(************** Content-type: application/mathematica ************** Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 33107, 1417]*) (*NotebookOutlinePosition[ 33964, 1446]*) (* CellTagsIndexPosition[ 33920, 1442]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["\t\tTHE JOULE-THOMSON COEFFICIENT FOR A SQUARE WELL \ GAS", "Title", AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["A computer algebra application in physical chemistry. ", "Subtitle", AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[StyleBox["\t\tM. Hanson, \n\t\tDepartment of Chemistry, \n\t\t\ Humboldt State University, \n\t\tArcata, California 95521\n\t\t\n\t\tBitnet: \ GFA001D@CCS.CSUSCC.CALSTATE.EDU\n\t\t(707) 826 3265", FontSize->12]], "Subsubtitle", AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["Introduction", "Subtitle", AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ \t\tThere are many problems in physical chemistry that are easy to solve \ formally but impossibly tedious in practice. The advent of computer algebra \ programs makes these problems tractable. The determination of the \ Joule-Thomson coefficient \[Mu]JT for a square well gas is such a problem. \ One determines the enthalpy as a function of the temperature and pressure, \ H(T,P), differentiates with respect to P, sets the result to zero, and solves \ for \[Mu]JT as (\[Paragraph]T/\[Paragraph]P)H. \t\tThe three parameters of the potential (the well depth \[Epsilon], the \ hard sphere size of the particle d, and the range parameter g) are set by \ fitting the second virial coefficient. The resulting Joule-Thomson \ coefficient for argon is found to agree remarkably well with experiment. \ \>", "Text", AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}] }, Closed]], Cell[CellGroupData[{ Cell["Model", "Subtitle", AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1. A collection of the Avogadro number of particles N having the argon atom \ mass in volume V at an equilibrium temperature T. 2. The interaction between particles is given by the potential \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \:f2e6\t\t\[Infinity], if r \[LessEqual] \ d \t\t\t\t\t\t\tU(r) = \:f2ed - \[Epsilon], if d < r \ \[LessEqual] g d\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t(1) \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \t\:f2e8\t\t 0, if g d < r \t\t\t\t\t\t\t\t\t 3. The pressure is sufficiently low that the equation of state satisfies \t\t\t\t\t\t\t\t\t\t\t\tpV = RT ( 1 + B(T)/V ) \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\ \t\t\t\t\t\t\t\t\t\t\t\t(2)\t \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\[TildeTilde] RT + B(T)p. 4. The second virial coefficient is given by \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\:f2f3 \[Infinity]\t\t\t\t\t\t\t\t \ 2 \t\t\t\t\t\t\t\t\t\tB(T) = 2 p N | ( 1 - exp(-U/kT) ) r dr.\t\t\t\t\t\ \t\t\t(3) \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0\:f2f5 \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t For the model potential we have (see the Appendix) \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \t\t\t\t\t\t\t\t\t\tB(T) = b - (a/N\[Epsilon]){exp(\[Epsilon]/kT) - 1}\t\t\ \t\t\t\t\t\t\t\t\t\t\t\t(4) \t\t\t\t\t\t\t\t\t\t \t\t\t\t\t\t\t\t\t\t \twhere \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t3 3 \t \t\t\t\tb = (2/3)\[Pi]Nd , a/N\[Epsilon] = (g - 1)br. \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\ \>", "Text", PageBreakAbove->True, AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}] }, Closed]], Cell[CellGroupData[{ Cell["Fitting the Parameters", "Subtitle", PageBreakAbove->True, AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["Get and Plot the Experimental Data", "Subsubtitle", AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ ArgBofT = ReadList[\"argboft.list\",{Number,Number}] ; (* see NBS reference *)\ \>", "Input", PageWidth->PaperWidth, AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["\<\ gbexp = ListPlot[ArgBofT, AxesLabel->{\"T/K\",\"\"}, \t\t\tPlotLabel-> \t\t\t\"B[T]/cm^3 The Second Virial Coefficient of Argon\"]\ \>", "Input", PageWidth->PaperWidth, AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart % Scaling calculations 0.02381 0.00141 0.57271 0.002 [ [(B[T]/cm^3 The Second Virial Coefficient of Argon)] 0.5 0.62428 0 -1 \ Msboxa [(100)] 0.16529 0.56021 0 1 Msboxa [(200)] 0.30677 0.56021 0 1 Msboxa [(300)] 0.44825 0.56021 0 1 Msboxa [(400)] 0.58973 0.56021 0 1 Msboxa [(500)] 0.73121 0.56021 0 1 Msboxa [(600)] 0.87268 0.56021 0 1 Msboxa [(T/K)] 1.00625 0.57271 -1 0 Msboxa [(-250)] 0.01131 0.07218 1 0 Msboxa [(-200)] 0.01131 0.17228 1 0 Msboxa [(-150)] 0.01131 0.27239 1 0 Msboxa [(-100)] 0.01131 0.37249 1 0 Msboxa [(-50)] 0.01131 0.4726 1 0 Msboxa [()] 0.02381 0.62428 0 -1 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 0.61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath %%Object: Graphics [ ] 0 setdash 0 setgray 0 setgray [(B[T]/cm^3 The Second Virial Coefficient of Argon)] 0.5 0.62428 0 -1 \ Mshowa gsave gsave 0.002 setlinewidth 0 0.57271 moveto 1 0.57271 lineto stroke 0.16529 0.56646 moveto 0.16529 0.57896 lineto stroke 0 setgray [(100)] 0.16529 0.56021 0 1 Mshowa 0.30677 0.56646 moveto 0.30677 0.57896 lineto stroke 0 setgray [(200)] 0.30677 0.56021 0 1 Mshowa 0.44825 0.56646 moveto 0.44825 0.57896 lineto stroke 0 setgray [(300)] 0.44825 0.56021 0 1 Mshowa 0.58973 0.56646 moveto 0.58973 0.57896 lineto stroke 0 setgray [(400)] 0.58973 0.56021 0 1 Mshowa 0.73121 0.56646 moveto 0.73121 0.57896 lineto stroke 0 setgray [(500)] 0.73121 0.56021 0 1 Mshowa 0.87268 0.56646 moveto 0.87268 0.57896 lineto stroke 0 setgray [(600)] 0.87268 0.56021 0 1 Mshowa 0 setgray [(T/K)] 1.00625 0.57271 -1 0 Mshowa 0.02381 0 moveto 0.02381 0.61803 lineto stroke 0.01756 0.07218 moveto 0.03006 0.07218 lineto stroke 0 setgray [(-250)] 0.01131 0.07218 1 0 Mshowa 0.01756 0.17228 moveto 0.03006 0.17228 lineto stroke 0 setgray [(-200)] 0.01131 0.17228 1 0 Mshowa 0.01756 0.27239 moveto 0.03006 0.27239 lineto stroke 0 setgray [(-150)] 0.01131 0.27239 1 0 Mshowa 0.01756 0.37249 moveto 0.03006 0.37249 lineto stroke 0 setgray [(-100)] 0.01131 0.37249 1 0 Mshowa 0.01756 0.4726 moveto 0.03006 0.4726 lineto stroke 0 setgray [(-50)] 0.01131 0.4726 1 0 Mshowa 0 setgray [()] 0.02381 0.62428 0 -1 Mshowa grestore grestore 0 0 moveto 1 0 lineto 1 0.618034 lineto 0 0.618034 lineto closepath clip newpath 0 setgray gsave 0.008 setlinewidth 0.13699 0.11644 Mdot 0.13699 0.01472 Mdot 0.15114 0.21371 Mdot 0.15114 0.13745 Mdot 0.16529 0.27107 Mdot 0.16529 0.21513 Mdot 0.17944 0.31051 Mdot 0.17944 0.27059 Mdot 0.20066 0.35444 Mdot 0.20066 0.33105 Mdot 0.23603 0.40777 Mdot 0.23603 0.40151 Mdot 0.23874 0.40749 Mdot 0.24012 0.40825 Mdot 0.24159 0.41019 Mdot 0.24524 0.41454 Mdot 0.24631 0.41404 Mdot 0.24923 0.42121 Mdot 0.25477 0.42811 Mdot 0.2652 0.44243 Mdot 0.26879 0.44393 Mdot 0.28706 0.46493 Mdot 0.30677 0.4759 Mdot 0.30677 0.48351 Mdot 0.3286 0.49859 Mdot 0.33953 0.49705 Mdot 0.37751 0.51623 Mdot 0.37751 0.52654 Mdot 0.41027 0.53957 Mdot 0.41027 0.5285 Mdot 0.41027 0.52976 Mdot 0.41027 0.53042 Mdot 0.41027 0.52746 Mdot 0.43912 0.5476 Mdot 0.44564 0.53999 Mdot 0.44564 0.54117 Mdot 0.44564 0.54171 Mdot 0.48101 0.55064 Mdot 0.48101 0.54972 Mdot 0.48101 0.5502 Mdot 0.48101 0.55058 Mdot 0.51638 0.55771 Mdot 0.51638 0.55819 Mdot 0.51638 0.55841 Mdot 0.55175 0.56412 Mdot 0.55175 0.5645 Mdot 0.55175 0.5647 Mdot 0.55175 0.56492 Mdot 0.55175 0.5629 Mdot 0.58712 0.57126 Mdot 0.58712 0.57034 Mdot 0.58712 0.57054 Mdot 0.62249 0.57503 Mdot 0.62249 0.57707 Mdot 0.62249 0.57547 Mdot 0.62249 0.57555 Mdot 0.65645 0.58013 Mdot 0.69323 0.58206 Mdot 0.83471 0.59517 Mdot 0.97619 0.60332 Mdot grestore % End of Graphics MathPictureEnd\ \>"], "Graphics", ImageSize->{395, 243}, ImageMargins->{{18, Inherited}, {Inherited, 1}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False], Cell[OutputFormData["\<\ The Unformatted text for this cell was not generated. Use options in the Actions Settings dialog box to control when Unformatted text is generated.\ \>", "\<\ -Graphics-\ \>"], "Output", AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Guess d, eps(", StyleBox["\[Epsilon]", FontSlant->"Plain"], "), & g, and Plot the Model Prediction" }], "Subsubtitle", PageBreakAbove->True, AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["\<\ ClearAll[BofT,T,No,d,eps,g,b,gbtheor] BofT[T_] := b*(1 - (g^3 - 1)*(Exp[eps/(k*T)] - 1) ) No = 6.0225 10^23; d = 316.2*10^-12 (* in meters *) eps = 69.4*k; g = 1.85; (* The parameters come from Guggenheim. Try others *) b = 2*Pi*No*d^3/3 ; gbtheor = Plot[BofT[T] 1 10^6,{T,80,700}] (* convert to cm^3 to compare \ with experimental data *)\ \>", "Input", PageWidth->PaperWidth, AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart % Scaling calculations 0.02381 0.00136 0.5649 0.00217 [ [(100)] 0.15986 0.5524 0 1 Msboxa [(200)] 0.29592 0.5524 0 1 Msboxa [(300)] 0.43197 0.5524 0 1 Msboxa [(400)] 0.56803 0.5524 0 1 Msboxa [(500)] 0.70408 0.5524 0 1 Msboxa [(600)] 0.84014 0.5524 0 1 Msboxa [(700)] 0.97619 0.5524 0 1 Msboxa [(-250)] 0.01131 0.02279 1 0 Msboxa [(-200)] 0.01131 0.13121 1 0 Msboxa [(-150)] 0.01131 0.23964 1 0 Msboxa [(-100)] 0.01131 0.34806 1 0 Msboxa [(-50)] 0.01131 0.45648 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 0.61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath %%Object: Graphics [ ] 0 setdash 0 setgray gsave gsave 0.002 setlinewidth 0 0.5649 moveto 1 0.5649 lineto stroke 0.15986 0.55865 moveto 0.15986 0.57115 lineto stroke 0 setgray [(100)] 0.15986 0.5524 0 1 Mshowa 0.29592 0.55865 moveto 0.29592 0.57115 lineto stroke 0 setgray [(200)] 0.29592 0.5524 0 1 Mshowa 0.43197 0.55865 moveto 0.43197 0.57115 lineto stroke 0 setgray [(300)] 0.43197 0.5524 0 1 Mshowa 0.56803 0.55865 moveto 0.56803 0.57115 lineto stroke 0 setgray [(400)] 0.56803 0.5524 0 1 Mshowa 0.70408 0.55865 moveto 0.70408 0.57115 lineto stroke 0 setgray [(500)] 0.70408 0.5524 0 1 Mshowa 0.84014 0.55865 moveto 0.84014 0.57115 lineto stroke 0 setgray [(600)] 0.84014 0.5524 0 1 Mshowa 0.97619 0.55865 moveto 0.97619 0.57115 lineto stroke 0 setgray [(700)] 0.97619 0.5524 0 1 Mshowa 0.02381 0 moveto 0.02381 0.61803 lineto stroke 0.01756 0.02279 moveto 0.03006 0.02279 lineto stroke 0 setgray [(-250)] 0.01131 0.02279 1 0 Mshowa 0.01756 0.13121 moveto 0.03006 0.13121 lineto stroke 0 setgray [(-200)] 0.01131 0.13121 1 0 Mshowa 0.01756 0.23964 moveto 0.03006 0.23964 lineto stroke 0 setgray [(-150)] 0.01131 0.23964 1 0 Mshowa 0.01756 0.34806 moveto 0.03006 0.34806 lineto stroke 0 setgray [(-100)] 0.01131 0.34806 1 0 Mshowa 0.01756 0.45648 moveto 0.03006 0.45648 lineto stroke 0 setgray [(-50)] 0.01131 0.45648 1 0 Mshowa grestore grestore 0 0 moveto 1 0 lineto 1 0.618034 lineto 0 0.618034 lineto closepath clip newpath 0 setgray gsave gsave 0.004 setlinewidth 0.13265 0.01472 moveto 0.14144 0.08359 lineto 0.15023 0.13942 lineto 0.1678 0.22419 lineto 0.18537 0.28534 lineto 0.20295 0.33142 lineto 0.22052 0.36734 lineto 0.2381 0.3961 lineto 0.27324 0.43922 lineto 0.30839 0.46997 lineto 0.34354 0.49298 lineto 0.37868 0.51084 lineto 0.41383 0.52509 lineto 0.44898 0.53673 lineto 0.48413 0.5464 lineto 0.51927 0.55458 lineto 0.55442 0.56158 lineto 0.58957 0.56763 lineto 0.62472 0.57293 lineto 0.65986 0.57759 lineto 0.69501 0.58173 lineto 0.73016 0.58543 lineto 0.76531 0.58876 lineto 0.80045 0.59177 lineto 0.8356 0.5945 lineto 0.87075 0.597 lineto 0.9059 0.59928 lineto 0.94104 0.60138 lineto 0.97619 0.60332 lineto stroke grestore grestore % End of Graphics MathPictureEnd\ \>"], "Graphics", ImageSize->{282, 174}, ImageMargins->{{17, Inherited}, {Inherited, Inherited}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False], Cell[OutputFormData["\<\ The Unformatted text for this cell was not generated. Use options in the Actions Settings dialog box to control when Unformatted text is generated.\ \>", "\<\ -Graphics-\ \>"], "Output", AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Comparison Model and Experimental Data", "Subsubtitle", PageBreakAbove->False, AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["Show[gbexp,gbtheor]", "Input", PageWidth->PaperWidth, PageBreakAbove->False, AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart % Scaling calculations 0.02381 0.00136 0.56814 0.00199 [ [(B[T]/cm^3 The Second Virial Coefficient of Argon)] 0.5 0.62428 0 -1 \ Msboxa [(100)] 0.15986 0.55564 0 1 Msboxa [(200)] 0.29592 0.55564 0 1 Msboxa [(300)] 0.43197 0.55564 0 1 Msboxa [(400)] 0.56803 0.55564 0 1 Msboxa [(500)] 0.70408 0.55564 0 1 Msboxa [(600)] 0.84014 0.55564 0 1 Msboxa [(700)] 0.97619 0.55564 0 1 Msboxa [(T/K)] 1.00625 0.56814 -1 0 Msboxa [(-250)] 0.01131 0.07171 1 0 Msboxa [(-200)] 0.01131 0.17099 1 0 Msboxa [(-150)] 0.01131 0.27028 1 0 Msboxa [(-100)] 0.01131 0.36956 1 0 Msboxa [(-50)] 0.01131 0.46885 1 0 Msboxa [()] 0.02381 0.62428 0 -1 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 0.61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath %%Object: Graphics [ ] 0 setdash 0 setgray 0 setgray [(B[T]/cm^3 The Second Virial Coefficient of Argon)] 0.5 0.62428 0 -1 \ Mshowa gsave gsave 0.002 setlinewidth 0 0.56814 moveto 1 0.56814 lineto stroke 0.15986 0.56189 moveto 0.15986 0.57439 lineto stroke 0 setgray [(100)] 0.15986 0.55564 0 1 Mshowa 0.29592 0.56189 moveto 0.29592 0.57439 lineto stroke 0 setgray [(200)] 0.29592 0.55564 0 1 Mshowa 0.43197 0.56189 moveto 0.43197 0.57439 lineto stroke 0 setgray [(300)] 0.43197 0.55564 0 1 Mshowa 0.56803 0.56189 moveto 0.56803 0.57439 lineto stroke 0 setgray [(400)] 0.56803 0.55564 0 1 Mshowa 0.70408 0.56189 moveto 0.70408 0.57439 lineto stroke 0 setgray [(500)] 0.70408 0.55564 0 1 Mshowa 0.84014 0.56189 moveto 0.84014 0.57439 lineto stroke 0 setgray [(600)] 0.84014 0.55564 0 1 Mshowa 0.97619 0.56189 moveto 0.97619 0.57439 lineto stroke 0 setgray [(700)] 0.97619 0.55564 0 1 Mshowa 0 setgray [(T/K)] 1.00625 0.56814 -1 0 Mshowa 0.02381 0 moveto 0.02381 0.61803 lineto stroke 0.01756 0.07171 moveto 0.03006 0.07171 lineto stroke 0 setgray [(-250)] 0.01131 0.07171 1 0 Mshowa 0.01756 0.17099 moveto 0.03006 0.17099 lineto stroke 0 setgray [(-200)] 0.01131 0.17099 1 0 Mshowa 0.01756 0.27028 moveto 0.03006 0.27028 lineto stroke 0 setgray [(-150)] 0.01131 0.27028 1 0 Mshowa 0.01756 0.36956 moveto 0.03006 0.36956 lineto stroke 0 setgray [(-100)] 0.01131 0.36956 1 0 Mshowa 0.01756 0.46885 moveto 0.03006 0.46885 lineto stroke 0 setgray [(-50)] 0.01131 0.46885 1 0 Mshowa 0 setgray [()] 0.02381 0.62428 0 -1 Mshowa grestore grestore 0 0 moveto 1 0 lineto 1 0.618034 lineto 0 0.618034 lineto closepath clip newpath 0 setgray gsave gsave gsave 0.008 setlinewidth 0.13265 0.11561 Mdot 0.13265 0.01472 Mdot 0.14626 0.21208 Mdot 0.14626 0.13644 Mdot 0.15986 0.26897 Mdot 0.15986 0.21349 Mdot 0.17347 0.30809 Mdot 0.17347 0.26849 Mdot 0.19388 0.35165 Mdot 0.19388 0.32846 Mdot 0.22789 0.40455 Mdot 0.22789 0.39834 Mdot 0.2305 0.40427 Mdot 0.23182 0.40503 Mdot 0.23324 0.40695 Mdot 0.23675 0.41126 Mdot 0.23778 0.41077 Mdot 0.24059 0.41788 Mdot 0.24592 0.42473 Mdot 0.25595 0.43892 Mdot 0.2594 0.44041 Mdot 0.27697 0.46124 Mdot 0.29592 0.47213 Mdot 0.29592 0.47967 Mdot 0.31691 0.49462 Mdot 0.32743 0.4931 Mdot 0.36395 0.51212 Mdot 0.36395 0.52235 Mdot 0.39546 0.53527 Mdot 0.39546 0.52429 Mdot 0.39546 0.52554 Mdot 0.39546 0.5262 Mdot 0.39546 0.52326 Mdot 0.4232 0.54323 Mdot 0.42947 0.53569 Mdot 0.42947 0.53686 Mdot 0.42947 0.5374 Mdot 0.46348 0.54625 Mdot 0.46348 0.54534 Mdot 0.46348 0.54582 Mdot 0.46348 0.54619 Mdot 0.4975 0.55326 Mdot 0.4975 0.55374 Mdot 0.4975 0.55396 Mdot 0.53151 0.55962 Mdot 0.53151 0.55999 Mdot 0.53151 0.56019 Mdot 0.53151 0.56041 Mdot 0.53151 0.55841 Mdot 0.56552 0.56671 Mdot 0.56552 0.56579 Mdot 0.56552 0.56599 Mdot 0.59954 0.57044 Mdot 0.59954 0.57246 Mdot 0.59954 0.57088 Mdot 0.59954 0.57096 Mdot 0.63219 0.5755 Mdot 0.66756 0.57741 Mdot 0.80362 0.59042 Mdot 0.93967 0.5985 Mdot grestore grestore gsave gsave gsave 0.004 setlinewidth 0.13265 0.06431 moveto 0.14144 0.12738 lineto 0.15023 0.1785 lineto 0.1678 0.25613 lineto 0.18537 0.31213 lineto 0.20295 0.35433 lineto 0.22052 0.38723 lineto 0.2381 0.41356 lineto 0.27324 0.45305 lineto 0.30839 0.48121 lineto 0.34354 0.50228 lineto 0.37868 0.51863 lineto 0.41383 0.53168 lineto 0.44898 0.54234 lineto 0.48413 0.5512 lineto 0.51927 0.55869 lineto 0.55442 0.56509 lineto 0.58957 0.57064 lineto 0.62472 0.57549 lineto 0.65986 0.57976 lineto 0.69501 0.58355 lineto 0.73016 0.58694 lineto 0.76531 0.58999 lineto 0.80045 0.59274 lineto 0.8356 0.59525 lineto 0.87075 0.59753 lineto 0.9059 0.59962 lineto 0.94104 0.60154 lineto 0.97619 0.60332 lineto stroke grestore grestore grestore grestore % End of Graphics MathPictureEnd\ \>"], "Graphics", ImageSize->{371, 228}, ImageMargins->{{17, Inherited}, {Inherited, Inherited}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False], Cell[OutputFormData["\<\ The Unformatted text for this cell was not generated. Use options in the Actions Settings dialog box to control when Unformatted text is generated.\ \>", "\<\ -Graphics-\ \>"], "Output", AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}] }, Closed]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["\t\t\t\t\tThe Energy and the Enthalpy\t\t\t\t\t", "Subtitle", PageBreakAbove->True, AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ The energy is made up of the sum of the contributions from kinetic and \ potential energies 2 E = N <(1/2)ms > + N \ (5) (Since U gives the potential for a pair of particles, U/2 gives that for a \ single particle.) Using the Boltzman distribution for speeds and the \ Maxwell-Boltzman distribution for positions we have 2 <(1/2)ms > = (3/2)kT \ (6) and \:f2e6\[Infinity] \ 2 = | U N exp(-U/kT)4\[Pi]r dr. \ (7) 0\:f2f5 2 V Using the given potential in this equation gives (see the Appendix) 3 = - (b\[Epsilon]/V) exp(\[Epsilon]/kT) (g - 1) \ (8) = - (a/N V) exp(\[Epsilon]/kT). With the enthalpy given as H = E + pV, \ (9) we have H(T,p) = (5/2) RT + pB(T) - a p exp(\[Epsilon]/kT) / [RT + \ pB(T)]. (10) \ \>", "Text", AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}] }, Closed]], Cell[CellGroupData[{ Cell["The Joule-Thomson Coefficient", "Subtitle", AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ The Experimental Data \ \>", "Subsubtitle", PageBreakAbove->True, AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["\<\ ArgMuJT = ReadList[\"argmujt.list\",{Number,Number}]; plot = ListPlot[ArgMuJT, AxesLabel -> {\"t/C\",\" \"}, \t\tPlotLabel -> \t\t\" The Joule-Thomson Coefficient for Argon\" \t\t] \t\t (* see Smithsonian reference *)\t\t\ \>", "Input", PageWidth->PaperWidth, AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart % Scaling calculations 0.36829 0.00203 0.01472 0.1951 [ [( The Joule-Thomson Coefficient for Argon)] 0.5 0.62428 0 -1 Msboxa [(-100)] 0.16565 0.00222 0 1 Msboxa [(100)] 0.57092 0.00222 0 1 Msboxa [(200)] 0.77356 0.00222 0 1 Msboxa [(300)] 0.97619 0.00222 0 1 Msboxa [(t/C)] 1.00625 0.01472 -1 0 Msboxa [(0.5)] 0.35579 0.11226 1 0 Msboxa [(1)] 0.35579 0.20981 1 0 Msboxa [(1.5)] 0.35579 0.30736 1 0 Msboxa [(2)] 0.35579 0.40491 1 0 Msboxa [(2.5)] 0.35579 0.50245 1 0 Msboxa [(3)] 0.35579 0.6 1 0 Msboxa [( )] 0.36829 0.62428 0 -1 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 0.61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath %%Object: Graphics [ ] 0 setdash 0 setgray 0 setgray [( The Joule-Thomson Coefficient for Argon)] 0.5 0.62428 0 -1 Mshowa gsave gsave 0.002 setlinewidth 0 0.01472 moveto 1 0.01472 lineto stroke 0.16565 0.00847 moveto 0.16565 0.02097 lineto stroke 0 setgray [(-100)] 0.16565 0.00222 0 1 Mshowa 0.57092 0.00847 moveto 0.57092 0.02097 lineto stroke 0 setgray [(100)] 0.57092 0.00222 0 1 Mshowa 0.77356 0.00847 moveto 0.77356 0.02097 lineto stroke 0 setgray [(200)] 0.77356 0.00222 0 1 Mshowa 0.97619 0.00847 moveto 0.97619 0.02097 lineto stroke 0 setgray [(300)] 0.97619 0.00222 0 1 Mshowa 0 setgray [(t/C)] 1.00625 0.01472 -1 0 Mshowa 0.36829 0 moveto 0.36829 0.61803 lineto stroke 0.36204 0.11226 moveto 0.37454 0.11226 lineto stroke 0 setgray [(0.5)] 0.35579 0.11226 1 0 Mshowa 0.36204 0.20981 moveto 0.37454 0.20981 lineto stroke 0 setgray [(1)] 0.35579 0.20981 1 0 Mshowa 0.36204 0.30736 moveto 0.37454 0.30736 lineto stroke 0 setgray [(1.5)] 0.35579 0.30736 1 0 Mshowa 0.36204 0.40491 moveto 0.37454 0.40491 lineto stroke 0 setgray [(2)] 0.35579 0.40491 1 0 Mshowa 0.36204 0.50245 moveto 0.37454 0.50245 lineto stroke 0 setgray [(2.5)] 0.35579 0.50245 1 0 Mshowa 0.36204 0.6 moveto 0.37454 0.6 lineto stroke 0 setgray [(3)] 0.35579 0.6 1 0 Mshowa 0 setgray [( )] 0.36829 0.62428 0 -1 Mshowa grestore grestore 0 0 moveto 1 0 lineto 1 0.618034 lineto 0 0.618034 lineto closepath clip newpath 0 setgray gsave 0.008 setlinewidth 0.02381 0.60332 Mdot 0.04407 0.48002 Mdot 0.06434 0.36823 Mdot 0.08967 0.27478 Mdot 0.11499 0.23166 Mdot 0.14032 0.20357 Mdot 0.16565 0.18259 Mdot 0.19098 0.1665 Mdot 0.21631 0.15323 Mdot 0.26697 0.13099 Mdot 0.31763 0.11314 Mdot 0.36829 0.09874 Mdot 0.41895 0.08729 Mdot 0.4696 0.07754 Mdot 0.52026 0.06729 Mdot 0.57092 0.06179 Mdot 0.62158 0.05578 Mdot 0.67224 0.05071 Mdot 0.77356 0.04158 Mdot 0.87487 0.03383 Mdot 0.97619 0.02726 Mdot grestore % End of Graphics MathPictureEnd\ \>"], "Graphics", ImageSize->{282, 174}, ImageMargins->{{17, Inherited}, {Inherited, Inherited}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False] }, Closed]], Cell[CellGroupData[{ Cell["\<\ The Model Prediction (About 30 Minutes on a IIci)\ \>", "Subsubtitle", AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ ClearAll[a,R,H,k,tmp1,mujt,muJTAr,P] a = (g^3 - 1)*b*No*eps ; R = 8.3144 ; H = 5 R T / 2 + P BofT[T] - a P Exp[eps/(k T)]/ \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t(R T + P BofT[T]) k = R/No ; tmp1 = Solve[D[H,P,NonConstants->{T}] == 0, \t\tD[T,P,NonConstants -> {T}]]; mujt[T_] = D[T, P, NonConstants -> {T} ] /. tmp1[[1]] ; P = 101325.(* The units are now K/Pa change them to K/atm. *) muJTAr[T_] = mujt[T] 101325. ;\ \>", "Input", PageWidth->PaperWidth, PageBreakAbove->False, AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["plot1 = Plot[muJTAr[t+273.15],{t,-170,300}]", "Input", PageWidth->PaperWidth, AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart % Scaling calculations 0.36829 0.00203 0.01472 0.27466 [ [(-100.)] 0.16565 0.00222 0 1 Msboxa [(100.)] 0.57092 0.00222 0 1 Msboxa [(200.)] 0.77356 0.00222 0 1 Msboxa [(300.)] 0.97619 0.00222 0 1 Msboxa [(0.5)] 0.35579 0.15205 1 0 Msboxa [(1.)] 0.35579 0.28938 1 0 Msboxa [(1.5)] 0.35579 0.42671 1 0 Msboxa [(2.)] 0.35579 0.56404 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 0.61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath %%Object: Graphics [ ] 0 setdash 0 setgray gsave 0.002 setlinewidth 0 0.01472 moveto 1 0.01472 lineto stroke 0.16565 0.00847 moveto 0.16565 0.02097 lineto stroke [(-100.)] 0.16565 0.00222 0 1 Mshowa 0.57092 0.00847 moveto 0.57092 0.02097 lineto stroke [(100.)] 0.57092 0.00222 0 1 Mshowa 0.77356 0.00847 moveto 0.77356 0.02097 lineto stroke [(200.)] 0.77356 0.00222 0 1 Mshowa 0.97619 0.00847 moveto 0.97619 0.02097 lineto stroke [(300.)] 0.97619 0.00222 0 1 Mshowa 0.36829 0 moveto 0.36829 0.61803 lineto stroke 0.36204 0.15205 moveto 0.37454 0.15205 lineto stroke [(0.5)] 0.35579 0.15205 1 0 Mshowa 0.36204 0.28938 moveto 0.37454 0.28938 lineto stroke [(1.)] 0.35579 0.28938 1 0 Mshowa 0.36204 0.42671 moveto 0.37454 0.42671 lineto stroke [(1.5)] 0.35579 0.42671 1 0 Mshowa 0.36204 0.56404 moveto 0.37454 0.56404 lineto stroke [(2.)] 0.35579 0.56404 1 0 Mshowa grestore 0 0 moveto 1 0 lineto 1 0.618034 lineto 0 0.618034 lineto closepath clip newpath gsave 0 setgray gsave 0.004 setlinewidth 0.02381 0.60332 moveto 0.04365 0.52213 lineto 0.06349 0.45828 lineto 0.10317 0.36485 lineto 0.12302 0.32978 lineto 0.14286 0.30015 lineto 0.18254 0.25293 lineto 0.22222 0.21703 lineto 0.2619 0.18887 lineto 0.30159 0.16622 lineto 0.34127 0.14762 lineto 0.38095 0.13208 lineto 0.42063 0.11891 lineto 0.46032 0.10761 lineto 0.5 0.09781 lineto 0.53968 0.08923 lineto 0.57937 0.08166 lineto 0.61905 0.07493 lineto 0.65873 0.06891 lineto 0.69841 0.06349 lineto 0.7381 0.0586 lineto 0.77778 0.05414 lineto 0.81746 0.05008 lineto 0.85714 0.04635 lineto 0.89683 0.04293 lineto 0.93651 0.03976 lineto 0.97619 0.03684 lineto stroke grestore grestore % End of Graphics MathPictureEnd\ \>"], "Graphics", PageWidth->PaperWidth, ImageSize->{365, 225}, ImageMargins->{{66, Inherited}, {Inherited, Inherited}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False], Cell[OutputFormData["\<\ The Unformatted text for this cell was not generated. Use options in the Actions Settings dialog box to control when Unformatted text is generated.\ \>", "\<\ -Graphics-\ \>"], "Output", PageWidth->PaperWidth, AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["\<\ Comparison Theory and Experiment\ \>", "Subsubtitle", AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["Show[plot,plot1]", "Input", PageWidth->PaperWidth, AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["(*just a spacer*)", "Input", AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart % Scaling calculations 0.36829 0.00203 0.01472 0.1951 [ [( The Joule-Thomson Coefficient for Argon)] 0.5 0.61803 0 -1 Msboxa [(-100.)] 0.16565 0.00222 0 1 Msboxa [(100.)] 0.57092 0.00222 0 1 Msboxa [(200.)] 0.77356 0.00222 0 1 Msboxa [(300.)] 0.97619 0.00222 0 1 Msboxa [(t/C)] 1.00625 0.01472 -1 0 Msboxa [(0.5)] 0.35579 0.11226 1 0 Msboxa [(1.)] 0.35579 0.20981 1 0 Msboxa [(1.5)] 0.35579 0.30736 1 0 Msboxa [(2.)] 0.35579 0.40491 1 0 Msboxa [(2.5)] 0.35579 0.50245 1 0 Msboxa [(3.)] 0.35579 0.6 1 0 Msboxa [( )] 0.36829 0.62428 0 -1 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 0.61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath %%Object: Graphics [ ] 0 setdash 0 setgray [( The Joule-Thomson Coefficient for Argon)] 0.5 0.61803 0 -1 Mshowa gsave 0.002 setlinewidth 0 0.01472 moveto 1 0.01472 lineto stroke 0.16565 0.00847 moveto 0.16565 0.02097 lineto stroke [(-100.)] 0.16565 0.00222 0 1 Mshowa 0.57092 0.00847 moveto 0.57092 0.02097 lineto stroke [(100.)] 0.57092 0.00222 0 1 Mshowa 0.77356 0.00847 moveto 0.77356 0.02097 lineto stroke [(200.)] 0.77356 0.00222 0 1 Mshowa 0.97619 0.00847 moveto 0.97619 0.02097 lineto stroke [(300.)] 0.97619 0.00222 0 1 Mshowa [(t/C)] 1.00625 0.01472 -1 0 Mshowa 0.36829 0 moveto 0.36829 0.61803 lineto stroke 0.36204 0.11226 moveto 0.37454 0.11226 lineto stroke [(0.5)] 0.35579 0.11226 1 0 Mshowa 0.36204 0.20981 moveto 0.37454 0.20981 lineto stroke [(1.)] 0.35579 0.20981 1 0 Mshowa 0.36204 0.30736 moveto 0.37454 0.30736 lineto stroke [(1.5)] 0.35579 0.30736 1 0 Mshowa 0.36204 0.40491 moveto 0.37454 0.40491 lineto stroke [(2.)] 0.35579 0.40491 1 0 Mshowa 0.36204 0.50245 moveto 0.37454 0.50245 lineto stroke [(2.5)] 0.35579 0.50245 1 0 Mshowa 0.36204 0.6 moveto 0.37454 0.6 lineto stroke [(3.)] 0.35579 0.6 1 0 Mshowa [( )] 0.36829 0.62428 0 -1 Mshowa grestore 0 0 moveto 1 0 lineto 1 0.618034 lineto 0 0.618034 lineto closepath clip newpath gsave gsave gsave 0.008 setlinewidth 0.02381 0.60332 Mdot 0.04407 0.48002 Mdot 0.06434 0.36823 Mdot 0.08967 0.27478 Mdot 0.11499 0.23166 Mdot 0.14032 0.20357 Mdot 0.16565 0.18259 Mdot 0.19098 0.1665 Mdot 0.21631 0.15323 Mdot 0.26697 0.13099 Mdot 0.31763 0.11314 Mdot 0.36829 0.09874 Mdot 0.41895 0.08729 Mdot 0.4696 0.07754 Mdot 0.52026 0.06729 Mdot 0.57092 0.06179 Mdot 0.62158 0.05578 Mdot 0.67224 0.05071 Mdot 0.77356 0.04158 Mdot 0.87487 0.03383 Mdot 0.97619 0.02726 Mdot grestore grestore gsave gsave 0 setgray gsave 0.004 setlinewidth 0.02381 0.43281 moveto 0.04365 0.37514 lineto 0.06349 0.32979 lineto 0.10317 0.26342 lineto 0.12302 0.23851 lineto 0.14286 0.21747 lineto 0.18254 0.18392 lineto 0.22222 0.15842 lineto 0.2619 0.13842 lineto 0.30159 0.12233 lineto 0.34127 0.10912 lineto 0.38095 0.09808 lineto 0.42063 0.08872 lineto 0.46032 0.0807 lineto 0.5 0.07374 lineto 0.53968 0.06764 lineto 0.57937 0.06227 lineto 0.61905 0.05749 lineto 0.65873 0.05321 lineto 0.69841 0.04936 lineto 0.7381 0.04588 lineto 0.77778 0.04272 lineto 0.81746 0.03983 lineto 0.85714 0.03719 lineto 0.89683 0.03475 lineto 0.93651 0.03251 lineto 0.97619 0.03043 lineto stroke grestore grestore grestore grestore % End of Graphics MathPictureEnd\ \>"], "Graphics", PageWidth->PaperWidth, ImageSize->{365, 225}, ImageMargins->{{66, Inherited}, {Inherited, Inherited}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False], Cell[OutputFormData["\<\ The Unformatted text for this cell was not generated. Use options in the Actions Settings dialog box to control when Unformatted text is generated.\ \>", "\<\ -Graphics-\ \>"], "Output", PageWidth->PaperWidth, AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["References", "Subtitle", AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ "Guggenheim, Edward A., ", StyleBox["Elements of the Kinetic Theory of Gases, ", FontSlant->"Italic"], "Oxford, 1960.\n\nNBS Circular 564, Tables of Thermal Properties of Gases\n\ \nSmithsonian Physical Tables nineth revised edition, volume 39, 1954\n\n" }], "Text", AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}] }, Closed]] }, Open ]] }, FrontEndVersion->"4.1 for Microsoft Windows", ScreenRectangle->{{0, 1024}, {0, 695}}, WindowToolbars->{}, CellGrouping->Manual, WindowSize->{499, 599}, WindowMargins->{{Automatic, 76}, {Automatic, 0}}, PrivateNotebookOptions->{"ColorPalette"->{RGBColor, -1}}, ShowCellLabel->True, ShowCellTags->False, RenderingOptions->{"ObjectDithering"->True, "RasterDithering"->False} ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. *******************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1727, 52, 134, 3, 280, "Title"], Cell[1864, 57, 134, 2, 93, "Subtitle"], Cell[2001, 61, 303, 5, 154, "Subsubtitle"], Cell[CellGroupData[{ Cell[2329, 70, 92, 2, 64, "Subtitle"], Cell[2424, 74, 885, 16, 70, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[3346, 95, 85, 2, 70, "Subtitle"], Cell[3434, 99, 1711, 42, 70, "Text", PageBreakAbove->True] }, Closed]], Cell[CellGroupData[{ Cell[5182, 146, 126, 3, 70, "Subtitle", PageBreakAbove->True], Cell[5311, 151, 117, 2, 70, "Subsubtitle"], Cell[5431, 155, 188, 6, 70, "Input"], Cell[CellGroupData[{ Cell[5644, 165, 242, 7, 70, "Input"], Cell[5889, 174, 3809, 182, 70, 3674, 178, "GraphicsData", "PostScript", \ "Graphics"], Cell[9701, 358, 271, 8, 70, "Output"] }, Closed]], Cell[CellGroupData[{ Cell[10009, 371, 229, 8, 70, "Subsubtitle", PageBreakAbove->True], Cell[CellGroupData[{ Cell[10263, 383, 456, 13, 70, "Input"], Cell[10722, 398, 3038, 149, 70, 2895, 145, "GraphicsData", "PostScript", \ "Graphics"], Cell[13763, 549, 271, 8, 70, "Output"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[14083, 563, 146, 3, 70, "Subsubtitle", PageBreakAbove->False], Cell[CellGroupData[{ Cell[14254, 570, 146, 4, 70, "Input", PageBreakAbove->False], Cell[14403, 576, 4716, 229, 70, 4573, 225, "GraphicsData", "PostScript", \ "Graphics"], Cell[19122, 807, 271, 8, 70, "Output"] }, Closed]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[19454, 822, 151, 3, 70, "Subtitle", PageBreakAbove->True], Cell[19608, 827, 1673, 42, 70, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[21318, 874, 109, 2, 70, "Subtitle"], Cell[21430, 878, 139, 6, 70, "Subsubtitle", PageBreakAbove->True], Cell[CellGroupData[{ Cell[21594, 888, 342, 11, 70, "Input"], Cell[21939, 901, 2841, 135, 70, 2698, 131, "GraphicsData", "PostScript", \ "Graphics"] }, Closed]], Cell[CellGroupData[{ Cell[24817, 1041, 141, 6, 70, "Subsubtitle"], Cell[24961, 1049, 567, 16, 70, "Input", PageBreakAbove->False], Cell[CellGroupData[{ Cell[25553, 1069, 145, 3, 70, "Input"], Cell[25701, 1074, 2407, 114, 70, 2239, 109, "GraphicsData", "PostScript", \ "Graphics"], Cell[28111, 1190, 296, 9, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[28456, 1205, 124, 5, 70, "Subsubtitle"], Cell[28583, 1212, 118, 3, 70, "Input"], Cell[CellGroupData[{ Cell[28726, 1219, 94, 2, 70, "Input"], Cell[28823, 1223, 3450, 160, 70, 3282, 155, "GraphicsData", "PostScript", \ "Graphics"], Cell[32276, 1385, 296, 9, 70, "Output"] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[32633, 1401, 90, 2, 70, "Subtitle"], Cell[32726, 1405, 353, 8, 70, "Text"] }, Closed]] }, Open ]] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************)