal bomb provides a constant-volume system in which the combustion
reaction will take place. The sample pellet is placed in the ignition cup and the fuse
wire is carefully arranged to touch the pellet but not the cup. The bomb is sealed
by screwing the cap on and then filled with a high pressure of pure into the water
bucket.
Precautions which must be followed to avoid explosion of Parr bomb
1. 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 submerged
in water.
4. The operator should stand back for at least 15 seconds after igniting the sample
and should keep clear of the top of the calorimeter. An explosion would be
most likely to drive the top upward.
5. Much less than 1 g sample should be used for testing materials of unknown
combustion characteristics.
6. The use of high-voltage ignition systems is to be avoided. Arcing between
electrodes may cause the electrode seals to fail and permit the escape of hot
gases with explosive force.
Standardizing the calorimeter
Standardization procedure: The term “standardization as used here denotes
the 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 one
degree, expressed as calories per degree Celsius. The procedure for a standardization
test is exactly the same as for testing a fuel sample. Use a pellet of calorific grade
benzoic acid weighing not less than 0.9 or more than 1.25 g. Determine the corrected
temperature rise, t, from the observed test data, also titrate the bomb washings to
determine the nitric acid correction and measure the unburned fuse wire. Compute
the energy equivalent by substituting in the following equation:
Hm + e1 + e3
t
W = energy equivalent of the calorimeter in cal/o C
H = heat of combustion of the standard benzoic acid sample in cal/g
m = mass of the standard benzoic acid sample in g
t = net corrected temperature rise in o C
e1 = correction for heat of formation of nitric acid in cal
e3 = correction for heat of combustion of the firing wire in cal
W =

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 11.9
ml of standard alkali and 8 cm of fuse wire were consumed in the firing. Substituting
in the standardization equation,
H = 6318 cal/g
m = 1.1651 g
e1 = (11.9 ml) (1 cal/ml) = 11.9 cal
e3 = (8 cm) (2.3 cal/cm) = 18.4 cal
t = 3.077 o C
Therefore,
W =

(6318)(1.1651) + 11.9 + 18.4
= 2402.1 cal/o C
3.077

(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 specific
which will assure complete combustions for all samples. However, two fundamental
conditions 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 sufficient
heat to support its own combustion regardless of the chilling effect of the adjacent
metal parts. Second, the combustion must produce sufficient turbulence within the
bomb 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 of
the following causes:
1. Excessively rapid admission of gas to the bomb during charging, causing part
of the sample to be blown out of the cup.
2. Loose or powdery condition of the sample that will permit unburned particles
to 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. Either
condition 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, causing
the fuse to break before combustion is under way.
140

6. Insertion of the fuse wire loop below the surface of a loose sample. Best results
are obtained by barely touching the surface or by having the wire slightly above
the sample.
7. The use of insufficient O2 to burn the charge, or conversely, the use of a very
high initial gas pressure that may retard the development of sufficient gas
turbulence 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 thermal
quenching.
Magnitude of Errors: The following examples illustrate the magnitude of errors
that may result from faulty calorimeter operations. They are based upon an assumed
test in which a 1.0000 g sample produced a 2.800o C temperature rise in a calorimeter
having an energy equivalent of 2400 cal/o C.
• An error of 1 ml in making the acid titration will change the thermal value 1.0
cal.
• An error of 1 cm in measuring the amount of fuse wire burned will change the
thermal value 2.3 cal.
• An error of 1 g in measuring the 2 kg of water will change the thermal value
2.8 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 thermal
value 4.8 cal.
If all of these errors were in the same direction, the total error would be 17.6 cal.

141

9.3

LabVIEW

Temperature Measurement Using Computer Data Acquisition System
and LabVIEW Program 11
In the tradition of calorimetry experiments, at least the one described in your
lab write-up, temperature is measured by a thermometer and a series of readings
are taken to follow the temperature change over the entire combustion and heat
transfer process. In this experiment, besides the conventional calorime6try method,
you will learn how to take advantage of the modern computerized data acquisition
technique. Instead of a thermometer, you will be using a thermocouple to measure
the temperature and letting the computer read and record the data. At the same
time, you will also have the opportunity to program the analog-to-digital converter
board using LabVIEW software.
Before the lab: Read “Getting Started with LabVIEW” and attend one of the
prelabs.
Procedure:
1. Practice programming in LabVIEW
(a) After attending the prelab, get a floppy disk from the stockroom. You
are allowed to use this disk on the PC designated for this lab experiment
ONLY during the lab period you are doing the lab. This means after the
lab, take it home and use whatever software you are comfortable with to
do the data analysis. NEVER bring it back.
(b) Turn on the computer and start Windows XP. Insert you floppy disk to
the drive and format it.
Using the mouse, double click on “My Computer,” then right click the
floppy drive icon to bring down the menu. Select ”Format” to format the
disk.
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 floppy
disk.
11

modified by Andrew Duffin, Spring 2007

142

Right click the file to open the drop-down menu, then choose “copy.”
Double click “My Computer” on the desktop background, then double click
the 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 allowed
to operate files ONLY on this floppy disk.
(c) Following the “Getting Started with LabVIEW” build your own Random
Number Generator and test it. When you succeed in Step 8 save your data
file into your own floppy disk as “data1.txt.” Also save your VI program
file. In the next step, use “Notepad” to open that data file.
Click “Start” at the bottom left corner of the computer screen. Move the
mouse 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 spreadsheet
software prefers all data listed in a column, which looks like
0.875
0.578
0.234
0.478
0.211
…
(d) To transpose the above data array, do the following: Right below the
picture of the “Write to Spreadsheet File.vi” (figure 9.4), create a Boolean
constant (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 finger
pointed 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 Boolean
constant (figure 9.5) icon. Make sure you find the correct terminal on the
icon 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 the
mouse 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 new
generated file to “data2.txt.” Use Notepad to check if your data array is
144

transposed. Close the program and all windows in LabVIEW and go back
to 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 LabVIEW
dialog page. It will be open as a panel. Click “Windows” on the top menu
bar and choose “Show Diagram.” In a new window, you should see the
diagram 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 signal
to temperature (in degrees C). You should build a complete program
based on it, without changing it too much:
• The whole program is inside a “For loop,” which controls everything
inside to repeat 100 times (preset by the number on the upper left
corner). The whole loop takes about 1 second to finish. When the
loop is running, data can be obtained from outside through tunnels
145

•

•
•
•

•

(black marks on the right side of the loop box in this handout, orange
boxes on the computer screen).
Inside the Loop on the left there are two analog input readout boxes
using channels 0 and 1 on the A-to-D board. Channel 0 reads the
thermocouple 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 reading
compensation” to correct the nonlinear readout behavior of the voltage readout. The equation box is obtained by calibrating the board
with a high precision digital voltmeter.
The corrected signal is then split. One way goes directly out of the
box, labeled as “TC output (mV).”
You do not really need to use this signal in the experiment, but it
helps to check how accurate out data acquisition board is, by hooking
the output to an indicator and comparing the reading with the digital
voltmeter reading. See 2h
The other goes to the second equation box labeled as “Voltage
→ Temperature Conversion,” in which the equation is obtained by
fitting data in the 20 to 30 degree C region in the standard type
E thermocouple output chart. Between 17 and 32 degrees C, the
accuracy of the equation is better than 0.01 C. A digital indicator
labeled as “T sample” and also directed out of the “For Loop,” ready
to use, then displays the output of this equation.

(b) Outside the “For Loop,” build a mean function and indicator. Using
the “Wiring” tool, wire the Temperature output (the lower tunnel) to
the X input terminal of the “Mean VI.” Now you can average the 100
temperature readouts generated by the “For Loop” and display the mean
value 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 test
purposes. Later, during the experiment, change it to 15-30 or whatever
you 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 inside
the “While Loop.” Then wire the switch terminal to the conditional
terminal.
(e) Select “Write to Spreadsheet File.vi” and place it outside the “While
Loop.” Transpose the data array, as described above in 1c. Wire the 1D
data 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 new
tunnel 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-Packard
Digital Multimeter and to the National Instruments AD board. Make
sure that throughout the entire lab the cold reference junction of the
thermocouple 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 your
hand) and see if the digital indicator and wave graph give you the correct
response. Do not forget to turn on the toggle switch to keep the “While
Loop” running. When you turn off the toggle switch, a file saving window
will pop out. If you like, save the data file, then open it by Notepad, and
check if the data are correctly reco…