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University of Notre Dame

CBE 358 (Junior Class)

Chemical & Biomolecular Engineering Laboratory I

LABORATORY MANUAL

Spring 2014

Salma Saddawissaddawi@nd.edu(574) 631-3324

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TABLE OF CONTENTS

Page

I. GENERAL INFORMATION 2

A. Safety 2

B. Laboratory Format and Procedures 2

1. Organization of Student Groups and Laboratory Projects 22. Laboratory Session 1 23. Laboratory Session 2 and the Progress Report 3

4. Session 3 3

5. Final Project Report and Oral Defense. 36. Oral Presentations 37. Laboratory Notebook 3

8. Student Responsibilities in the Laboratory 4

9. Grading 4

II. Guidelines for the Preparation of Written Reports 4

1. Title Page 4

2. Abstract 53. Table of Contents 5

4. Introduction 5

5. Theory 56. Experimental 5A. Apparatus 5

B. Procedure 6

7. Results 6

8. Discussion 69. Conclusions and Recommendations 6

10. Literature Cited 6

11. Nomenclature 7

12. Appendices 7

III PROJECT STATEMENT 9(Page 9 gives page reference to the individual statements.)

IV. Appendix A 142

A NOTE ON STATISTICS 142

Sample Output 146

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I. GENERAL INFORMATION

A. Safety

Laboratory safety is the top priority and this requires all people in the lab to be observingsafe practices at all times!

Safety glasses must always be worn by everyone in the laboratory.

Make sure you understand how the experimental apparatus works and what all

of the adjustments do before you attempt to operate it.

Be sure you have asked, and received an answer, from the Professor or the TA,about any possible hazards related to your experiment before attempting to

operate it.

Care must be used in the handling of chemicals to avoid spills and to avoidcontact with the skin.

B. Laboratory Format and Procedures

1. Organization of Student Groups and Laboratory Projects

Students will organize into groups of three persons. Each group is to perform four

projects during the semester. (A roster of the groups and a schedule of projects will be

supplied separately.)

A group leader, who is in charge of directing the work for the lab, should be selected by,

and from among, the members of the group. (This responsibility should rotate among the

members.) All group members must be prepared for the laboratory and contributeequally to the laboratory work and preparation of the reports. However, the group leader

is in charge of assigning and coordinating tasks for the laboratory period and maintaining

the group notebook. He or she is ultimately responsible for making sure that everything

is done to ensure a successful experiment.

Each project consists of three laboratory sessions and a series of three reports --a

preliminary report, a progress report and a final report. A description of each of these

components follows.

2. Laboratory Session 1

At the beginning of the first session for a given experiment, a paragraph describing the

experimental plan and procedure should be submitted to the TA who is in charge at that

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7. Laboratory Notebook

Part of the purpose of the chemical engineering laboratories is to learn good laboratory

and research practices. An important aspect of this is safety. Another important aspect isrecord-keeping and documentation. In industry you will find that all experiments have to

be carefully recorded in an official laboratory notebook and signed by the investigator on

a daily basis. To help foster these professional practices, each group is required to keep a

laboratory notebook documenting the group's work. Each group should purchase theEngineering & Science Notebook, available at the Bookstore. In the notebook should be

kept a neat, labeled and dated record of all work associated with the experiment,

including a copy of the precis, all raw data, the settings on the experimental controls, any

problems encountered in the experiment and what was done to fix them and why, allcalculations, a copy of your progress report, etc. The laboratory notebooks will be

handed in at the end of the semester and will contribute to the laboratory participation

portion of your grade.

8. Student Responsibilities in the Laboratory

Condition of Working Area. Students are responsible for the condition of their working

area at the end of each laboratory period. All power to the equipment and instrumentsshould be turned off, and steam and cooling water flows should be shut off. Glassware

used should be cleaned and dried. Any equipment or instrumentation malfunctions

should be reported promptly to the instructor or the TA.

Checkout before Leaving Laboratory. The students must have their notebooks initialed

by a faculty member or the teaching assistant prior to leaving at the end of the laboratory

period. At that time the faculty member or teaching assistant will check the working area

and take information about any equipment or instrumentation problems.

9. Grading

Report grading is done by the Professors who are in charge of a given experiment. This

grade will be based on the written report, the oral defense and other pertinent factors(e.g., if you are totally unprepared to do an experiment, you will be docked.) Grades for

this course will be determined by the grades on the four experiments as well as yourlaboratory participation. The laboratory participation portion of your grade in will

include how well you followed laboratory safety guidelines (did you wear safety glasses

at all times in the lab? did you follow the special safety precautions required for each

experiment?), attendance, tardiness, participation, professionalism, how effective a group

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leader you were, and the quality of your laboratory notebook. Both laboratory instructors

and teaching assistants will contribute towards this portion of your grade.

II. Guidelines for the Preparation of Written Reports

A technical report is a medium commonly used by scientists and engineers to

communicate the results of their work. Frequently the report is the only tangible product

and thus the only evidence for evaluation of the work. Consequently, it deserves careful

attention to quality, packaging, and distribution.

It is important that the writer(s) of an engineering report keep in mind the needs and

interests of the anticipated readers of the report. The laboratory report should be written

with the same professionalism that would be used to present the results of a majorindustrial project. The people who will read it, and need to draw conclusions from it, can

be expected to have technical training, but probably would not be familiar with the details

of the work.

A good report of technical work quantitatively states significant results of experiments

and computations and explains how they were obtained, what they mean, and how they

are useful. The report should be clear, concise, and accurate. Often the structure of the

report must conform to specific conventions. A format for laboratory reports that is to beused in this course is given below.

1. Title Page

The title of the report is followed by names of the authors and laboratory group, the date

of submission, and identification of the institution or organization supporting the work(University of Notre Dame, Department of Chemical Engineering, CHEG 358).

2. Abstract

The abstract is a tightly written summary, typically 100 to 300 words long. This sectionis important because it is the first impression your report will make to a reader, and it

could very well be the only part of it he or she will read! (Because of its importance, it is

a significant part of the overall grade.) The abstract should be written as stand alone

section of just text. Its independence means that the use of symbols, tables, and graphs aswell as literature references should be avoided. A good abstract states the principal

objective of the investigation, describes the methodology used and summarizes the resultsand conclusions in statements as quantitative and as general as possible.

The abstract should provide ranges of the experimental parameters (e.g. the Reynolds

number was varied from 100 to 10000), report the most important results and state how

these values compare to expected (i.e., literature) ones. (e.g., values for the friction

factor in the laminar flow regime were consistently 15% higher that the predictions ofPoiseuille flow). If the value of a single variable or a short list of numbers is given, the

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numbers should give the uncertainty (e.g., solubility at 25C was 25 3 moles/liter) and

of course units should be included.

We recommend that you write the abstract last, when your thoughts are most clearly in

focus (i.e., you know all the answers and thus know what to say!).

3. Table of Contents

A Table of Contents should be included in the report, including a listing of the Abstract.

Appendices should also be listed. All pages should be numbered, including tables,figures, and appendices.

4. Introduction

The purpose of the Introduction is to place the work in the perspective of prior work

including key literature references, demonstrate its importance, and state the specific

objectives. The Introduction should not exceed two pages.

5. Theory

This section is a short, concise statement of the essential empirical and theoretical

relations to be used in interpreting the data or to be tested by the data. Equations areusually stated with a reference, along with the pertinent assumptions and limitations.

Brief manipulations may be appropriate, but long derivations are relegated to an

appendix. The physical significance of equation parameters should be pointed out.

6. Experimental

A. Apparatus

The objective of this section of the report is to describe the experimental set-up in

enough quantitative detail to enable the reader to completely understand the

experiment. Ranges of independent variables are cited. The model and supplier

of any unique equipment should be cited. Also, a schematic diagram of theexperimental apparatus should be included.

B. Procedure

The objective of this section of the report is to describe the materials and methods

used to obtain the experimental data. Emphasis is placed on general procedures

that are not routine

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7. Results

The data, or a representative fraction of them, must be included in this section. They

should be presented graphically. If there are only a few (i.e. 2-3) numbers, these could

put into a table if they can be understood. Data are often not presented in raw form, but

are reduced and shown in the way most clearly supporting the conclusions.Representation of scatter in data is essential. For example, the experimentally determined

heat transfer coefficient is meaningless unless it is accompanied by units and an

estimated uncertainty. Comparison of data with theoretical predictions and/or previously

published values should be included whenever possible. This may require searching forinformation in reference books or research articles. Comment briefly on unique aspects

of the results, in particular its accuracy. Also comment on the range of the variables

covered.

Each graph or diagram is assigned a number (e.g., Figure 1) and should have a caption

that is descriptive of the information contained in the figure. A restatement of the

information on the axes is not an acceptable title.

8. Discussion

All important interpretations which follow from the results and the underlying theory are

logically and quantitatively compared in the Discussion section. The positiveconclusions, comparison with literature data, and the significance applicability, and

reproducibility of the results are stressed. Quantitative statements about the accuracy and

precision of the results are required. However, when a detailed error analysis is essentialto the work, it should be relegated to an Appendix.

9. Conclusions and Recommendations

This section is a summary of the most significant conclusions developed in the precedingsection. Quantitative statements are best. Useful recommendations to improve the

experiment and to extend the work to other systems, should be included here.

10. Literature Cited

Only references cited in the report are to be listed is this section since it is not a

bibliography covering all references but only the most pertinent ones. Footnotes onindividual pages of the report are not to be used. References cited in the text of the final

project report should give the last name of the author (both authors when only two; first

author et. al. when more than two) and the corresponding page numbers. An example is

given below.

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The Reynolds number can be interpreted as the ratio of inertial to viscous forces at work

in the fluid (Denn 37-39).

References are to be listed in alphabetical order according to author or equivalent and

should not be numbered. Use Chemical Abstracts Service Source Index journal

abbreviations. For the previous example the citation would be the following:

Denn, M. M. Process Fluid Mechanics; Prentice-Hall; New Jersey, 1980

Typical citations for a journal are given below.

Danckwerts, P. V.; Sharma, M. M. Chem. Eng. (London) 1966, 202, 244.

Danckwerts, P. V. Chem. Eng. Sci. 1979, 34, 443.

11. Nomenclature

Symbols used in the report are defined immediately after they are presented the first time.This section of the report lists all of the symbols used. Units should be included.

12. Appendices

The appendices contain material of secondary importance: sample calculations (a sample

of all calculations done for the experiment must be included in the report), error analysis,

derivation of theoretical relations, and perhaps graphs, calibration curves and/orschematics. Note that the appendices should be named in the order of which they appear

in the final project report. In other words Appendix A should be the first appendix

referred to in the text of the report.

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III PROJECT STATEMENT

1. FM = Pipe Flow 102.

HT2 = Heat Exchanger 18

3. HT1 = Natural Convection 364. MT = Diffusivity Measurement 445. MT2 = Leaching Rate Measurement 506. TD1 = Phase Equilibrium 567. FM2 = Fluidization and fluid Bed Heat Transfer 728. TD2 = Liquid mixture viscosities 869. HT3 = Unsteady State Heat Transfer Thermal Diffusivities And

Heat Transfer Coefficients 93

10.PI-plus-Feedforward Water Level control for Coupled WaterTanks 109

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EXPERIMENT FM1

FLOW IN CIRCULAR PIPES

OBJECTIVE

To measure the pressure drop in the straight section of smooth, rough, and packed pipesas a function of flow rate, to correlate this in terms of the friction factor and Reynolds number

and to compare results with available theories and correlations. To determine the influence of

pipe fittings on pressure drop. To determine the discharge coefficients of the Orifice plate and

the Vernturii meter.

APPARATUS

Pipe Network Rotameters

Manometers

The pipe network consists of seven flow loops. The first three flow loops are smoothround pipes with inside diameters (ID) of 0.269", 0.622" and 0.824". The fourth loop is 0.824"

ID and has rough walls. The fifth loop is 0.824" ID. In it there is a 12" long section packed with

0.92 mm spheres that is 0.8" ID. The last two loops have a gate valve, a globe valve, a strainer,

an orifice plate, and a venturi meter.

The flow of distilled water is directed through a particular loop by valves located at the

entrance to each loop. The flow rate through the system is controlled by adjustments to the valvein front of the rotameters. The two rotameters allow for a wide range of flow rates. The pressure

differences are measured with heavy liquid manometers and electronic manometers. The ends of

the pressure taps are connected to the manometers and to different locations along the piperesulting in varying lengths. Note: Pipe Network diagrams are included.

THEORETICAL DISCUSSION

a. Pipe Flow

Fluid flow in pipes is of considerable importance in process plants, long distance

pipelines and has applications to circulation systems in animals and plants. Fluids could be, for

example, a single phase liquids or gases, mixtures of gases, liquids and solids, nonNewtonianfluids such as polymer melts, mayonnaise or potato salad. For any of these flows a key issue is

the relation between flow rate and pressure drop.

Recall from CBE 355 that for a Newtonian fluid such as water, which will be used in thisexperiment, the Navier-Stokes equations will govern the flow field. If the flow is steady, fully

developed, laminar (straight streamlines), the velocity distribution and the average velocity are

(Bird, Stewart, Lightfoot, 2002)

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vz

vz,max

=1" r

R

#

$%

&

'(

2

andvz

vz,max

=

1

2 (1)

then, the Navier-Stokes equations can be solved exactly to obtain the Hagen-Poiseuille relation

(Middleman, 1998),

Q =!R

4

8

"P

L (2)

where Qis the volumetric flow rate,Ris the tube radius, is the dynamic viscosity, and !P/Lis

the pressure drop. It will be interesting to verify this result with experiments.

At higher flowrates, the streamlines are not steady and straight and the flow is not

laminar. Generally, the flow field will vary in both space and time with fluctuations that

comprise "turbulence". For this case almost all terms in the Navier-Stokes equations areimportant and there is no simple solution. Fortunately dimensional analysis of the pertinent

variables (Middleman, p233), !P= F(D, , !,L, U, plus some further arguments about a fully-developed flow not depending on distance,L, yields an expected relation between two

dimensionless groups. The first is the Reynolds number,

Re!DU"

, (3)

which gives the ratio of inertial to viscous forces. The second one is the friction factor,

f !"P

L

D

2#U2 (4)

relating pressure drop to inertia forces. The expected function is thus

f =F(Re) (5)

For laminar flow it can be shown that equation (1) yields

f =16

Re Re < 2100 stable

Re > 2100 unstable

"

#$

%

&' (6)

For turbulent flows, the appropriate function is obtained through experiments. A relation that fitsdata reasonably well is (Bird, Stewart, Lightfoot, 2002)

f = 0.079Re!0.25

2.1*103< Re < 105 (7)

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If the pipe is not smooth, there is (at least) one additional length scale, ", that is needed to

characterize the roughness. This leads to an additional dimensionless group, "/D, and thus more

than one curve on the friction-Reynolds number plot (see Bird, Stewart, Lightfoot, 2002 page182).

b. Flow through fittings.

Any interesting piping system will have a variety of fittings. These could include valves,

couplings, expansions, and contractions. Denn (1980), notes that pressure losses caused by these

devices are usually correlated by an equation of the form

Ev ="p

#=

K

2U

2, (8)

whereEvare the losses in terms of "velocity heads" and K is a coefficient depending upon the

fitting. For a piping system, the total losses, in terms of, say, a Bernoulli equation are obtained

by summing contributions from eq(7) for all of the fittings and adding to all of the straightsections of pipe.

Flow measuring devices such as orifice plates or Venturi meters can also be present.

Q =CdAo2"p

#1$%2( )

&

'((

)

*++

1/ 2

(9)

where Cdis the discharge coefficient for these devices, and "is the ratio between the throat andthe pipe cross sectional areas (Ao/Ap) (see Middleman page 476).

c. Flow in a packed region

Chemical Engineers often deal with packed-bed reactors where the "pipe" is filled with

solid catalyst particles. The equations for empty pipe flow do not work without considerablemodification. What does work is an empirical relation called the Ergun equation (Middleman,

1998),

f !"PDp#

3

L$Uo2(1 % #)

=

150(1% #)

UoDp$+1.75. (10)

It is common to define the Reynolds number for a packed bed flow as

Re =UoDp!

(1" #). (11)

In these equations,Dpis the particle diameter, #is the volume fraction that is not occupied byparticles (void fraction and Uois the superficial velocity. Equation (10) contains the interesting

behavior that the pressure drop varies as the first power of Uofor smallReand as Uo2for higher

Re(see Bird, Stewart, Lightfoot, 2002 page 189-192).

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Experimental ProcedureMake sure the back valve is open before turning on the pump. This will prevent pressure

buildup in the somewhat fragile acrylic pipe.

Open all valves leading to the flow loops in the pipe network. Turn on the valves used to adjust

the rotameters flow rate to get a maximum flow and allow the water to flow for 10 minutes to de-aerate the pipe network form the air. Close all valves except one of the valves leading to the

chosen flow loop, and then adjust the rotameters flow rate to get a desired flow rate then.

Calibrate the rotameters using the graduated cylinder and a stopwatch.

To prevent damage to the manometers, connect the pressure taps of the high scale manometer(channel 4) at the desired positions. If the differential pressure is too low, use the low scale

manometer.

Measure the pressure drop with the liquid manometers and the electronic manometers for the

first four pipes over various lengths of pipe and at various flow rates. Make sure that the gatevalve and the globe valve are fully open before you open the valve leading to the flow loop

containing them. Measure the pressure drop across the gate valve, globe valve at fully, half and

quarter opining andthe strainer at various flow rates. Measure the pressure drop across thepacked pipe, the orifice plate, and the venturi meter at various flow rates as well. Selectconditions enabling you to cover laminar and turbulent flow regimes. Then, establish the

reproducibility of your measurements.

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1. a smooth pipe of ID =

2. a smooth pipe of ID =

3. a smooth pipe of ID =

4. a rough pipe of ID = 0.824"

5. a packed pipe of ID = 0.8"

6. a smooth pipe of ID = 0.824"

has a gate valve, a globe valve and a strainer

7. a smooth pipe of ID = 0.824"has an orifice plate and a venturi

Pipe Network

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Pipe Flow program

I. Create a new folder on the computer desktop for your work group.II. LaunchLabViewwhich located on the disktop.III. Open the file called Flow Through.IV.

Select a channel to be monitored before starting the run.V. Start the program by clicking on the arrow located in upper left-hand corner.

VI. Choose a name for the file that will be created by the run and save it to the new folderyou created in the first step.

Note: Changes during the run

1. The graph view can be altered. Holding down the mouse button with the handcursor positioned over the graphing area will allow the graphing view to be

moved to a desired position.2. The X, Y axis can also be changed while the program is running. Highlight the

value that is to be changed then type in the new value and hit-enter.

3.

Changing the channel during a run will result in faulty data. The correct channelmust be selected before the run begins.

VII. When the run is complete hit the Stop button.VIII. LaunchMicrosoftExcelfrom the Apple menu and open the new file created from the

run. The first column of data is the time in seconds. The second column containspressure differences data.

IX. May be you need to calibrate the data with the liquid manometers data for various flowrates.

Suggested Report Items

1. Verify the universality of your friction factor- Reynolds number relations for a smooth pipes.2. Verify the form of the equations for a packed bed and rough pipes.

3. Determine the head losses due to fittings and K coefficient values.

4. Provide an assessment of the quantitative agreement between your data and established

correlations. Use a systematic error analysis technique to justify the extent of agreement.

More details can be found on the Saddawi webpage

DYE DEMONSTRATION

In 1883 Osborne Reynolds made an important contribution to the field of fluid mechanics

when he demonstrated with his famous dye stream experiment that two flow regimes areexpected to exist. For sufficiently small flow velocities the dye stream did not disperse radially.

This type of flow came to be known as "laminar" flow. For faster flow the dye stream mixed

very rapidly; this is the so-called "turbulent" flow regime. It is expected, therefore, that some

sort of transition region exists between laminar and turbulent flows. (See the table below.)

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Similar transitions can frequently be observed in a rising smoke stream as illustratedbelow. Or from the Notre Dame power-plant gas turbine stack on a very cold, still day.

Your report should include a description of your observations.

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REFERENCES

1. Bird, R. B., Stewart, W. E., Lightfoot, E. N., Transport Phenomena, Wiley, 2002.

2. Bennett, C. O., J. E. Myers, Momentum Heat and Mass Transfer, McGraw - Hill, 1982.

3. Denn, M. M., Process Fluid Mechanics, Prentice-Hall, New Jersey, 1980

4. Geankoplis, C., Unit Operations and Transport Processes, 3rd Ed., Prentice Hall, 1993.5. Middleman, S., An Introduction to Fluid Dynamics, Wiley, 1998

5. Nevers, N, Fluid Mechanics For Chemical Engineers 2nd Ed, McGraw-Hill, Inc., 1976

6. Welty, J. R., Wicks, C. E., Wilson, R. E., Fundamentals of Momentum, Heat and Mass

Transfer, 3rd Ed., John Wiley & Sons, 1984.

S. Saddawi,

January, 2014

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EXPERIMENT HT3

HEAT EXCHANGER

Heat Transfer and Heat Exchangers

Heat transfer is one of the most studied subjects of engineering because virtually every

industrial process involves at least some heat exchange. A device whose primary purpose is thetransfer of energy between two fluids is called a heat exchanger. Traditionally, equipment was

designed with the aid of correlations that were expected to be accurate for the specific flow

geometry and conditions. Recent advances in numerical techniques combined with greater speed

and memory in computers has lead to an increasing reliance on calculated results that may be"exact" if the flow is laminar or obtained from models for turbulent flow.

Figure 1. A double-pipe heat exchanger

The closed-type exchanger is the most popular one. (One example of this type, the

double-pipe exchanger, is shown above in Figure 1.) In this type the hot and cold fluid streamsdo not come into direct contact with each other but are separated a tube wall or a surface which

may be a flat or curved in some manner. Energy exchange is thus accomplished from one fluid

to a surface by convection, through the wall or plate by conduction, and then by convection from

the surface to the second fluid.

T1 T2T4 T5

T6T3

T7

T8 T9

T10

T1 T2T4 T5

T3

T7 T8 T9

T10

T6

Parallel Flow

Counter - Current Flow

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When a fluid flowing through a conduit is at a temperature different from that of thewalls of the conduit, heat is transferred between the surrounding walls and the fluid. This flow of

heat can be expressed as being proportional to the product of a characteristic area for the system

and a characteristic temperature-difference for the system . The proportionality factor is known

as the heat-transfer coefficient . It is evident that the magnitude and nature of the heat-transfercoefficients are directly related to the definitions of the characteristic area and characteristic

temperature-difference. For the fully developed and steady flow of fluids through circular tubes

of uniform cross-section, the heat-transfer coefficient is a function of the diameter and length of

the tube and the density, viscosity, heat capacity, thermal conductivity and average velocity ofthe fluid.

For circular tubes of uniform cross-section, which are completely filled with a flowing

fluid, the characteristic area is defined as the wetted surface through which the heat is transferred

A = !DL (1)

where: D = tube diameter

L = tube length

The characteristic temperature-difference can be determined in a number of ways,

depending on the application. In heat exchangers of the type described here, it is appropriatelydefined as the logarithmic-mean temperature difference:

("T)lm= ("T1 - "T2) / ln("T1 /"T2) (2)

where "T1= (T3-T7)

"T2 = (T6-T10) (See figure 2.)

Figure 2. Variation of !T in a counter-current heat exchanger

A = area= !DdL (where dL distance from point 1)

For steady flow the rate of heat transfer (gained by the cold fluid or lost by hot fluid) "Q" is

QH= #!Ri2CP(T3-T6) (3)

Metal

T3

T1

T7

T6

T2

T10

T5T4

T8 T9

1 2

#A

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Where #fluid density, Cpheat capacity (for hot fluid determined at its mean temp

(T3+T4+T5+T6)/4), Riinternal hot tube radius,

time-average velocity (for hot fluid) and

m

0

="< v > #Ri2

QH =

mo

Cp(T3 " T6)

Another common way of expressing the rate of heat transfer for a situation involving a

composite material or combination of mechanisms is with the overall heat-transfer coefficient:

Q = U A !Tlm

(4)

The value of the overall heat-transfer coefficient, U, can be calculated from Equations (3) and(4).

U = [(T3-T

6)/!T

lm] [#C

p/4] [Di/L] (5)

Or U = [(T3-T

6)/!T

lm] [m0 C

p/A

lm]

WhereAlm

mean surface area (logarithmic mean for cylindrical conduits).

Alm

= (Ao-Ai)/ln(Ao/Ai)

The rate ofheat transfer can also be evaluated from the heat flux at the wetted surface of the tube

if the temperature gradient in the flowing fluid can be determined at the solid-fluid interface.

For steady and fully-developed flow of fluids where forced convection exists:

Nu = ( Re, Pr, L/D) (6)

where Nu = (hiDi)/ k; Nusselt number

Pr = (Cp)/k; Prandtl number

Re = (#D < v >) /; Reynolds number

h i= individual heat-transfer coefficient

Di= internal tube diameterk = thermal conductivity of fluid = fluid viscosity

Cp

= heat capacity

All above physical properties should be determined at hot fluid mean temperature T m

Tm= (T3+T4+T5+T6)/4)

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When the temperature gradient in the fluid is known, the exact functional form of Equation (6)can be determined. For laminar flow in a tube of circular cross section, where the velocity

profile is parabolic, the dimensionless, independent variables given in Equation (6) appear in

combined form as the single, dimensionless, independent variable, [ ( Re Pr D)/L]. In particular,

a limiting exact formof Equation (6) for conditions of constant temperature at the interface andshort tube-lengths or high flow-rates is

Nu = 1.62 [ (Re Pr D) /L]1/3 (7)

Owing to the complicated nature of the temperature distribution in turbulent flow, which

in turn requires a knowledge of the rate of momentum transfer at the solid-fluid interface, a

precise, functional form of Equation (7) cannot be determined in the same exact manner as forlaminar flow. It has been possible, however, to predict the local Nusselt number as a function of

the independent variables given in Equation (7) in a semi-theoretical manner. For highly

turbulent flow (Re > 10, 000) the function is of the form

Nu = a RebPrc (8)

where a, b, and c are constants.

The overall coefficient, U, can be expressed in terms of the individual fluid coefficients,

hiand ho, and the thermal resistance of the separating wall as follows:

1/Uo= Ao/hiAi + $Ao/kwAm + 1/ho (9)

where Uo= overall coefficient based on area Ao.Aoand Ai= surface areas on the respective sides of the separating wall.

Am= mean surface area (logarithmic mean for cylindrical conduits).

$= wall thickness.

kw= thermal conductivity of the wall material.

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The Experiment

This experiment is intended to demonstrate some of the basic principles of single phase

force convective heat transfer in closed conduits. Students will use a double-pipe heat exchanger

to determine individual and overall coefficients for heat transfer from hot to cold water over a

range of flow rates. The experimental plan should include an observation of the effects of co-current versus countercurrent operation.

Equipment

Copper-Constant thermocouples and an electronic meter are used to measure the temperature.The water flow rates are measured by rotameters. An electric heater is used to adjust the

temperature of the hot water. Students should understand the principles of operation of all of

these devices before beginning the experiment. See figure 3.

General Objectives

Develop one or more correlations for the experimental heat-transfer coefficients and

compare them to appropriate literature correlations. For this purpose, give careful thought to the

type of experimental data required and to the methods of analyzing and plotting the data. Besure to explain the theoretical basis of the literature correlation and why it is expected to describe

the present experiment. Give reasons for any disagreement between theory and experiment.

Use the experimental results in the simulation program provided in the computer withMicrosoft Excel, Macro sheet. Observe the influence of each parameter on the temperature

profile and compare it with the experimental data.

Some useful information

Heat Exchanger: Core tube Material - Copper

External diameter (do) = 9.5mm

Internal diameter (di) = 7.9mm

Length = 3*350mm

Outer tube Material - CopperExternal diameter =12.7mm

Internal diameter =11.1mm

The physical properties of the water - see appendix

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Observation Sheet

Co - Current Flow* Counter - Current Flow**

Test 1 2 3 4 5 6

Metal Wall at inlet T1 / oCMetal Wall at inlet T2 / oC

Hot stream at inlet T3 / oC

Hot stream 1st intermediate T4 / oC

Hot stream 2nd intermediate T5 / oC

Hot stream at outlet T6/ oC

Cold stream at entry/exit T7 / oC

Cold stream intermediate T8 / oC

Cold stream intermediate T9/ oC

Cold stream at entry/exit T10 / oC

Hot water flowrate l min-1

Hot water actual flow kg s-1

Cooling water flowrate kgs-1

Mean hot water temperature oC

Specific heat at mean temp. Cp /kJkg-1K-1

Density at mean temp. (hot) #/kgm-3

Thermal Conductivity

at mean temp. k /Wm-1K-1

Viscosity at mean temp. /106Nsm-2

Heat transfer from hot water Qh/Watts

Heat transfer to cold water Qc/Watts

Local heat transfer coefficient at inner

surface of core tube hi/Wm-2K-1

Local heat transfer coefficient at outer

surface of core tube ho/Wm-2K-1

Over all heat transfer coefficient U / Wm-2K-1

Over all heat transfer coefficient

Uo/ Wm-2K-1

Prandtl No. at mean temp. Pr

Reynolds No. at mean temp. Re

Nusselt No Nu

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Figure 3.

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References

1. Geankoplis, C., Unit Operations and Transport Processes, 3rd Ed., Prentice Hall, 1993.

2. Welty, J. R., Wicks, C. E., Wilson, R. E., Fundamentals of Momentum. Heat and MassTransfer, 3rd Ed., John Wiley & Sons, 1984.

3. Bird, R. B., Stewart, W. E., Lightfoot, E. N., Transport Phenomena, Wiley, 1960.

4. Bennett, C. O., J. E. Myers, Momentum. Heat and Mass Transfer, McGraw - Hill, 1982.

5. Foust, A. S. et al., Principles of Unit Operations, Wiley, 1960.6. McCabe, W. L., Smith, J. C.~ Unit operations in chemical engineering, McGraw-Hill, 1985.

Saddawi

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Appendix

Figure 4-1.

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Figure 4-2.

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Figure 4-3.

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Figure 4-4.

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Figure 4-5

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Figure 5.

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Figure 6.

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Figure 7.

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EXPERIMENT HT2

NATURAL CONVECTION AND RADIATION HEAT TRANSFER

FROM AN ELECTRIC LIGHT BULB

Objective

The aim of this experiment is to measure local natural convection heat transfer coefficients from

spheres. The Nusselt number is obtained and compared with an existing literature correlation.

Apparatus . Infra-red Electric Bulb and Protractor Support Stand

. Portable Potentiometer

. A. C. Auto. Transformer

. Lab View computer program

Introduction

Although mean natural convection heat transfer coefficients from spheres have been reported in

the literature, we know of no studies which have reported local natural convection heat transfer

coefficients from spheres. In this experiment, local natural convection heat transfer coefficients

from a horizontally mounted electric light bulb are measured. A 500 watt infra-red "spherical"bulb is employed. The bulb is obviously not a true sphere since it has a stem; however, by

mounting a fine thermocouple as a temperature sensor in a certain location on the bulb, it is

hoped that the effect of the stem of the bulb on the thermal measurements will be largelyeliminated. The essential apparatus making up the experiment is shown below.

The electric light bulb is mounted on a stand and the power to the lamp is supplied by a variableautotransformer which has a voltmeter, ammeter, and watt meter built into it. Eightthermocouples attached to the electric light bulb, one located in the front of the light bulb and the

others will distributed in an angle of 30ostarting from the top of the light bulb, the lead wires areattached to a thermocouple interface. The thermocouple interface is hooked to the computer

which contain a Lab View program. The data will be saved in a spreadsheet format for farther

analysis.

The electric light bulb is regarded to be a true sphere of diameter 3.783 inches. The voltage

delivered to the tungsten filament of the sphere is assumed to be radiated in an uniform intensity

in all directions. However, of the wattage which is delivered to the filament, a small amount is

radiated as light which is transmitted through the glass; a larger amount is radiated as short-waveinfra-red radiation which is also transmitted through the glass - the rest is absorbed by the glass

and then lost by direct radiation and natural convection. The fraction of the wattage, which is

absorbed by the glass, is converted to Joules, and this is divided by the area of the idealized

sphere to give a heat flux. This heat flux is assumed to be of uniform magnitude in all directions.However, it is likely that convection heat transfer from the filament by argon gas within the bulb

causes local overheating near the top of the bulb.

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Procedure

Start the computer program which is described below. Turn on the auto transformer by turning

the lower toggle switch on the right-hand side of the transformer to 120 or 140 V. Adjust the

wattage to the desired value (0-300) watts. The pens on the recorder should move accordingly.

Check all thermocouple graphs on the computer Lab-View program. When no furthertemperature variation is observed, (generally at least 5 minutes is necessary) the following

readings may be taken: Voltage, amperage, and wattage and thermocouple readings (i.e. at 0, 30,

60, 90, 120, 150, 180, and 270 degrees).

Note: Please do not exceed 300 watts

Thermocouple Tracking Program

1.Create a new folder on the computer desktop for your work group.2.Launch LabView from the Apple pull down menu.3.Open the file called Natural Convection.4.Start the program by clicking on the arrow located in upper left-hand corner.5.A configuration subroutine will launch automatically called Instrunet.6.Click the Restore button. This will configure all analog inputs to monitor 'K' type

thermocouples.7.Once the inputs are monitoring readings in degrees C, close the Instrunet window by clicking

in the upper left-hand corner of that window.

8.Choose a name for the file that will be created by the run and save it to the new folder youcreated in the first step.

9.End the run after equilibrium has been reached by pushing the Stop button.10. Launch Microsoft Excel from the Apple menu and open the new file created from the run.

The first column of data is the time in seconds. The other eight columns contain temperaturedata.

11. The file can be copied to your AFS space or placed on floppy.12. To mount your AFS space go to the Apple menu and select AFS Logon and follow the

prompts. Just remember to drag your AFS space icon to the Trash once you are done.

Note: Changes during the run

1.The graph view can be altered. Holding down the mouse button with the hand cursorpositioned over the graphing area will allow the graphing view to be moved to a desiredposition.

2.The X, Y axis can also be changed while the program is running. Highlight the value that isto be changed then type in the new value and hit-enter.

Suggestion:

Keep in mind that controlling the power to the bulb is done manually. This program

is just a data gathering program. So feel free to start and stop the program at any time. To

keep down the size of the data file, the last 3 to 5 minutes of the experiment may be all you

need to save.

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Analysis

Calculate the local natural convection heat transfer coefficients ( hc ) for both wattages at allangular positions, the plot hcversus angular position. Determine the mean ( ) by means of

Simpsons rule. Compute the mean Nusselt numbers Nu and compare with the equation

suggested by McAdams.

Nu =hc

!

r

k

where r is the radius of the bulb.

Nu = 0.53 (GrPr)

Gr = Grashof Number =

g"#2$TR3

2

Pr = Prandtl Number =

Cp

k

The thermal properties of air for use in the above dimensionless numbers are taken at the

arithmetic mean temperature of the air film, and may be interpolated from Table 3.

Determine the light efficiency of the electric light bulb (% of energy delivered as light) at both

wattages used.

It has been determined with an optical pyrometer that when 256 watts is delivered to the tungsten

filament that its black body temperature TBB is 3400R. Since the hemispherical emissivity of

tungsten is low (at %= 0.230 Table 2) the true temperature of the tungsten coil is

TBB

4=!T

s

4

or

Ts =

TBB

!

1

4

=

3400

0.693

Tsis the temperate of radiation source filament (tungsten coil)

The glass bulb transmits all of the radiation between 0.35 micron and 2.70 micron.

&1TBB= 0.35 x 3400= 1190

&2TBB= 2.7 x 3400 = 9200

h

1

4

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From the Table of Planck radiation functions (Table 1) determine f values (the fraction of wattsdelivered to the filament)

f1= 0.0000 at &1TBB= 1190

f2= 0.6477 at &2TBB= 9200

Thus 0.6477 is the fraction of the watts delivered to the filament, which is transmitted by the

glass.

The remainder watts which is absorbed on the glass and is lost by convection and radiation from

the glass =(1-0.648) * 256 = 90.1

The area of the ideal glass bulb is 0.315 ft2so that the thermal flux leaving the bulb is

qA=" = 90.1# 3.412

0.315= 975.94 Btu/hr x ft -2

The flux is transported out both by radiation and natural convection. Thus

'= hT(T - T#)

where

hT= total heat transfer coefficient

hT = hc+ hR

wherehc= the convection transfer coefficient and

hR= the radiation transfer coefficient

T = the localized bulb temperature which is a function of position (in Rankine )

and T#is a the ambient temperature in the laboratory

hR = 0.173*!glas*

T

100

!

"#

$

%&

4

' T(

100

!

"#

$

%&

4)

*++

,

-..

T'T(

%glass = 0.876 (independent of temperature for all practical purposes)

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For different power settings: less than or more than 256 watts is delivered to the bulb, the black

body temperature of the filament may be determined by a simple computation.

Let TBB2be the black body temperature of the tungsten coil when the power delivered to it is P2

watts. Then

TBB2

= 3400* P

2

256

"

#$

%

&'

1

4

In this experiment, Prandtal Number, Nusselt Number, and Grashofe Number may be calculated.

However, to calculate these numbers, it is necessary to determine the mean heat transfer

coefficient. This can be done by applying the Simpsons Rule using the heat transfer coefficient

(hc) at several positions on the bulb.

Simpsons Rule is

[f(A) + 4f(A+h) + 2f(A+2h) + 4f(A+3h

+...2f(B-2h) + 4f(B-h) + f(B)]

hc

"

=

1

2h

c

0

#

$ cos #

2"%

&

'(

)

*+d%

(h ="

6)

Thus

hc

"

=

#

2*3*6*[0 + 4hc(30) x cos 60 + 2hc(60) x cos 30

+ 4hc(90) cos (0) + 2hc(120) x cos 30+ 4hc(150) cos (60) +0]

The mean temperature difference (glass surface temperature-ambient temperature) may be

computed by dividing the total heat flux by hTobtained from Simpsons rule as above.

"T=# hT

=# (hc

+ hR )

The mean air film temperature to use in the Grashof, Prandtl and Nusselt numbers is thus

where T#is the ambient temperature.

I = AB f(x) dx =

h

3

Tf= T!+"T

2

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Although natural convection is mostly turbulent flow of fluid, there is always a layer near

the surface that is laminar (Welty 209). The approximate thickness of the boundary layermay be found by the following equation

! =k

hc

where k is the thermal conductivity and $is the boundary layer thickness.

Table I

Planck Radiation Functions

&TBB(R) f &TBB(R) f &TBB(R) f

1600 0 7000 0.4607 12400 0.8017

1800 0.0003 7200 0.4812 12600 0.8082

2000 0.001 7400 0.501 12800 0.8145

2200 0.0025 7600 0.5201 13000 0.8205

2400 0.0053 7800 0.5384 13200 0.8263

2600 0.0098 8000 0.5561 13400 0.8318

2800 0.0164 8200 0.573 13600 0.8371

3000 0.0254 8400 0.5892 13800 0.8422

3200 0.0368 8600 0.6048 14000 0.8471

3400 0.0507 8800 0.6197 15000 0.8689

3600 0.0668 9000 0.634 16000 0.8869

3800 0.0851 9200 0.6477 17000 0.9018

4000 0.1052 9400 0.6608 18000 0.9142

4200 0.1269 9600 0.6733 19000 0.92474400 0.1498 9800 0.6853 20000 0.9335

4600 0.1736 10000 0.6968 21000 0.9411

4800 0.1982 10200 0.7078 22000 0.9475

5000 0.2232 10400 0.7183 24000 0.9579

5200 0.2483 10600 0.7284 26000 0.9657

5400 0.2735 10800 0.738 28000 0.9717

5600 0.2986 11000 0.7472 30000 0.9764

5800 0.3234 11200 0.7561 40000 0.9891

6000 0.3477 11400 0.7645 50000 0.9941

6200 0.3715 11600 0.7726 60000 0.99656400 0.3948 11800 0.7803 70000 0.9977

6600 0.4174 12000 0.7878 80000 0.9984

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Table II

Emissivity of Tungsten

Temp. F0 %

100 0.031000 0.092

2000 0.162

3000 0.23

4000 0.281

5000 0.32

6000 0.35

6190 0.355 (melting point of tungsten)

Silica glass transmits all of the incident radiation in the wave-length range between 0.35 and 2.7microns and is opaque at longer and shorter wave-lengths.

The emissivity of glass for long wave-length radiation is 0.876.

The optical spectrum is from 0.4 to 0.7 microns

The average thickness of the glass bulb is 0.027".

Table III

Properties of Air

____________________________________________________________

T(F) k(Btu/hrxftxF) Pr g"#2

2

1

oF" ft

3

_____________________________________________________________

100 0.0154 0.72 1.76 x 106

200 0.0174 0.72 0.850 x 106

300 0.0193 0.71 0.444 x 106

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References

1. Incropera, F. P. and D. P. Dewitt, Fundamentals of Heat and Mass Transfer, John Wiley

and Sons, NY (1985).

2. Rohsenow, W. M. and H. Y. Choi, Heat Mass and Momentum Transfer, Prentice Hall,NY (1961).

Revised by SaddawiJanuary 2014

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EXPERIMENT MT1

MEASUREMENT OF THE BINARY DIFFUSIVITY OF DIETHYL ETHER IN AIR

Objective Use a Stefan diffusion cell to obtain values of the diffusivity of diethyl ether

in air at temperatures in the range 25-32C. Report on the sensitivity of the

measurements as a function of temperature.

Apparatus: . Capillary Diffusion Cell

. Constant Temperature Bath

. Cathetometer

Introduction

Whenever a concentration gradient exists, species are transported by diffusion from a region ofhigh concentration to a region of low concentration, in a similar way heat is conducted fromregions at high temperature to regions of low temperature. Because of the similarities between

heat and diffusion mass transport, Adolph Fick proposed that the diffusional mass flux is

proportional to the concentration gradient, i.e.,

JA(- )cA [1]

where the proportionality factor in Eq. [1] is prefixed with a minus sign to indicate that the net

flux of material is in the direction of decreasing concentration. When the fluid is a binary

mixture of ideal gases, it can be shown using kinetic theory that this proportionality factor is

equal to the binary diffusivity, DABof the gas mixture.

A consideration of Eq. [1] indicates that DAB may be determined experimentally if the molar

flux and the concentration gradient are known. In the latter part of the nineteenth century, Stefan

devised a convenient technique for determining the diffusivities of vapors of volatile liquids byplacing the liquid in the lower part of a vertical capillary. As the fluid A evaporates, its vapor

diffuses through a nonvolatile vapor, B, to the mouth of the capillary where it is swept away by a

stream of vapor, B.

Under these conditions the flux is determined by following the descent of the liquid-vapor

meniscus due to evaporation from the liquid phase. The boundary conditions on the vapor phase

in the capillary are then set by assuming that the vapor is in equilibrium with the fluid at thefluid-vapor interface and that the concentration of the diffusing vapor at the mouth of thecapillary is identical to its concentration the purge vapor.

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.

[9]

or in terms of partial pressure

N A = - P

RT

DAB

z*

PA1 - P A2

PB LM [10]

where PA1and PA2are the partial pressures of ethyl ether at the vapor-liquid interface and at the

mouth of the capillary respectively. (PB)LMis the log mean partial pressure of air between the

mouth of the capillary and the meniscus. A mass balance for A in the liquid gives:

d

dt

!A

MwA

"r2z*( )=#NA"r

2 ordz*

dt=!

MwANA

"A

[11]

Combining Eqs. [10 and 11] and integrating over time yields

Z*2

! Zo

*2=

2tPMwAD

AB

RT"A

{PA1! PA2} (PB)LM [12]

which gives the height of the vapor column in the capillary as a function of time.

The slow flow of air at the top of the capillary flushes the vapor from the top, hence one canassume that PA2 = 0. The partial pressure of A at the interface is calculated from the vaporpressure of A.

Procedure

Anhydrous Diethyl Ether (Mallinckrodt, Mw = 74.12) is placed in the lower two-thirds of a glass

capillary which has an inner diameter of 0.1 cm. The capillary is then placed in a cell which hasbeen inserted in the thermostatted bath. Dry air (Mw ~ 29.) is provided at bath temperatures by

passing air through an in-line gas filter (Gelman), and a silica gel moisture trap (AmericanScientific). The air should be admitted at a rate which is sufficient to flush the vapor from the tip

of the capillary without inducing mixing inside the mouth of the capillary. The optimum ratemay be determined by trial and error.

The capillary is readily filled with the syringe inserting the needle into the capillary until it justtouches the closed end. When the liquid level is near the mouth of the capillary, withdraw the

N A =PDABRTz*

ln1 - y A

*

1 - y A

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syringe. The syringe is now used to withdraw fluid to a specified level. An initial vapor column

height of about 1.1cm affords a good balance between accuracy and duration of the experiment.

Insert the capillary into the glass holder and measure the height of the Top of the CAPILLARY

FIRST. The value of Z*is relative to the top of the capillary, consequently without an accurate

reading of this first point the experiment is useless.

After allowing approximately ten minutes for the fluxes to come to a pseudo steady-state,2,3the

height of the vapor column from the meniscus to the capillary tip is recorded as a function of

time using the cathetometer. Readings of the cathetometer should be taken at five minuteintervals and the experiment should run for at least one hour.

Repeat this experiment at other temperatures in the range of something around 1 - 33C in orderto obtain the binary diffusivity* as a function of temperature. Using ice obtained from the TA,make at least one run below room temperature. Compare this functionality with that predicted

by theory (e.g., the Chapman-Enskog theory).

NOTE: PLEASE CLOSE THE FLOW VALVE (located at the top of the water bath feed line)WHEN YOU SHUT DOWN THE WATER BATH.

Data Analysis

The diffusivity can be determined by a linear least squares analysis of the experimental data.

Plot the square of the column height, z*2 - zo*2 , against time elapsed from the start of the

experiment and determine the slope of this curve. Report your results as the value of thediffusivity at the conditions under which it was measured and then give your results corrected to

a pressure of 760 mmHg.** Plot log DABvs. log T(K) to obtain the temperature exponent with

those predicted by theory. Typical experimental results at low temperatures give an exponent in

the range, 1.5 - 2.0.

Consider the sources of experimental error and deviations between the experimental results and

the theory used in analysis of the experiment.

_______________________________

* Strickly speaking, air is a two component gas with trace impurities of argon, carbon dioxide,

etc., and therefore the proportionality constant is a multi-component diffusion coefficient.

However, since oxygen and nitrogen do not separate to any appreciable extent in this experiment,the coefficient measured may be considered a pseudo-binary diffusivity.

** Do not forget to record the barometric pressure and room temperature during this experiment.

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Notation

c - Total molar concentration of gas.

cA - Molar concentration of volatile vapor.

DAB - Binary diffusivity of gas A in gas B.

JA - Vector form of the diffusive molar flux of gas A.

- Molar flux of gas A or gas B.

P - Pressure.

R - Gas constant.

T - Absolute temperature.

yA - Mole fraction of gas A.

yA* - Mole fraction of gas A at the vapor-liquid interface.

z - Distance measured along capillary starting at the tip.

z* - Distance from the capillary tip to the vapor-liquid inter-face.

Zo*

- Height of the vapor column at the start of the experiment.

A - Vapor from the volatile liquid.

B - Nonvolatile gas.

#A - Density of A in the liquid phase.

) - Grad operator.

References

1. Cussler, E. L., Multicomponent Diffusion, Elsevier Scientific Publishing Co., New York

1976.

2. Bird, R. B., W. E. Stewart and E. N. Lightfoot, Transport Phenomena, John Wiley andSons, Inc., New York 1960.

NA,NB

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3. Welty, J. R., C. E. Wicks, and R. E. Wilson, Fundamentals of Momentum, Heat and

Mass Transfer, Third Edition, John Wiley and Sons, New York 1984.

Revised By Saddawi

January 2014

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Leaching Rate Measurement

Phosphate Rock in 2% Citric Acid

OBJECTIVETo determine the leaching rates in a rock phosphate 2% citric acid system, the mass

transfer coefficient from experimental data, and to compare the results obtained with theoretical

values for laminar and turbulent agitation, and to study the factors that influence the leaching rate

such as particle size and temperature.

APPARATUS

Constant temperature bath

MixerMixer speed measuring device

Jacketed batch reactor)

Sampling equipment and glass wareChemicalsLab-view computer program

Leaching rate

Theoretical discussionPhosphates are essential ingredients in the fertilizers. Rock phosphate is the only source as raw

material in the production of phosphate fertilizer. The demand for phosphate is proportional to

the world populations increasing rate. Therefore the leaching of rock phosphate using 2% citricacid solution is important for two reasons: 1) the leaching of phosphates contained in phosphate

rock is the process that simulate the digestion of phosphate rock with soil by rain solution when

rock phosphates are applied as a fertilizer, 2) it is often used for testing the reactivity of rawmaterials containing phosphorus compounds.

The leaching process refers to the extraction of soluble constituents from a solid by means of a

solvent. The process may be employed either for the production of a concentrated solution of a

valuable solid material, or in order to free an insoluble solid from a soluble material with whichit is contaminated.

In the mass transfer controlled leaching process, the fluids are always in motion e.g. batch

processes with continuous mixing thus means that the fluid flows in a turbulent state past a solid

surface, however, because the fluid velocity is zero at the surface of the solid particles, theremust be a film of fluid adjacent to the surface. Hence, from this point of view there are two

forms of mass transfer from the particle surface to the fluid. 1) It is controlled by moleculardiffusion in the laminar flow region, and 2) it is controlled by turbulent transport in the turbulent

region core.Using the idea that a thin film is responsible for the resistance of transfer, one can write the

equation for mass transfer asdM

dt =

!k A(cs" c)

b 1

where

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A, is the area of solid -liquid interface,

b, is the effective thickness of the liquid film surrounding the particles,c, is the concentration of the solute in the solution bulk at time t,

cs, is the concentration of the saturated solution in contact with the particles.

M, is the mass of solute transferred in time t, and

k',is the diffusion coefficient.

For a batch reactor in which the total volume (V) of a solution remains constant,

dM = Vdc dc

dt =

!k A(cs" c)

bV 2

Assuming both bandAremain constant, the time taken to increase the concentration of the

solution from its initial value coto ccan be determined by integration of the above equation

dc

cs! c =#k A

Vb" dt 3

lnc

s ! c

o

cs! c

="k A

Vbt 4

For pure solvent co=0, therefore

1"c

cs

= e

" #k AVb

t

5

c = cs(1! e

! "k AVb

t

) 6

In the turbulent region the moving eddies transport matter from one location to another, just as

they transport momentum and energy. As mentioned above, when the flow past an interface islaminar, however, the mass-transfer rate is based on molecular diffusion. Thus, when the

Reynolds number is above the critical value, the usual buffer zone and turbulent core appear and

the mass transfer coefficient, KLwill become a resultant of both turbulent and molecular

diffusion.

KL =

!k +ED

b 7

where,ED, is the eddy diffusivity

Hence the mass transfer equation for turbulent region is

C = Cs(1! e

!

KLA

Vt

) 8

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From the mechanism of the mass transfer, it can be expected that, the mass transfer coefficient

will depend on the diffusivityDLon the fluid properties and mass velocity.

In a batch leaching process using a fine particle size and a continuous mixing, the effect of

mixing on mass transfer is expressed by the mixing speed, which is defined by the dimensionless

group (Nd2!

)

whereNis the number of revolutions per unit time of the mixer

dis the diameter of the vessel

#is the density of the fluid, and

is its viscosity

When the value of the dimensionless group (Nd

2!

) is less than 67,000 the mass transfer

coefficient will be

KLd

DL

= 2.7!10"5

(Nd

2#

)

1.4(

#DL

)0.5

9

and for higher values of (Nd

2!

) ,

KLd

DL

= 0.16!10"5

(Nd

2#

)

0.62(

#DL

)0. 5

10

where KL the mass transfer coefficient, equals!kb

in equation 1.

Analytical method of phosphate determination

The Molybdenate - Vanadate Phosphate method

This method is based on the reaction of phosphate with ammonium vanadate and molybdenate in

an acidic solution to form a yellow complex, who's color intensity in the solution is proportionalto the phosphoric acid content. The color solution does not obey Beers law, therefore a

calibration curve is necessary.

Applied solutions

1. Standard phosphate calibration solutions.

To prepare a standard phosphate solution with a concentration equal 1 mg/ml, 4.3900 g of

KH2PO4was dried at 110oC and dissolved in 1 liter distilled water in a calibration flask. The

working calibration samples are obtained by appropriate dilution of this standard solution with

distilled water. Or you can use the ready phosphate standard calibration solution.

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2. The reference solution

To prepare a reference solution, 15 ml of ammonium vanadate solution, 15 ml of ammonium

molybdenate solution, and 20 ml nitric acid solution pour into a calibrated bottle of 100 ml

volume, where distilled water was added to the solution until it reached the mark (100 ml). In the

case you have all the three solutions in one named as (AVAM), then you need to pour 10 ml ofthat solution and complete the volume to 100 ml.

1. The ammonium vanadate solution (0.25% solution of NH4VO3)

2.5 g of pure NH4VO3was dissolved in 500 ml of boiling distilled water, with intensive mixing.

After the solution was cooled ,20 ml of nitric acid of density 1.4 g/cm3was added and thevolume was completed to 1 liter. The solution should be kept in a dark glass bottle

2. The 5% ammonium molybdenate solution

Dissolve 50 g of pure ammonium molybdenate in 600 ml distilled water. Mix and heat thesolution continuously (without boiling) until the solid is completely dissolved. Filter the solution

while it is still hot. After cooling complete the volume to 1 liter. Keep the solution in dark glassbottle.

3. The nitric acid solution (HNO3)

Mix one volume of nitric acid of density equal to 1.4 g/cm3with two volumes of distilled water.

Note

The above three solution, ammonium vanadate, ammonium molybdenate, and nitric acid are

mixed together (AVAM Solution) in one container and ready to use.

Calibration Curve

To obtain a calibration curve, calibration solutions need to be prepared first.

Into a calibrated bottle of 100 ml volume add 1 to 7 ml, of the standard calibration solution ofphosphate for a desired phosphate concentration, and 10 ml of the AVAM Solution. Complete

with distilled water to the mark and mix very well.

Warm up the colorimeter for one hr, adjust the wave length to 450 nm. Fill one cuvette with thereference solution and transfer it to the colorimeter cell. Adjust the absorption reading to zero.

Wait about 60 min. for the calibration solution to reacts and gives a constant yellow color, fill a

cuvette with it and transfer it to the cell of the colorimeter, and read the intensity of the color

(absorbance).Draw the concentration of phosphate as Phosphorous ions in phosphate (mg/ml) versus the

intensity gotten from the colorimeter.

PROCEDURE

1. Citric acid solution preparation.Insert 20.0 g of pure dry citric acid into the jacketed Batch Reactor. Pour 1 liter of distilledwater into the reactor and connect it to the water bath. Adjust the bath water temperature, and

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the mixing rate to the desired values. Wait until all citric acid crystals are completely dissolved

and the reactor temperature reaches a steady state.

2. Add 10.0 g of rock phosphate of a known particle size to the reactor. Start the time at themoment you add the rock phosphate. Because the leaching process between the rock phosphateand the citric acid takes place very quickly during the first 10 min. Samples should be taken

after 1, 2, 3, and 5 min and so on. The samples are taken should include solids with thewithdrawn solution, so that the ratio of solid to solvent in the reactor will remain constant.

3. Use the sampling equipment to pull 7 to 8 ml from the reactor mixture at the desired time.This sample should filter directly by a filter found inside the sampling syringe.

4. Calculations of the P2O5concentration and the conversion percent (x)Pour the filtered solution into a small beaker, and take from it a small volume noted by (A) ml.

Pour this (A) volume into a calibrated 50 ml bottle, then complete the volume to the mark with

distilled water. Take from this solution a volume noted by (B) and pour it into a 50 ml calibratedbottle. Add to it 10 ml of the AVAM solution, and fill to the mark with distill water. Mix it

well. This solution should give a yellow color. To obtain a stable yellow color, a time interval ofmore than 30 min is needed. Prepare the colorimeter at least one hr before reading. Put the

wave length in the filter of the colorimeter at &= 410 nm. Fill a cuvette with the solution andtransfer it to the colorimeter cell, read the color intensity. From the calibration curve, get the

corresponding concentration noted by (C).

The concentration of the phosphorus ion in the leaching liquid is noted by (Cp)

CP =

C ! 50

A ! B = mg /ml

CP2 O5 = CP ! 2.29 (mg / ml)

X =The amount of P 2O5in the leaching liquid

The amount of P 2O5in the raw phosphate rocks

X =C

P2O

5

! Vr

m ! o.3!100

where

Vr, is the liquid volume in the reactor

m, is the mass of the raw phosphate rock0.3, is the weight fraction of P2O5 in the raw phosphate rock.

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Sampling Device

Suggested report items

1. Summarize the experimental results in a table.2. Provide some of estimate of your experimental error

3. Plot the conversion versus time for different particle size and different

temperatures.

4. Determine the mass transfer coefficient from theexperimental data and the empirical equations

6. Plot on natural log-log scale the concentration of P2O5versus time and

determine the slope. Calculate the leaching rate.

REFERENCES

1. Geankoplis, Christie J., Transport Process and Unit operations, 3rd Ed., Prentice Hall,1993.

2. Coulson, J. M., Richrdson, J. F., Chemical Engineering, vol 2., 3rd ED 2., McGraw-hill,1978

3. Perry, John H., Chemical Engineering Handbook, 4th ED, 1963Saddawi

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EXPERIMENT TD1

PHASE EQUILIBRIA AND LIQUID DIFFUSION

Objective

Determine the solubility, diffusion coefficient, and the enthalpy of solution of carbon dioxide in

Stoddard solvent in the range of 18 - 35C and at 1.0 atmosphere pressure.

Apparatus Integral Phase Equilibria Unit

Vacuum Pump

Digital Absolute Pressure Gage

Precision Temperature Controller

Introduction

When a gas and a liquid phase which are not thermodynamically in equilibrium are brought intoclose contact, transfer of one or more components may occur from the gas phase to the liquid or,vice versa, by the mechanism of molecular diffusion. Mass transfer by molecular diffusion is the

basic physical mechanism underlying many important areas of soil science, petroleum

engineering, chemical engineering, biotechnology and nuclear engineering. In this experiment, a

method for determining diffusion coefficients of Carbon dioxide gas in Stoddard solvent atconstant volume and temperature is developed using Integral Phase Equilibria Unit.

The solubility of a gas in a liquid solvent may be represented to good accuracy at dilute

concentrations of the dissolved gas by Henry's Law:

f = H X (1)

where, f is the fugacity of the gas in the gas phase in equilibrium with the liquid phase of

concentration X of dissolved gas. H is the Henrys law constant, which is a function of

temperature. Thus, by measuring the solubility one can obtain an estimate of the Henry's law

constant.

By measuring the solubility of gas in a liquid at several different temperatures, one can evaluate

the enthalpy of solution (heat of solution) of the gas in the specific liquid solvent. In this case

the heat of solution/R is equal to the slope of the plot of ln (H) versus 1/T. A derivation of thisrelationship should appear in the final report. (See the Gibbs-Helmholtz equation, which can be

found in many thermodynamics texts, including the Appendix of Smith & Van Ness, 3rd ed.)The diffusion coefficient of the dissolved gas in the liquid phase may be determined by

measuring the rate at which the gas dissolves in the quiescent liquid phase at a constanttemperature.

Phase Equilibrium Computations

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Compute the moles of carbon dioxide dissolved from stoichiometry using the pump temperature,

cell pressure and corrected barometer reading and total volume of carbon dioxide delivered fromthe pump. The following equation gives the details

n =PT ("VP #Vd)

ZpRTP#Vcg(PT #P1

o)

ZcRTc (2)

Where:

n = gram moles of carbon dioxide absorbed in the liquid phase

PT = corrected barometer reading

= vapor pressure of Stoddard Solvent at cell temperature

Tp = temperature at the pump

Tc = temperature of the cell (bath temperature)

= total gas volume delivered from the pump to the cell

Vcg = volume of the gas phase in the cell

Zp = compressibility factor of CO2at pump T and PT

Zc = compressibility factor of CO2at cell T and PT

Vd = dead volume in the system (cc)

The fugacity, f, can be determined from the Lewis and Randall Rule, which gives

f = foy (3)

where

f = fugacity of CO2in the gas phase

fo = fugacity of pure gaseous CO2at PTand cell T

y = mole fraction of CO2in gas phase

= (PT- Plo)/PT

Therefore f = (fo/PT)(PT- Pl

o) (4)

and by definition: fo/PT = *, the fugacity coefficient for pure CO2 (5)

in the gas phase at cell T and PT.

P 1

!Vp

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One can compute the fugacity coefficient by using the Generalized Second virial Equation. ofState. Virial coefficients for carbon dioxide can be found in the compilation by Dymond (1969).

Determination of diffusion coefficient from experimental data

A number of mathematical models have been proposed to determine the diffusion coefficients

from experimental volumetime profiles, however all these models are developed from the

equation of continuity for the solute component:

rJCut

C vv+!=!+

"..

" (6)

where r = Rate of reaction (kg/m3s)J = Mass transfer by the mechanism of molecular diffusion (kg/m2s)

v= Molar volume (m3)

Fig. 1. One-dimensional diffusion process in the diffusion cell.

Referring to Fig. 1, for a one-dimensional diffusion cell in the absence of chemical reaction, and

including the movement of the interface in the boundary conditions of the system, and based

upon a model proposed by Higbie (penetration theory) in which a component in the gas phase is

C

Liquid phase Gas phase

Interface

Z Z(t) Z=0

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NT = 2AC

i

D12

"

#$%

&'(

1

2

t (9)

If one plots NTversus t1/2, the slope of this line is equal to 2ACi(D12/,)1/2. Thus, one can easily

determine the diffusion coefficient from the slope of the line. Of course, the volume of gas fedto the interface is actually being measured, so it is preferable to plot VTvs. t1/2. However, this is

not a problem because one can use the simple relation that PTVT= ZpNTRTp. The slope of the

line should be determined by least square methods and an estimate of the uncertainty in D12

given. A brief treatment of the diffusion problem is presented on pages 70-71 of Sherwood et al.Lab reports must include estimates of experimental errors and estimates of the uncertainty in the

final values calculated. For instance, the mathematical uncertainty in the Henry's law constants,

enthalpy of solution and diffusion coefficients must be included.

Procedure

Properties of Stoddard Solvent and Cell Dimensions

Molecular Weight of Stoddard Solvent = 136 g/mole

Density of Stoddard Solvent: #= 0.7726 g/cc at 20C

(The isobaric expansion coefficient is 0.00104/oC.)

Weight of Stoddard Solvent in the cell = 39.04 gm at room temp

Volume of the Cell 150 ml

Volume of the magnetic stirrer = 1.45 mlLength of the tube from the top of the cell to the bulkhead = 9.75

Length of the tube going through the panel to valve 4 = 7.5Di of the tube 1/8

From these info please Calculate the Void volume (gas volume above the liquid phase)

(A) Preparation.

-----------------------------------------------------------------------------------------------------------

Set the Water Bath for desired temperature.

Out gas (removal of CO2 from the system).

2. Open valvesV3 - Valve 3 leading to vacuum pump.

V4 - Valve 4 - To remove CO2 from the cell.

V5 - Valve 5 From the pressure gauge line.

Valves 1A, 1B, 2A, and 2B closed, since no gas in pumps as plunger is in.3. Connect vacuum pump to system

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4. Start vacuum pump and start the magnetic stirrer. It helps quick degassing*

Degassing period is around 20 min.*You can calculate the degassing time by taking the average convective diffusivity value

and knowing the volume of the cell given to you. The Stoddard solvent is basically a mixture of

solvents containing predominantly heptane.

So, now degassing is done (you decide the time).5. Close the valve 3. There wont be any harm to the vacuum pump since it is just working

against valve 3 from the surface of the solvent.

6. Switch on pressure gauge. Perform this check. Look at the pressure gauge.

If pressure gauge reading is,# Constant (variation in decimal is considered constant) = vacuum is alright

# Change in the readings = a leak in the system.

So this check is important.

7. Close valve 4 to isolate the cell.7. Close vacuum line V3. Disconnect the pump hose*. Switch off the vacuum pump.

(C) Filling of pumps A&B with CO2.

-----------------------------------------------------------------------------------------------------------

There are three valves on the cylinder.I Top valve (A) (main vale that lets out CO2)

To open rotate counter clockwise (direction given on knob)

II Regulator valve (B) (with black cover & direction attached to it)This regulates the flow of CO2 from cylinder to pump.

III Release valve (C) This is the third valve (facing downwards). This allows CO2 from

entrance of cylinder to valve 1, which is closed now.RHS pressure gauge shows pressure in cylinder.LHS pressure gauge shows pressure in line.

13. Open top valve A

14. LHS gauge - Keep it at 20 psi (approx.) using regulator. (only recommended)

15. Open valve C on the cylinder slowly. One rotation of knob should be enough (clockwise).16. Open valve 1A on the board slowly. Plunger of pump A slowly moves out indicating CO2is

going into pump. Once plunger comes out close valve 1A

17. Gently tap/twist plunger slightly so that it comes out completely if stuck.

Caution Open valve 1A slowly, otherwise plunger will be thrown out of the pump due to highpressure. Note: the handle of the plunger is graduated. It is the scale you need to look at when

you are doing your experiment.18. Fill pump B in same way described for pump A, in this case the valve is 1B.

(D) Setting up of pressure gauge.

-----------------------------------------------------------------------------------------------------------

19. Switch on the gauge and change to PSI mode. Open valves A2, and B2. The pressure in the

line will be 20 PSI (greater than atm. pressure).

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20. Open valve 3. Switch the pressure gage to mm Hg mode.

21. Allow stabilization.This helps to bring pressure inside the lines to atm. pressure. Note, since pressure inside is high,

gas only goes out through line with valve 3.

22. Close V3. Do this once the gauge reading stabilizes.

At this point there is CO2in the line with V2A, V2B, V3 & V5. V1A, V1B & V4 are stillclosed.

23. Adjust the pressure reading to zero*. Adjust the knob on the right side to zero. and

(E) Actual experiment.

-----------------------------------------------------------------------------------------------------------

Students:

#1 should note pump readings.

#2 should maintain time (using stop watch).#3 should enter readings.

Because there are two pumps (A&B) in the apparatus, you should isolate one of them by closing

valve 2B if you decide to use pump A.24. Opens V4 and immediately starts stopwatch.Remember, there is vacuum after V4 So gauge reading goes down to negative value and also the

piston attached to the pump goes in automatically. Note, the pressure gauge readings show

negative*. Thats fine. Now,

25. Push plunger to a known quantity (any qty according to your choice). Smaller increments arerecommended. Observe that pressure gauge goes to a positive value.

26. Allow the pressure to fall* to zero

27. Note the time for zero pressure.28. Again push plunger, pressure becomes >0,

29. Allow it to fall to zero and

30. Note time for this fall.31. Repeat this procedure till all CO2 from the pump is over.32. Close valve 2A and open valve 2B and continue

(F) Reloading gas in pump.

-----------------------------------------------------------------------------------------------------------During this entire process stopwatch is on and time is measured*.

33. Close V4, V2B. V2A V1A, and V1B are closed .

34. Open V1A. Allow CO2 to fill the pump A.

35. Close V1A. Fill pump B in same way.36. Time is measured.

37. Bring back to atmospheric pressure. (Follow steps 19 to 22).37.5. Open V 2A and V4.

38. Go back to step 25. It takes roughly 120 200 ml of the pump volume of gas for the timedexperiment. It may vary. It is just a rough estimate.

You do this till pressure does not decrease.

(G) Total solubility estimation.

-----------------------------------------------------------------------------------------------------------

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38. Now start magnetic stirrer. Pressure starts decreasing*.

39. Continue with addition of CO2. You may stop noting time now*. A point is reached whenyou see pressure does not decrease after addition*. At this time, the solvent in the cell has

reached saturation point. Stop CO2 addition. This gives solubility of CO2 at infinite time*.

40. Repeat the above procedure for two more different temperatures* of your choice.

H) Winding up

-----------------------------------------------------------------------------------------------------------

Monitor of the group has to ensure the following.

CO2 cylinder (all three valves) is closed except regulator. It is not necessary.Pump is evacuated of any CO2.i.e. plungers are inside the pumps completely.

All valves (V1A, V1B, V2A, V2B, V3, V4, V5) are closed.

Water Bath is switched off.Stirrer is switched off.Cooling water tap is closed.

7. Pressure gauge is switched off.

Vacuum pump is off.

Work place is restored to the same condition as when given.Stopwatch returned to concerned TA.

For clarifications, you can contact your TA

After the run is over the bath temperature may be lowered which causes additional gas to

dissolve in the cell. Thus equilibrium solubilities may be determined at several lowertemperatures without starting from the beginning. When all experimentation is done make sureto close the valve on the CO2 cylinder.

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Properties of Stoddard Solvent and Cell Dimensions

The viscosity of Stoddard solvent as a function of TK is (centipoises) = 0.0895 exp (631/T).The volume of Stoddard Solvent is 100 ml at room temp.Diand Hi of the cell are (49.73 mm) and (61.72 mm) respectively.

Vapor Pressure of Stoddard Solvent

T,F Plo(atm)

60 0.001470 0.0016

80 0.0024

90 0.0035

100 0.0050

References

1. Smith, J. M. and Van Ness, H. C., "Introduction to Chemical Engineering

Thermodynamics," 4th Ed., McGraw-Hill, 1987.

2. Sherwood, T. K., Pigford, R. L. and Wilke, C. R. "Mass Transfer," McGraw-Hill, 1975.

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Figure 3. Experimental setup

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Note on: Phase equilibria and diffusion experiment.

Davide A. Hill May 5, 2004

The measurement of the diffusion coefficient of CO2 in the Stoddard solvent using the

laboratory apparatus is deceptively simple. The phenomenology of the experiment is, in fact,

quite complex, involving several transport mechanisms that become active at different times

during the run. In order to understand and sort out these mechanisms, one needs to examine the

way the experiment is conducted as well as possible causes for discrepancies.

First the cell is evacuated to desorbs the CO2from the liquid. As it will become apparent

later on, this should be done by putting the cell under vacuum while vigorously stirring the

liquid. Stirring is necessary to enhance convective mass transfer from the bulk of the liquidtowards the interface as much as possible. This, in turn, allows one to reduce the time needed to

eliminate the CO2from the liquid.

Prior to opening the valve to let the CO2in (at very beginning of the run), the cell is at a

pressure much lower than atmospheric. Also the liquid is stagnant (not stirred), as it should be in

order to allow only molecular diffusion to occur as specified by penetration theory. That the

liquid must be stagnant (zero velocity) is an important point, since an