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Notebook[{
Cell[CellGroupData[{
Cell["The Entropy of Lead", "Title",
TextAlignment->Center],
Cell["Computational Document", "Text"],
Cell["\<\
by
George Hardgrove
Chemistry Department
St. Olaf College
Northfield, MN 55057
hardgrov@lars.acc.stolaf.edu\
\>", "Text",
TextAlignment->Center],
Cell["\<\
The instuctions for using this document are in the file cppbins.mcd\
\>", "Text"],
Cell["\<\
\[Copyright] Copyright George Hardgrove 1996-2004. All rights reserved. You \
are welcome to use this document in your own classes but commercial use is \
not allowed without the permission of the author.\
\>", "Text"],
Cell[TextData[{
StyleBox["Translated from Mathcad to Mathematica by",
FontWeight->"Bold"],
": Laura Rachel Yindra, Journal of Chemical Education, University of \
Wisconsin-Madison, August 2003."
}], "Text"],
Cell["\<\
The heat capacity data are located in a file called cplead. Values of Cp and \
absolute temperature are read into the computer. The computer then \
calculates values of ds = Cp/T for each temperature.\
\>", "Text"],
Cell[BoxData[
\(A := Import["\", "\"]\)], "Input"],
Cell["\<\
note: if Mathematica cannot find this file, open and evaluate cplead.nb\
\>", "SmallText"],
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Cell["\<\
This assigns the columns of the A matrix to temperature and heat capacity \
vectors.\
\>", "Text"],
Cell["Next view the contents of these vectors.", "Text"],
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0.1048`, 0.08926174496644296`}\)], "Output"]
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Cell["\<\
To use the simple formula for trapezoid integration with evenly spaced \
points, we need to use interpolation methods. First we split up the space \
between the first and last points into n segments where we can adjust n.\
\>", "Text"],
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\(n := 10\)], "Input"],
Cell[CellGroupData[{
Cell[BoxData[
\(\[CapitalDelta]x = N[\((Last[T] - T[\([1]\)])\)/\((n)\)]\)], "Input"],
Cell[BoxData[
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Cell[CellGroupData[{
Cell[BoxData[
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}, Open ]],
Cell["\<\
We can now find the value of the function at each x[[j]]. On the graph below \
the black + signs are the experimental data, the red bars indicate the value \
of the function at evenly spaced points fx[j].\
\>", "Text"],
Cell[BoxData[
\(fx :=
Interpolation[
Table[{T[\([i]\)], dS[\([i]\)]}, {i, 1, ndata}]]\)], "Input"],
Cell["The evenly spaced points are put into the area formula", "Text"],
Cell[CellGroupData[{
Cell[BoxData[
\(area =
Sum[\[CapitalDelta]x\ fx[x[\([j]\)]], {j, 2,
n}] + \((fx[x[\([1]\)]] + fx[x[\([n + 1]\)]])\)/
2\ \[CapitalDelta]x\)], "Input"],
Cell[BoxData[
\(60.123149822455595`\)], "Output"]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell["Graph Setup", "Subsubtitle"],
Cell[CellGroupData[{
Cell[BoxData[
\(plot1 =
MultipleListPlot[
Table[{x[\([i]\)], fx[x[\([i]\)]]}, {i, 1, Length[x]}],
SymbolShape \[Rule] Stem, Frame \[Rule] True,
FrameLabel \[Rule] {"\", "\<\[FilledCircle] fx, * dS\>"},
DisplayFunction \[Rule] Identity];
plot2 = MultipleListPlot[Table[{T[\([i]\)], dS[\([i]\)]}, {i, 1, ndata}],
DisplayFunction \[Rule] Identity]\)], "Input"],
Cell[BoxData[
TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\),
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Cell[CellGroupData[{
Cell[BoxData[
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Cell[GraphicsData["PostScript", "\<\
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