Teaching Students to Teaching Students to Think Using Topics in Think Using Topics in

Thermodynamics: The Thermodynamics: The Virtual Substance Virtual Substance

ProgramProgram

Chrystal D. Bruce, Erskine College Chrystal D. Bruce, Erskine College and and

Carribeth Bliem and John Papanikolas, Carribeth Bliem and John Papanikolas, University of North Carolina at Chapel Hill University of North Carolina at Chapel Hill

OutlineOutline

Virtual SubstanceVirtual Substance Program Program Lab Assignments at ErskineLab Assignments at Erskine

– Ideal Gas LawIdeal Gas Law– Real GasesReal Gases– Thermodynamic PropertiesThermodynamic Properties

Independent ProjectsIndependent Projects Student CommentsStudent Comments Additional ModulesAdditional Modules

Modeling with Modeling with Virtual Virtual SubstanceSubstance

What is What is Virtual SubstanceVirtual Substance? ?

A numerically accurate, inquiry driven, A numerically accurate, inquiry driven, molecular dynamics software program.molecular dynamics software program.

Ideal Gas LawIdeal Gas Law

Calculate Gas Constant, RCalculate Gas Constant, R– Measure pressure at series of Measure pressure at series of

volumesvolumes Slope = RTSlope = RT

Argon: R = Argon: R = 0.0820.082 L atm/mol KL atm/mol KXenon: R = Xenon: R = 0.0830.083 L atm/mol KL atm/mol K

– Measure pressure at series of Measure pressure at series of temperaturestemperatures

Slope = R/VSlope = R/Vmolarmolar

Argon: R = Argon: R = 0.0830.083 L atm/mol KL atm/mol KXenon: R = Xenon: R = 0.0820.082 L atm/mol K L atm/mol K

0

10

20

30

40

50

60

70

80

90

0 2 4 6 8 10 12

1/Volume (mol/L)

Pre

ssur

e (a

tm)

ArgonXenon

T = 100K

0

5

10

15

20

25

30

35

40

0 100 200 300 400 500

T (K)

Pre

ssur

e (a

tm)

Argon 1L/molXenon 2L/mol

Virtual Substance is Numerically Accurate

Real Gas BehaviorReal Gas Behavior

RT

PVZ m

NVT simulations of Argon at 165 K using periodic boundary conditions

0

0.5

1

1.5

2

2.5

3

0 100 200 300 400 500

Pressure (atm)

Z, c

om

pre

ssio

n f

acto

r

Lennard JonesSoft SphereNIST Datavan der Waals EOSHard Sphere

Thermodynamic PropertiesThermodynamic Properties Calculate expansion coefficient, Calculate expansion coefficient, and isothermal and isothermal

compressibility, compressibility, TT, for Argon behaving as an ideal gas., for Argon behaving as an ideal gas.

nPT

V

V ,

1

Expansion Coefficient Determination (P=10 atm)

y = 0.0083x - 0.0488

0

1

2

3

4

5

0 100 200 300 400 500 600

Temperature (K)

Vol

ume

(L/m

ol)

NPT simulations

Isothermal Compressibility Determination (T=298 K)

y = 24.8x-1.0043

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 10 20 30 40 50 60

Pressure (atm)

Vo

lum

e (L

/mo

l)

NVT simulations

TT

V

V nP

11

,

For an Ideal Gas:

Virtual Substance

Error: < 2%

P

nRTV

Topic Measurement

Kinetic Theory of Gases

Velocity DistributionSpeed DistributionCollision FrequencyMean Free Path

Determine average and RMS speeds from data

Real Gases P(V) Identify limit(s) of ideal behaviorDetermine critical constants

Energy and Enthalpy

E(T)H(T)E(V)H(P)

Determine CV and CP from data

Determine ∆Hvap and ∆Hfus

Internal PressureCombine with CP to get Joule-

Thomson coefficient

Entropy CP(T) Calculate Sm(T)

Calculate ∆Sfus and ∆Svap

Internal Pressure

P(T) Confirm that πT = T(∂P/∂T)V – P

Phase Diagrams

Construct phase diagram from Tfus and Tvap

measurements

Phase transitionsIdentification of phase boundariesComparison with Clausius-Clapeyron equation

Using Using Virtual SubstanceVirtual Substance in in Independent ProjectsIndependent Projects

Submit Proposal Revise Proposal Conduct Research

Submit Report and Present Results to Department

Sample Student ProjectsSample Student Projects

– Determination of Joule-Thomson Determination of Joule-Thomson coefficient values with coefficient values with Virtual Virtual Substance Substance

– Calculating Internal Pressure (Calculating Internal Pressure (TT) ) for Ideal and Real Gasesfor Ideal and Real Gases

– Evaluation of the Redlich-Kwong Evaluation of the Redlich-Kwong Equation of StateEquation of State

– Determination of (CDetermination of (CPP – C – CVV) for ) for ArgonArgon

Student CommentsStudent Comments Virtual SubstanceVirtual Substance … … made [concepts] real and made [concepts] real and

concrete. concrete. It gave the visual/tactile learner in me a way to It gave the visual/tactile learner in me a way to

grab hold of the topicsgrab hold of the topics [The independent project] was probably the most [The independent project] was probably the most

valuable assignment … I had to think of a problem valuable assignment … I had to think of a problem …, consider the capabilities of …, consider the capabilities of Virtual SubstanceVirtual Substance, , write a proposal …, and write a proposal …, and use critical thinking skills use critical thinking skills to execute and analyze the project. It wasn't just to execute and analyze the project. It wasn't just following a simple recipe to obtain some data for a following a simple recipe to obtain some data for a lab report. lab report.

[the independent project] was … [the independent project] was … good preparation good preparation for graduate studies.for graduate studies.

The most important thing was a good The most important thing was a good understanding of the chemistry.understanding of the chemistry.

Phase TransitionsPhase Transitions– Measure E, P, and V

at different temperatures

– Combine to get H(T) using H = E + PV

200 K 80 K 10 K-8

-6

-4

-2

0

2

4

0 50 100 150

Temperature (K)

H (

kJ/m

ol)

P = 8.5 atm

Ar (actual)

Vm (L/mol)

P (

atm

)

151 K (Tc)

130 K

NIST data

Real Gas IsothermsReal Gas Isotherms

Output agrees with actual data Numerically Accurate

Measure Pressure for series of Volumes at constant Temperaturefor Ar

Polymer StatisticsPolymer Statistics

0.5

1

1.5

2

2.5

1 1.2 1.4 1.6 1.8 2log N (number of atoms)

log

End

to

End

Dis

tanc

e

Virtual Substance Data (LJ + FENE)Rigid RodRandom WalkSelf Avoiding Walk

LJ: Lennard Jones – Non-bonded atoms

FENE: Finite Extension Nonlinear Elastic Potential – Bonded Atoms

AcknowledgementsAcknowledgements

For More Information:

cbruce@erskine.edu

www.unc.edu/~jpapanik/VirtualSubstance/VGMain.htm

•BCCE Symposium Organizers

•Our Students

More Student CommentsMore Student Comments VS could be running in the VS could be running in the

dorm room while you were dorm room while you were doing other homework or doing other homework or laundry.laundry.

I will use [I will use [Virtual Virtual SubstanceSubstance] as a teaching ] as a teaching tool when I become a tool when I become a professor.professor.

© Sidney Harris

Forms of Various PotentialsForms of Various Potentials Hard SphereHard Sphere

– Billiard Balls of radius Billiard Balls of radius

Soft Sphere Soft Sphere – Repulsive forces; typically n=12Repulsive forces; typically n=12

Lennard – JonesLennard – Jones– Repulsive and attractive forcesRepulsive and attractive forces

FENE – Use instead of harmonic oscillator or FENE – Use instead of harmonic oscillator or Morse Potential to treat polymer bindingMorse Potential to treat polymer binding

r if

r if 0HardSphereU

n

SoftSphere rU

612

4rr

U JonesLennard