(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 8.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       157,          7]
NotebookDataLength[    159790,       3237]
NotebookOptionsPosition[    156016,       3126]
NotebookOutlinePosition[    156381,       3142]
CellTagsIndexPosition[    156338,       3139]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell[TextData[{
 "pressure gradient dP/dz = -",
 StyleBox["r",
  FontFamily->"Symbol"],
 "g with T = To - c*z"
}], "Subsubsection",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.5560159079377375`*^9, 3.5560159598504424`*^9}, 
   3.5560159981619453`*^9}],

Cell[BoxData[{
 RowBox[{"f1", "=", 
  RowBox[{"1", "/", 
   RowBox[{"(", 
    RowBox[{"To", "-", 
     RowBox[{"c", "*", "z"}]}], ")"}]}]}], "\[IndentingNewLine]", 
 RowBox[{"f2", "=", 
  RowBox[{"1", "/", 
   RowBox[{"(", 
    RowBox[{"To", "-", 
     RowBox[{"c", "*", 
      RowBox[{"z", "^", "2"}]}]}], ")"}]}]}], "\[IndentingNewLine]", 
 RowBox[{"f2a", "=", 
  RowBox[{"f2", "/.", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"c", "\[Rule]", 
      RowBox[{"-", "7"}]}], ",", 
     RowBox[{"To", "\[Rule]", "285"}]}], "}"}]}]}], "\[IndentingNewLine]", 
 RowBox[{"Integrate", "[", 
  RowBox[{"f1", ",", "z"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"Integrate", "[", 
  RowBox[{"f2", ",", "z"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Integrate", "[", 
   RowBox[{"f2a", ",", 
    RowBox[{"{", 
     RowBox[{"z", ",", "0", ",", "4300"}], "}"}]}], "]"}], "//", 
  "N"}]}], "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.556015730922366*^9, 3.5560158913686476`*^9}, 
   3.5560159981619453`*^9}],

Cell[BoxData[
 FractionBox["1", 
  RowBox[{"To", "-", 
   RowBox[{"c", " ", "z"}]}]]], "Output",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.5560157557576094`*^9, 3.556015766428028*^9}, {
   3.5560158035248933`*^9, 3.5560158341009474`*^9}, {3.55601588689144*^9, 
   3.5560158922422495`*^9}, 3.5560159981619453`*^9}],

Cell[BoxData[
 FractionBox["1", 
  RowBox[{"To", "-", 
   RowBox[{"c", " ", 
    SuperscriptBox["z", "2"]}]}]]], "Output",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.5560157557576094`*^9, 3.556015766428028*^9}, {
   3.5560158035248933`*^9, 3.5560158341009474`*^9}, {3.55601588689144*^9, 
   3.5560158922422495`*^9}, 3.5560159981619453`*^9}],

Cell[BoxData[
 FractionBox["1", 
  RowBox[{"285", "+", 
   RowBox[{"7", " ", 
    SuperscriptBox["z", "2"]}]}]]], "Output",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.5560157557576094`*^9, 3.556015766428028*^9}, {
   3.5560158035248933`*^9, 3.5560158341009474`*^9}, {3.55601588689144*^9, 
   3.5560158922422495`*^9}, 3.5560159981619453`*^9}],

Cell[BoxData[
 RowBox[{"-", 
  FractionBox[
   RowBox[{"Log", "[", 
    RowBox[{"To", "-", 
     RowBox[{"c", " ", "z"}]}], "]"}], "c"]}]], "Output",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.5560157557576094`*^9, 3.556015766428028*^9}, {
   3.5560158035248933`*^9, 3.5560158341009474`*^9}, {3.55601588689144*^9, 
   3.5560158922422495`*^9}, 3.5560159981619453`*^9}],

Cell[BoxData[
 FractionBox[
  RowBox[{"ArcTanh", "[", 
   FractionBox[
    RowBox[{
     SqrtBox["c"], " ", "z"}], 
    SqrtBox["To"]], "]"}], 
  RowBox[{
   SqrtBox["c"], " ", 
   SqrtBox["To"]}]]], "Output",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.5560157557576094`*^9, 3.556015766428028*^9}, {
   3.5560158035248933`*^9, 3.5560158341009474`*^9}, {3.55601588689144*^9, 
   3.5560158922422495`*^9}, 3.5560159981619453`*^9}],

Cell[BoxData["0.03513483867422335`"], "Output",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.5560157557576094`*^9, 3.556015766428028*^9}, {
   3.5560158035248933`*^9, 3.5560158341009474`*^9}, {3.55601588689144*^9, 
   3.5560158923514495`*^9}, 3.5560159981619453`*^9}]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[{
 "pressure gradient dP/dz = -",
 StyleBox["r",
  FontFamily->"Symbol"],
 "g with T = To - c*z^2, homework #2"
}], "Subsubsection",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.5560159079377375`*^9, 3.5560159598504424`*^9}, 
   3.5560159981619453`*^9, {3.556274005152324*^9, 3.556274019551124*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"f1", "=", 
   RowBox[{"1", "/", 
    RowBox[{"(", 
     RowBox[{"To", "-", 
      RowBox[{"c", "*", 
       RowBox[{"z", "^", "2"}]}]}], ")"}]}]}], "     ", 
  RowBox[{"(*", " ", 
   RowBox[{"basic", " ", "temperature", " ", "function"}], " ", 
   "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"c1", "=", 
   RowBox[{"7", "*", 
    RowBox[{"10", "^", 
     RowBox[{"(", 
      RowBox[{"-", "6"}], ")"}]}]}]}], "     ", 
  RowBox[{"(*", " ", 
   RowBox[{
   "define", " ", "the", " ", "constant", " ", "to", " ", "make", " ", 
    "things", " ", "easy"}], " ", "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"f2", "=", 
   RowBox[{
    RowBox[{
     RowBox[{"-", "1"}], "*", "f1"}], "/.", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"To", "\[Rule]", "280"}], ",", 
      RowBox[{"c", "\[Rule]", "c1"}]}], "}"}]}]}], "    ", 
  RowBox[{"(*", " ", 
   RowBox[{"just", " ", "the", " ", 
    RowBox[{"temp", ".", " ", "function"}]}], " ", 
   "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"f3", "=", 
   RowBox[{
    RowBox[{"-", "1"}], "*", 
    RowBox[{"(", 
     RowBox[{"M", "*", 
      RowBox[{"g", "/", "k"}]}], ")"}], "*", "f1"}]}], "       ", 
  RowBox[{"(*", " ", 
   RowBox[{"put", " ", "all", " ", "the", " ", "constants", " ", "in"}], " ", 
   "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{"f4", "=", 
  RowBox[{"f3", "/.", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"To", "\[Rule]", "280"}], ",", 
     RowBox[{"c", "\[Rule]", "c1"}], ",", 
     RowBox[{"M", "\[Rule]", 
      RowBox[{"4.81", "*", 
       RowBox[{"10", "^", 
        RowBox[{"(", 
         RowBox[{"-", "26"}], ")"}]}]}]}], ",", 
     RowBox[{"g", "\[Rule]", "9.8"}], ",", 
     RowBox[{"k", "\[Rule]", 
      RowBox[{"1.38", "*", 
       RowBox[{"10", "^", 
        RowBox[{"(", 
         RowBox[{"-", "23"}], ")"}]}]}]}]}], "}"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Integrate", "[", 
   RowBox[{"f1", ",", "z"}], "]"}], "    ", 
  RowBox[{"(*", " ", 
   RowBox[{"just", " ", "integrate", " ", "the", " ", 
    RowBox[{"temp", ".", " ", "function"}]}], " ", 
   "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"Integrate", "[", 
    RowBox[{"f2", ",", 
     RowBox[{"{", 
      RowBox[{"z", ",", "0", ",", "1430"}], "}"}]}], "]"}], "//", "N"}], 
  "     ", 
  RowBox[{"(*", " ", 
   RowBox[{"get", " ", "a", " ", "numerical", " ", "value"}], " ", 
   "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"ans1", "=", 
   RowBox[{
    RowBox[{"Integrate", "[", 
     RowBox[{"f4", ",", 
      RowBox[{"{", 
       RowBox[{"z", ",", "0", ",", "1430"}], "}"}]}], "]"}], "//", "N"}]}], 
  "     ", 
  RowBox[{"(*", " ", 
   RowBox[{"integrate", " ", "the", " ", "real", " ", "thing"}], " ", 
   "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{"Pf", "=", 
  RowBox[{"1.00", "*", 
   RowBox[{"Exp", "[", "ans1", "]"}], "      ", 
   RowBox[{"(*", " ", 
    RowBox[{
    "get", " ", "this", " ", "in", " ", "terms", " ", "of", " ", "a", " ", 
     "final", " ", "pressure"}], " ", "*)"}], " "}]}]}], "Input",
 CellChangeTimes->{{3.5562738506759243`*^9, 3.556273944302724*^9}, {
  3.556274040007924*^9, 3.556274218007324*^9}, {3.556274551808524*^9, 
  3.556274576674924*^9}, {3.5562849499422283`*^9, 3.5562850273338284`*^9}, {
  3.5562850757302284`*^9, 3.5562851201746283`*^9}, {3.5562854591002283`*^9, 
  3.5562854756518283`*^9}, {3.5564457819257817`*^9, 3.5564457854667816`*^9}}],

Cell[BoxData[
 FractionBox["1", 
  RowBox[{"To", "-", 
   RowBox[{"c", " ", 
    SuperscriptBox["z", "2"]}]}]]], "Output",
 CellChangeTimes->{
  3.5562738624071245`*^9, {3.556273896273124*^9, 3.556273947578724*^9}, 
   3.5562741358237243`*^9, {3.556274183156724*^9, 3.5562742189589243`*^9}, 
   3.5562745541485243`*^9, 3.556274584556924*^9, 3.556284970222228*^9, 
   3.5564457960767817`*^9}],

Cell[BoxData[
 FractionBox["7", "1000000"]], "Output",
 CellChangeTimes->{
  3.5562738624071245`*^9, {3.556273896273124*^9, 3.556273947578724*^9}, 
   3.5562741358237243`*^9, {3.556274183156724*^9, 3.5562742189589243`*^9}, 
   3.5562745541485243`*^9, 3.556274584556924*^9, 3.556284970222228*^9, 
   3.556445796080782*^9}],

Cell[BoxData[
 RowBox[{"-", 
  FractionBox["1", 
   RowBox[{"280", "-", 
    FractionBox[
     RowBox[{"7", " ", 
      SuperscriptBox["z", "2"]}], "1000000"]}]]}]], "Output",
 CellChangeTimes->{
  3.5562738624071245`*^9, {3.556273896273124*^9, 3.556273947578724*^9}, 
   3.5562741358237243`*^9, {3.556274183156724*^9, 3.5562742189589243`*^9}, 
   3.5562745541485243`*^9, 3.556274584556924*^9, 3.556284970222228*^9, 
   3.5564457960837817`*^9}],

Cell[BoxData[
 RowBox[{"-", 
  FractionBox[
   RowBox[{"g", " ", "M"}], 
   RowBox[{"k", " ", 
    RowBox[{"(", 
     RowBox[{"To", "-", 
      RowBox[{"c", " ", 
       SuperscriptBox["z", "2"]}]}], ")"}]}]]}]], "Output",
 CellChangeTimes->{
  3.5562738624071245`*^9, {3.556273896273124*^9, 3.556273947578724*^9}, 
   3.5562741358237243`*^9, {3.556274183156724*^9, 3.5562742189589243`*^9}, 
   3.5562745541485243`*^9, 3.556274584556924*^9, 3.556284970222228*^9, 
   3.556445796085782*^9}],

Cell[BoxData[
 RowBox[{"-", 
  FractionBox["0.03415797101449274`", 
   RowBox[{"280", "-", 
    FractionBox[
     RowBox[{"7", " ", 
      SuperscriptBox["z", "2"]}], "1000000"]}]]}]], "Output",
 CellChangeTimes->{
  3.5562738624071245`*^9, {3.556273896273124*^9, 3.556273947578724*^9}, 
   3.5562741358237243`*^9, {3.556274183156724*^9, 3.5562742189589243`*^9}, 
   3.5562745541485243`*^9, 3.556274584556924*^9, 3.556284970222228*^9, 
   3.556445796088782*^9}],

Cell[BoxData[
 FractionBox[
  RowBox[{"ArcTanh", "[", 
   FractionBox[
    RowBox[{
     SqrtBox["c"], " ", "z"}], 
    SqrtBox["To"]], "]"}], 
  RowBox[{
   SqrtBox["c"], " ", 
   SqrtBox["To"]}]]], "Output",
 CellChangeTimes->{
  3.5562738624071245`*^9, {3.556273896273124*^9, 3.556273947578724*^9}, 
   3.5562741358237243`*^9, {3.556274183156724*^9, 3.5562742189589243`*^9}, 
   3.5562745541485243`*^9, 3.556274584556924*^9, 3.556284970222228*^9, 
   3.556445796604782*^9}],

Cell[BoxData[
 RowBox[{"-", "5.196943866791802`"}]], "Output",
 CellChangeTimes->{
  3.5562738624071245`*^9, {3.556273896273124*^9, 3.556273947578724*^9}, 
   3.5562741358237243`*^9, {3.556274183156724*^9, 3.5562742189589243`*^9}, 
   3.5562745541485243`*^9, 3.556274584556924*^9, 3.556284970222228*^9, 
   3.5564457984387817`*^9}],

Cell[BoxData[
 RowBox[{"-", "0.17751705796582012`"}]], "Output",
 CellChangeTimes->{
  3.5562738624071245`*^9, {3.556273896273124*^9, 3.556273947578724*^9}, 
   3.5562741358237243`*^9, {3.556274183156724*^9, 3.5562742189589243`*^9}, 
   3.5562745541485243`*^9, 3.556274584556924*^9, 3.556284970222228*^9, 
   3.556445798562782*^9}],

Cell[BoxData["0.8373467157822726`"], "Output",
 CellChangeTimes->{
  3.5562738624071245`*^9, {3.556273896273124*^9, 3.556273947578724*^9}, 
   3.5562741358237243`*^9, {3.556274183156724*^9, 3.5562742189589243`*^9}, 
   3.5562745541485243`*^9, 3.556274584556924*^9, 3.556284970222228*^9, 
   3.556445798564782*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"   ", 
  RowBox[{"(*", " ", 
   RowBox[{
   "see", " ", "how", " ", "the", " ", "2", " ", "temperature", " ", 
    "functions", " ", "compare"}], " ", "*)"}], " ", "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"f0", "=", 
    RowBox[{"To", "-", 
     RowBox[{"c0", "*", "z"}]}]}], "   ", 
   RowBox[{"(*", " ", 
    RowBox[{"linear", " ", 
     RowBox[{"temp", ".", " ", "function"}]}], " ", "*)"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"f0a", "=", 
     RowBox[{"f0", "/.", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"To", "\[Rule]", "290"}], ",", 
        RowBox[{"c0", "\[Rule]", 
         RowBox[{"7", "/", "1000"}]}]}], "}"}]}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{"f1", "=", 
    RowBox[{"To", "-", 
     RowBox[{"c1", "*", 
      RowBox[{"z", "^", "2"}]}]}]}], "  ", 
   RowBox[{"(*", " ", 
    RowBox[{"quadratic", " ", 
     RowBox[{"temp", ".", " ", "function"}]}], " ", "*)"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"f1a", "=", 
     RowBox[{"f1", "/.", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"To", "\[Rule]", "290"}], ",", 
        RowBox[{"c1", "\[Rule]", 
         RowBox[{"7", "/", "1000000"}]}]}], "}"}]}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{"Plot", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"f0a", ",", "f1a"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"z", ",", "0", ",", "5000"}], "}"}]}], "]"}]}]}]], "Input",
 CellChangeTimes->{{3.5562851491594286`*^9, 3.5562853874026284`*^9}, {
  3.5562854446234283`*^9, 3.5562854513470287`*^9}}],

Cell[BoxData[
 RowBox[{"To", "-", 
  RowBox[{"c0", " ", "z"}]}]], "Output",
 CellChangeTimes->{
  3.5562852260830283`*^9, 3.5562852992002287`*^9, {3.5562853354858284`*^9, 
   3.5562853550794287`*^9}}],

Cell[BoxData[
 RowBox[{"To", "-", 
  FractionBox[
   RowBox[{"7", " ", 
    SuperscriptBox["z", "2"]}], "1000000"]}]], "Output",
 CellChangeTimes->{
  3.5562852260830283`*^9, 3.5562852992002287`*^9, {3.5562853354858284`*^9, 
   3.5562853550794287`*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJwVzXs0VAkABvBhskNFtbPlUUilrLKYXcnYPb5qRdFUjjX21LTjWU7l3jsi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     "]]}, 
   {Hue[0.9060679774997897, 0.6, 0.6], LineBox[CompressedData["
1:eJwV1Hk01VsbB3AyVmYNZmVoMJbIFL5CKXJdZMg5ZqcM1xlIFCmVOhL3SEIl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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 120.},
  PlotRange->{{0, 5000}, {115.00000714285707`, 289.99999999999994`}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02]}]], "Output",
 CellChangeTimes->{
  3.5562852260830283`*^9, 3.5562852992002287`*^9, {3.5562853354858284`*^9, 
   3.5562853550794287`*^9}},
 ImageCache->GraphicsData["CompressedBitmap", "\<\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\
\>"]]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["Boltzmann distribution", "Subsubsection",
 CellChangeTimes->{{3.561131532892935*^9, 3.561131537682143*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", 
   RowBox[{"Dv", ",", "Dv1", ",", " ", "Dv2", ",", "v"}], "]"}], "  ", 
  RowBox[{"(*", " ", 
   RowBox[{
   "this", " ", "is", " ", "how", " ", "to", " ", "clear", " ", "variables"}],
    " ", "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{"Dv", "=", 
  RowBox[{
   RowBox[{
    RowBox[{"(", 
     RowBox[{"m", "/", 
      RowBox[{"(", 
       RowBox[{"2", "*", "Pi", "*", "k", "*", "T"}], ")"}]}], ")"}], "^", 
    RowBox[{"(", 
     RowBox[{"3", "/", "2"}], ")"}]}], "*", "4", "*", "Pi", "*", 
   RowBox[{"v", "^", "2"}], "*", 
   RowBox[{"Exp", "[", 
    RowBox[{
     RowBox[{"-", "B"}], "*", 
     RowBox[{"(", 
      RowBox[{"1", "/", "2"}], ")"}], "*", "m", "*", 
     RowBox[{"v", "^", "2"}]}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Dv1", "=", 
   RowBox[{"Dv", "/.", 
    RowBox[{"{", 
     RowBox[{"B", "\[Rule]", 
      RowBox[{"1", "/", 
       RowBox[{"(", 
        RowBox[{"k", "*", "T"}], ")"}]}]}], "}"}]}]}], "  ", 
  RowBox[{"(*", " ", 
   RowBox[{"the", " ", "/.", " ", 
    RowBox[{"is", " ", "the", " ", "substitution"}]}], " ", 
   "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{"Dv2", "=", 
  RowBox[{"Dv1", "/.", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"m", "\[Rule]", 
      RowBox[{"1.674", "*", 
       RowBox[{"10", "^", 
        RowBox[{"(", 
         RowBox[{"-", "27"}], ")"}]}]}]}], ",", 
     RowBox[{"k", "\[Rule]", 
      RowBox[{"1.38066", "*", 
       RowBox[{"10", "^", 
        RowBox[{"(", 
         RowBox[{"-", "23"}], ")"}]}]}]}]}], "}"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Dv293", "=", 
   RowBox[{"Dv2", "/.", 
    RowBox[{"{", 
     RowBox[{"T", "\[Rule]", "293"}], "}"}]}]}], "    ", 
  RowBox[{"(*", " ", 
   RowBox[{"specific", " ", "temperature"}], " ", 
   "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{"Dv5000", "=", 
  RowBox[{"Dv2", "/.", 
   RowBox[{"{", 
    RowBox[{"T", "\[Rule]", "5000"}], "}"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Dv10000", "=", 
   RowBox[{"Dv2", "/.", 
    RowBox[{"{", 
     RowBox[{"T", "\[Rule]", "10000"}], "}"}]}]}], "\[IndentingNewLine]", 
  "   ", 
  RowBox[{"(*", " ", 
   RowBox[{
   "plotting", " ", "things", " ", "with", " ", "various", " ", "options"}], 
   " ", "*)"}], " "}], "\[IndentingNewLine]", 
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"Dv5000", ",", "Dv10000"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"v", ",", "0", ",", 
     RowBox[{"10", "^", "4.5"}]}], "}"}], ",", 
   RowBox[{"PlotRange", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"0", ",", 
      RowBox[{"10", "^", 
       RowBox[{"(", 
        RowBox[{"-", "4"}], ")"}]}]}], "}"}]}], ",", 
   RowBox[{"PlotLabel", "\[Rule]", "\"\<Boltzmann distribution\>\""}], ",", 
   RowBox[{"AxesLabel", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"\"\<x\>\"", ",", "\"\<D(v)\>\""}], "}"}]}]}], "]"}]}], "Input",
 CellChangeTimes->{{3.5611315406617484`*^9, 3.5611315412701497`*^9}, {
  3.5611315897706347`*^9, 3.561132045511835*^9}, {3.5611320820314994`*^9, 
  3.5611321708590555`*^9}, {3.561132816026189*^9, 3.5611328506426497`*^9}, {
  3.5611421231577797`*^9, 3.5611422246983585`*^9}}],

Cell[BoxData[
 RowBox[{
  SuperscriptBox["\[ExponentialE]", 
   RowBox[{
    RowBox[{"-", 
     FractionBox["1", "2"]}], " ", "B", " ", "m", " ", 
    SuperscriptBox["v", "2"]}]], " ", 
  SqrtBox[
   FractionBox["2", "\[Pi]"]], " ", 
  SuperscriptBox[
   RowBox[{"(", 
    FractionBox["m", 
     RowBox[{"k", " ", "T"}]], ")"}], 
   RowBox[{"3", "/", "2"}]], " ", 
  SuperscriptBox["v", "2"]}]], "Output",
 CellChangeTimes->{
  3.5611316612031603`*^9, 3.5611317280336776`*^9, 3.561131826797451*^9, {
   3.561131868247724*^9, 3.5611318887617598`*^9}, {3.561131924111422*^9, 
   3.5611320467286377`*^9}, 3.5611320979123273`*^9, {3.5611321453520107`*^9, 
   3.5611321714986563`*^9}, {3.56113281112778*^9, 3.561132851313451*^9}, {
   3.5611421934827037`*^9, 3.56114222568116*^9}}],

Cell[BoxData[
 RowBox[{
  SuperscriptBox["\[ExponentialE]", 
   RowBox[{"-", 
    FractionBox[
     RowBox[{"m", " ", 
      SuperscriptBox["v", "2"]}], 
     RowBox[{"2", " ", "k", " ", "T"}]]}]], " ", 
  SqrtBox[
   FractionBox["2", "\[Pi]"]], " ", 
  SuperscriptBox[
   RowBox[{"(", 
    FractionBox["m", 
     RowBox[{"k", " ", "T"}]], ")"}], 
   RowBox[{"3", "/", "2"}]], " ", 
  SuperscriptBox["v", "2"]}]], "Output",
 CellChangeTimes->{
  3.5611316612031603`*^9, 3.5611317280336776`*^9, 3.561131826797451*^9, {
   3.561131868247724*^9, 3.5611318887617598`*^9}, {3.561131924111422*^9, 
   3.5611320467286377`*^9}, 3.5611320979123273`*^9, {3.5611321453520107`*^9, 
   3.5611321714986563`*^9}, {3.56113281112778*^9, 3.561132851313451*^9}, {
   3.5611421934827037`*^9, 3.56114222568116*^9}}],

Cell[BoxData[
 RowBox[{"1.0652293593787803`*^-6", " ", 
  SuperscriptBox["\[ExponentialE]", 
   RowBox[{"-", 
    FractionBox[
     RowBox[{"0.00006062318021815653`", " ", 
      SuperscriptBox["v", "2"]}], "T"]}]], " ", 
  SuperscriptBox[
   RowBox[{"(", 
    FractionBox["1", "T"], ")"}], 
   RowBox[{"3", "/", "2"}]], " ", 
  SuperscriptBox["v", "2"]}]], "Output",
 CellChangeTimes->{
  3.5611316612031603`*^9, 3.5611317280336776`*^9, 3.561131826797451*^9, {
   3.561131868247724*^9, 3.5611318887617598`*^9}, {3.561131924111422*^9, 
   3.5611320467286377`*^9}, 3.5611320979123273`*^9, {3.5611321453520107`*^9, 
   3.5611321714986563`*^9}, {3.56113281112778*^9, 3.561132851313451*^9}, {
   3.5611421934827037`*^9, 3.56114222568116*^9}}],

Cell[BoxData[
 RowBox[{"2.1239373258572694`*^-10", " ", 
  SuperscriptBox["\[ExponentialE]", 
   RowBox[{
    RowBox[{"-", "2.0690505193910078`*^-7"}], " ", 
    SuperscriptBox["v", "2"]}]], " ", 
  SuperscriptBox["v", "2"]}]], "Output",
 CellChangeTimes->{
  3.5611316612031603`*^9, 3.5611317280336776`*^9, 3.561131826797451*^9, {
   3.561131868247724*^9, 3.5611318887617598`*^9}, {3.561131924111422*^9, 
   3.5611320467286377`*^9}, 3.5611320979123273`*^9, {3.5611321453520107`*^9, 
   3.5611321714986563`*^9}, {3.56113281112778*^9, 3.561132851313451*^9}, {
   3.5611421934827037`*^9, 3.56114222568116*^9}}],

Cell[BoxData[
 RowBox[{"3.0129236141429492`*^-12", " ", 
  SuperscriptBox["\[ExponentialE]", 
   RowBox[{
    RowBox[{"-", "1.2124636043631307`*^-8"}], " ", 
    SuperscriptBox["v", "2"]}]], " ", 
  SuperscriptBox["v", "2"]}]], "Output",
 CellChangeTimes->{
  3.5611316612031603`*^9, 3.5611317280336776`*^9, 3.561131826797451*^9, {
   3.561131868247724*^9, 3.5611318887617598`*^9}, {3.561131924111422*^9, 
   3.5611320467286377`*^9}, 3.5611320979123273`*^9, {3.5611321453520107`*^9, 
   3.5611321714986563`*^9}, {3.56113281112778*^9, 3.561132851313451*^9}, {
   3.5611421934827037`*^9, 3.56114222569676*^9}}],

Cell[BoxData[
 RowBox[{"1.0652293593787803`*^-12", " ", 
  SuperscriptBox["\[ExponentialE]", 
   RowBox[{
    RowBox[{"-", "6.062318021815653`*^-9"}], " ", 
    SuperscriptBox["v", "2"]}]], " ", 
  SuperscriptBox["v", "2"]}]], "Output",
 CellChangeTimes->{
  3.5611316612031603`*^9, 3.5611317280336776`*^9, 3.561131826797451*^9, {
   3.561131868247724*^9, 3.5611318887617598`*^9}, {3.561131924111422*^9, 
   3.5611320467286377`*^9}, 3.5611320979123273`*^9, {3.5611321453520107`*^9, 
   3.5611321714986563`*^9}, {3.56113281112778*^9, 3.561132851313451*^9}, {
   3.5611421934827037`*^9, 3.56114222569676*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJwVl3c81d8fx4WQyHZVSmkplZlIzuddUVr2SmbZ+2uvkFFkhGxCEZmVlRX3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     "]]}, 
   {Hue[0.9060679774997897, 0.6, 0.6], LineBox[CompressedData["
1:eJwV1nc4l10YB3CkyHxCSEORMirREjnnThJFJLOMCJlRGdlllBFlhqRkVKKB
bLJ+08ge4Vcpyi7US0nv01/P9bmedZ1xf++zxdbd0J6DjY1Nk52N7d/Vwv8x
d6HMUcyuz0E5bLX5kN+ACieXgzT8XZT53hY9oK7A7CobtN8Dmk+4qo2jf6un
bYuZeS2uDgk74h7ELAmgsDqpBJr9Ebiw+roRf/R6VDkTtGsv1obEGs6muDAZ
NLtxgPFQXA/yz38yOLy0C4nk3itctWgAlYJ+Qdqi+9Duah22avvT8EDy7Eh1
lBrS7fpP70qHMcR+4FyqcTuMLkzk3JPDZiDQY1aqEXYUhXAYjb1/dga6ss7q
f+U+jjLWcRxIFrcE3kGL6oLfJ1H57pdhuuHWsE4nx057lyEal1Z0Yl88By26
/WG0tcZoldpQSan9efD49vjoWORZlKhVPCSUbgfdGx3YI0WtkZRhNOfFDntY
LdatJe5mg9SdDhpuxY7wyFJfUjvUHjE9Cd9gLyc4URFh8aj0AjK79uXBu2fO
UHSC3hvA5Yw87yZN3RF3g/fz/ibPFy8ijixXkcmTFyH7qngce6sHuvP8iNqx
cHf4mXiANbbjMuoZvtq4vOABPM/rCr8Le6Hvi9uEXttfgdGQouimG/6oLDg+
Z5jNE0TCr9/vOBqIglYuqxDpnsDbGfk3TigY8a3ptnbp8AKrgbmD95yvI1nZ
0IIt+CooXIhnDw4ORzMF06D/7ipEGMZ29ibdQCV7znQFePkCV5W7+uqim0gT
K/3ufeYH9qUBPXPsUeicyXvtWPFAMEu3s+n/Hou2Dx4frCwKhBVfumQ8Je+g
aZsS97GTQRAo8LrKnnEHBbjFJGuGB0OcdNjGG9vjkW79xst/Fq7BDLP0ZyFf
ErrQ3/SmyD4Unotl21z2u4d2rU7UaS8Pha8vg9P2OKejeRWLzmn+MEhV0i//
bnkfhaRMjsqVhIG55+Uc21MPULopv8DDVTdgndwjY87iTNTWfdLi1uMIaAxs
Ffshl4uSV4qNPv0dAf4qphHpdbnIct97d5p+JCwXyU2qn32MxhPdQzkWIuG4
+jkdt8QnaKXRnbyr2tHQ4bdew2vTM6Ta0b5gNxYDv9ycVrprv0TsHGkhIeqx
IK24QWs56yWiK9nyPYyLhYqqtVU32V4h47hZyYGDt+Hsj/awiKpXSOVJZJbs
0TsgP5wodgiKkOGFPGZGUhzovHrGjbxL0I2RCfHo/Ylwv1G6WfZeNWLLmLNq
s0yEv1TRHZf5a5Cfye/steGJ0GteE3P7Wg26SONRetiZCHul9UKPOr1Bpk/l
dF57JMHVln2Kuo9qkazbBd/3ecmw9eqGcaO4esSYH+7fI5kKCnNmOz2rqUiz
YFzSVysV5LYIXXi0goZq7Gfta9xSodNw09L+4zRU2MM+q12VCne2GZTG99FQ
WtlmHivzNAj1W/pI/KIj5wAr1YiEe+Bz0niWx6AJ8XG+SxvkyoABsFwdIt2G
HD6fyrfYlQHhkX1v+XXbUG0jo3rQKAMI07zndM82dCW8/MNgZgYIKKy/2ERt
Q+9WpW4bUnsAK4JN/3C4taMuzh390wceQvsBA3v5+g6UxTVhN+OSCTIlW+/2
xHYj4HcK+NaZBT+rr9UcKxhAuSly+zq+ZkG78Gs/+5EBxLd1fKroTxZENwQW
Fm8cRL2qLtY+27OBsubPli+xg+iio5vGsl82uEZ39qZcGUL3Gi5x80nlABHv
wyOq9R799PVL3O6RC5ecqkVO3/yI8kej8634nkLd9TPPsxNG0FyHFPv9iQLg
Ds77EfRrCpVoeTzLSn0F5S8DbpbyzaPpzFMxMkrFMH3/8NP3NosoYZXbdcH0
EuCmrdv9KWoZnepY762oVg5zbx54zYlx4IDHnIGlBZXAUHbblfqcE2f9mlGd
FK4B95dMHcuNXPjymdIABdNa8DBNCJuMX421q4RHRGLroPbuyx8NObw4w6jk
p1lCHTjbCG1Wec6L5ybNuO+n1AF7kpTX4xLy/sYMBZmsOnhUfjTBh8aL54Nk
L+8rq4NkJ07doa+8OPOw+l/j4TroWa7ZUCXPh39RHdbd3V8PA6tktYry+PCz
9nK9de/r4fw6wz2zafx46SKzTPNzPeyXXmxezOTHJ/kGpD3G6oE/q2P90hN+
PKu1tEidq4d38KztWwk/VqlCuZ7cDXDfIMAirYMfN+Y2LL9VaoBY9kfKk9wC
eNC/5cWNsAbgtBGXCbwkgHetY0kURjbAp1m2G70+Aji4ZDp8KLYBEkwOWO0I
EsBS3wUt9qY2gGBJihslSgA7OhhyDxc0wMZ90n3FWQJ43qD3nHpvA1wv67C/
2SWA+bZ9XDMv1wiBg8m635QEsccBUT3qrkaYaF4rv++AIO7WPhGRsqcRfn/k
5vM6JIgzXF4vH1JvBNlrg30jWoJY8VXkRLhBI5Q5vfCJPiuIDQ8pU8R8GuGZ
2aahkVBBnGIYelWtsREGE26atLUJ4qXzZUX8jEbgP+dHu9ItiG28pqbftzSC
Y3rpRqF3glg+xdQ+rLcR7oo1eONPgrhySMGwZbwRXFJ9Gi1+CGKWY5eC9RoK
qAShOwZ8BJYOlnkfYkUB6vOqbzk7CWxSevZG9XkKqBm7ObcpEjhiJm7ngiMF
zu737PlPicDT1sv+blcosDNCMkx9P4HLoFfcLIICqiuDdmQjAutyRBruLKSA
cMGoM+skgb3CJym9K6mQeMmqgtONwE+qpdyEeKmw8kPMdPNFAr/7YSaiR1CB
qdvKF+9BYHCg2NZLUOGlNGuVsCeBeY5l/M1XpIIuz5qpGT8CZ3AbHAwxpwLv
G3P7tREEpkUX5e8ooMLeZRt3gYcE5lMR2CpQSAXzRts/ZzMJbPjZ8d5MCRUi
tij25z4i8OChTVGFtVT4NnLIb28OgWenIi6odFGhyXzMVjGPwJsMrKQ0f1Ph
UsJib1YRge2WylJl2GiQeVz0GLWYwE+fCK/hWkmDazspnKOvCbyXnfGXIUCD
odLdrhvLCKxTuGdIX4oGfXpDUy5VBPYUWZ1yVocGodm/um42Erii9ryg+kka
VJrkHgymEPiva82NTadp8HBT1fQVKoGjKFe8PlrQ4HtJ7XFjOoEfeLMML3jQ
4AUzq/W/JgIz+4r4r9ylweH2kR1VHQQmwgXCjdJpkLbknx/RSWBjJaelfZk0
2OlqHWzYReAPkZsmFvJooNY+LsnqJvBP1Uh6UA0NTB8aG3b3EXjLfavQqBEa
6CkNvDrCIsfjUeHQNU6DmQarsVnS2kdEj2/6RoMz3vHsD94T2GOshSj8RYOs
CK/uqQ8ErtmnntEvSAcziv1ah08E7uBOvS69lg7uUukWS6RHBubt3CToMB4T
cPP2Z3J9QvIV2GXoELm3IzJ/hMBnWteXy6rSYe9JVd26LwS+mOmTfhnTgaq2
pQp9JfB1z87gKk061GlyCJeTfiIRrWWgT4fcuSs+2WMErpoalUszokNV9Nfw
teMEbqvV4P9sTodtUpKBoaT/c/jV6WNHB9nsJ9tNJsj9pGpSWudEhxsc4wMV
pDfxF6bxutPB5AjTb8MkgbWKnGwe+NJB7ImhXw/pxL9909RYOtxSVo2VmSb/
37G3g0ikg0Hp5pxLpCtz7rw+k0qHFKWMvArSwye0A6az6DDkezn0yAw535uy
rVWe0kHxVY9pKGme2b8aIc9Jv5jcUEtaKaV0tWg5HVbTTPx3fyOwpovwlHUN
HXjd6tfakTZD7m1PG+gQ9U0gK5G065qmojk6HXwONUnXk772edtd9VZy/gNu
pkySTiwN8bvZSYeQ9d3sIt8J/DiKZdneRyfrQeucCukKS9XD61l0iLH2KDYn
3bo7eav9JzqcEv6y7EN6eMUs14uvdEjTOAwJpH/06E0sTJHv3xL1fUaaO+9p
q8YcHYqZf5/Wkt4QuLLw1gIdDgnd7ewgvdvAJqnnDx2UXvn8/EhaU7r66uYV
DMjfhYSnSZv9FLdw5mbAF50I+f9IuzA8cTE/A2wX5w/9IR2U3ia1LMQAeeet
J9hmCRzvvmOVtjgD+P6WGv9zrkbEWNxGBtTrG1r+e75i7efmASkG7JW9a/vv
e61f8UsZWQY8uang8O9/HyvvJbjvZMCPB68dh0nPx/7nXa7MgOquQefOf+Ox
PX1mhQoD0ip03OpIi6tuvLtXnQHI27A/n/R2oS+d9hoM2MaZZptEev/4S+Lu
MQa0HGlY7U9aq95Pj67LgA07L7+1JG2Sphm1eIoBOW9PFKuTtr8sQJM3ZcDU
qZ9lEqTDpB5BjA0D1i6f3dr8b71+uQTWODCA56PjrYekszr2Vcy4MMBVZFz0
Mun6EMYeQ28GeT5eSOIj3XEmwSPUnwEjvh+iu8n9M6xsWVB8jQEKSt9z75Fm
//Rtm1g0A54P6OlLkiYqK85r32HA66yloUFyf25OCHvom8SAOO60xLuk4Yi4
xOADBnCPXQrgJG2wftiEP4cBW7PEXpRMEdh67lkCymNAvFcInwPpoCzMn1lM
rqdx5PEqsj5i/Vcf7yhngNpcyo7zpO+f7ryx4g0DrGlGh7hIV624wObAYEDt
jYYvWmS9/TofOyfPYoBXnWnov/rlOWS22+ITA76rpX/ZS3qdiJRbzFcG2Ojd
Cq4n612l8fXozCwDEkRD9LrJfPDZOtRfzMWEMu1rPv1kftxYyhUd5WOCrldP
7GnSyV0ep8WEmHCvU+wDk8ybkjDOFt8NTLAuiN3zisyj+c8KtUiJCcPcI8UW
HwnMWf1jyX0/+bzotsJaMs+Ek94czFRjwlRq28wW0spHTxet0GLCI/sixUEy
Dz1y/HLpZ5gQObqpX3GQwFP2jFuGYUzIkxePM+oh57uwNFU+kgmJrsc908i8
VV7OyeWIZUIyL+ffITKPvZNDagvvMkGna5rfisxrNpravNAzJmxon5XRaCOw
iOzzs53tTGj84vIpjUHuN890x2c9TKDKjSRXkv3AvDbKK3SACWnXyv/008h+
aHbh9p4RJjh4BH8VJPvH9sjNDQkLTNgSunDsXD2BVcfj5Y0km4By32cwoYLA
FvuvH9ixtQkeLllI3SkncHCIuyanXBPEKorJRpH9q1FC16pYuQlO6SNvnxIC
nzyxMl5EqwnOb/+y50AhgW3yfRa7XJtAO1V84sRT8nxw0YJuXNEEs8Y269uS
CHz144nDyW+a4NIpSQHnRAI7GalV9DQ2wdEBCX/2BAIfV5XIN33bBMXv1Omy
dwjMv6rvtvnnJjjnE3rSPIqs9/unTS0FmoESP8l1JIjA6c3HR+1sm2FrDY/q
YTsC38Kq1jkXmoHtZf3TW7YEDiyU6xtxbQYNyadl3ecIbJXCzXTwaQa+Lc1l
5yzJ/mZHLXC81QygLG53xoTMj9+HvVxLmuGv4z7voWMEfil/kNOTpwVaItql
FOQIXLxGT++sYAsEOjrXndxO4NKFc8kaIi0w4ZDu7iFD9jtqhOyaTS3Ad3xq
uWALgZtt+3SfK7WA1sYjq4QkCPw1zSfpq1kLSHCxZwbxEFiSt2Sb5eMWsr8M
0IY7BXHshLKOlmYr7DhQD7Pk+S+2t3hCRKcV2i0O6jhpCOKYhv2xn/RaIZ49
cf2QuiC+dU+185ppK1x/aLitcq8gjjqhYVnp3Ao8w9kCp6QEcfizU5d2x7WC
W/0V9tElARzg4pEqwWqF1S/jVRteCGDniYKxaZ+3MCqqc6GeTwA76R882m/b
Bv6qrmmpN/mwr4K8RNJyG7yMce1MWeDB+h+xu9XjdvjMsFN7rLAaZ+8XnRXS
64BXR5rYooy4sJGAv2/mlw6I+/EErUlaiZlvOK+r3+4EjeSFPb4vVuD0uQ0x
RQpdcDvSKavhGzuepP6gilC6oGXV27XJWmx4hefctVCXbpgwePD4s8gf5JUV
jJtX9YAdjZepwvELFeTvDpJ60QNdXnb+4x9/IlDxqDPU7QVZ74DUDTvmkeF5
D+WLo73QLGwVcrHsO1JwTJK+G9MHNQtjDSPJ08h6Rntdmlw/NIRyyDwOHkfm
Bltu53X0g76LRQHz5ijqMKhQzr36Dhb/u+T7ee0nlNv58Z2/8AD8kfXpTYEP
6PDuXSusKwegLnX5saTUADoguHr3BrNBOF9FT/Fk9KD8mOyoxu+DIGsrf6Na
vBN9GbGz90sZgs6Lr9h9Td6iwNoiTZ69LGBGiAgsfWEgbU6t4dr9LNA97D1f
0M5AItp9wT4HWWCXbXnIo5KB8t8uVXxGLDiwKNYsc5uBBllHld7osOA3df/E
6QMMdOhP70ZPaxaojBUqFkfR0a+DSz+HolggHPPg1lF1GqIGxiYmxrCAzHVi
VpaG4us2K5+4w4If2826C0RoSF7nqFtZEgsi1lkvG05SkblZ7Kf4hyzIG4js
MUynojLvzW3HSlgwdqdzcvNfCgqrKHRbLmMBR4CtVfUEBRksa/K+rmQB9Zd1
mGMfBX0Nd9KSqmPBm6xPzPFXFCSWVFi11ER+P0pfP8Oegob7NM8UtbJg+56Q
Sy8MKej5ht7/nNpZoE/5xPEWU5BW9m/l3h4WuGbRDA5KUJDQ15i2mH4W8LRK
LIVyURBLYfNFzUEWVD1C84PzjSjPvZD3N4sFYlcf7dYcbkTeRZpPX31kwTXn
siflbxvR/03LnWU=
     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesLabel->{
    FormBox["\"x\"", TraditionalForm], 
    FormBox["\"D(v)\"", TraditionalForm]},
  AxesOrigin->{0, 0},
  ImageSize->{447.22750603334725`, Automatic},
  PlotLabel->FormBox["\"Boltzmann distribution\"", TraditionalForm],
  PlotRange->NCache[{{0, 31622.776601683792`}, {0, 
      Rational[1, 10000]}}, {{0, 31622.776601683792`}, {0, 0.0001}}],
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], Automatic}]], "Output",
 CellChangeTimes->{
  3.5611316612031603`*^9, 3.5611317280336776`*^9, 3.561131826797451*^9, {
   3.561131868247724*^9, 3.5611318887617598`*^9}, {3.561131924111422*^9, 
   3.5611320467286377`*^9}, 3.5611320979123273`*^9, {3.5611321453520107`*^9, 
   3.5611321714986563`*^9}, {3.56113281112778*^9, 3.561132851313451*^9}, {
   3.5611421934827037`*^9, 3.56114222569676*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Dv", "   ", 
  RowBox[{"(*", " ", 
   RowBox[{
   "back", " ", "to", " ", "the", " ", "general", " ", "distribution"}], " ", 
   "*)"}], " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"D", "[", 
   RowBox[{"Dv", ",", "v"}], "]"}], "   ", 
  RowBox[{"(*", " ", 
   RowBox[{
   "take", " ", "the", " ", "derivative", " ", "with", " ", "respect", " ", 
    RowBox[{"to", " ", "'"}], 
    RowBox[{"v", "'"}]}], " ", "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{"ExpandAll", "[", 
  RowBox[{
   RowBox[{"Solve", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"D", "[", 
       RowBox[{"Dv", ",", "v"}], "]"}], "\[Equal]", "0"}], ",", "v"}], "]"}], 
   "/.", 
   RowBox[{"{", 
    RowBox[{"B", "\[Rule]", 
     RowBox[{"1", "/", 
      RowBox[{"(", 
       RowBox[{"k", "*", "T"}], ")"}]}]}], "}"}]}], 
  "]"}], "\[IndentingNewLine]", 
 RowBox[{"Pi", "  ", 
  RowBox[{"(*", " ", 
   RowBox[{"symbolic", " ", "value"}], " ", "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Pi", "//", "N"}], "  ", 
  RowBox[{"(*", " ", 
   RowBox[{"forces", " ", "numerical", " ", "evaluation"}], " ", 
   "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"N", "[", 
   RowBox[{"Pi", ",", "20"}], "]"}], "     ", 
  RowBox[{"(*", " ", 
   RowBox[{
   "control", " ", "the", " ", "number", " ", "of", " ", "decimal", " ", 
    "places"}], " ", "*)"}], " "}], "\[IndentingNewLine]", 
 RowBox[{"ScientificForm", "[", 
  RowBox[{"N", "[", 
   RowBox[{
    RowBox[{"Pi", "^", "5"}], ",", "20"}], "]"}], "   ", 
  RowBox[{"(*", " ", 
   RowBox[{"self", "-", "explanatory"}], " ", "*)"}], " "}]}], "Input",
 CellChangeTimes->{{3.561132164977845*^9, 3.561132165336646*^9}, {
  3.561132216301935*^9, 3.561132335704545*^9}, {3.561132405639468*^9, 
  3.561132522324473*^9}, {3.561142259283619*^9, 3.5611423286569405`*^9}, {
  3.561142363341002*^9, 3.561142389471048*^9}}],

Cell[BoxData[
 RowBox[{
  SuperscriptBox["\[ExponentialE]", 
   RowBox[{
    RowBox[{"-", 
     FractionBox["1", "2"]}], " ", "B", " ", "m", " ", 
    SuperscriptBox["v", "2"]}]], " ", 
  SqrtBox[
   FractionBox["2", "\[Pi]"]], " ", 
  SuperscriptBox[
   RowBox[{"(", 
    FractionBox["m", 
     RowBox[{"k", " ", "T"}]], ")"}], 
   RowBox[{"3", "/", "2"}]], " ", 
  SuperscriptBox["v", "2"]}]], "Output",
 CellChangeTimes->{
  3.5611322176123376`*^9, {3.5611322648804207`*^9, 3.5611323364845467`*^9}, {
   3.561132408915474*^9, 3.5611325230108743`*^9}, 3.561142329327742*^9, {
   3.561142364245804*^9, 3.5611423820142345`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"2", " ", 
   SuperscriptBox["\[ExponentialE]", 
    RowBox[{
     RowBox[{"-", 
      FractionBox["1", "2"]}], " ", "B", " ", "m", " ", 
     SuperscriptBox["v", "2"]}]], " ", 
   SqrtBox[
    FractionBox["2", "\[Pi]"]], " ", 
   SuperscriptBox[
    RowBox[{"(", 
     FractionBox["m", 
      RowBox[{"k", " ", "T"}]], ")"}], 
    RowBox[{"3", "/", "2"}]], " ", "v"}], "-", 
  RowBox[{"B", " ", 
   SuperscriptBox["\[ExponentialE]", 
    RowBox[{
     RowBox[{"-", 
      FractionBox["1", "2"]}], " ", "B", " ", "m", " ", 
     SuperscriptBox["v", "2"]}]], " ", "m", " ", 
   SqrtBox[
    FractionBox["2", "\[Pi]"]], " ", 
   SuperscriptBox[
    RowBox[{"(", 
     FractionBox["m", 
      RowBox[{"k", " ", "T"}]], ")"}], 
    RowBox[{"3", "/", "2"}]], " ", 
   SuperscriptBox["v", "3"]}]}]], "Output",
 CellChangeTimes->{
  3.5611322176123376`*^9, {3.5611322648804207`*^9, 3.5611323364845467`*^9}, {
   3.561132408915474*^9, 3.5611325230108743`*^9}, 3.561142329327742*^9, {
   3.561142364245804*^9, 3.5611423820142345`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"v", "\[Rule]", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"v", "\[Rule]", 
     RowBox[{"-", 
      FractionBox[
       RowBox[{
        SqrtBox["2"], " ", "k", " ", 
        SqrtBox[
         FractionBox["1", 
          RowBox[{"k", " ", "T"}]]], " ", "T"}], 
       SqrtBox["m"]]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"v", "\[Rule]", 
     FractionBox[
      RowBox[{
       SqrtBox["2"], " ", "k", " ", 
       SqrtBox[
        FractionBox["1", 
         RowBox[{"k", " ", "T"}]]], " ", "T"}], 
      SqrtBox["m"]]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{
  3.5611322176123376`*^9, {3.5611322648804207`*^9, 3.5611323364845467`*^9}, {
   3.561132408915474*^9, 3.5611325230108743`*^9}, 3.561142329327742*^9, {
   3.561142364245804*^9, 3.561142382045435*^9}}],

Cell[BoxData["\[Pi]"], "Output",
 CellChangeTimes->{
  3.5611322176123376`*^9, {3.5611322648804207`*^9, 3.5611323364845467`*^9}, {
   3.561132408915474*^9, 3.5611325230108743`*^9}, 3.561142329327742*^9, {
   3.561142364245804*^9, 3.561142382045435*^9}}],

Cell[BoxData["3.141592653589793`"], "Output",
 CellChangeTimes->{
  3.5611322176123376`*^9, {3.5611322648804207`*^9, 3.5611323364845467`*^9}, {
   3.561132408915474*^9, 3.5611325230108743`*^9}, 3.561142329327742*^9, {
   3.561142364245804*^9, 3.561142382045435*^9}}],

Cell[BoxData["3.1415926535897932384626433832795028841971693993751058202853`20.\
"], "Output",
 CellChangeTimes->{
  3.5611322176123376`*^9, {3.5611322648804207`*^9, 3.5611323364845467`*^9}, {
   3.561132408915474*^9, 3.5611325230108743`*^9}, 3.561142329327742*^9, {
   3.561142364245804*^9, 3.561142382045435*^9}}],

Cell[BoxData[
 TagBox[
  InterpretationBox[
   RowBox[{"\<\"3.0601968478528145326\"\>", "\[Times]", 
    SuperscriptBox["10", "\<\"2\"\>"]}],
   306.0196847852814532627413100434356064803`20.,
   AutoDelete->True],
  ScientificForm]], "Output",
 CellChangeTimes->{
  3.5611322176123376`*^9, {3.5611322648804207`*^9, 3.5611323364845467`*^9}, {
   3.561132408915474*^9, 3.5611325230108743`*^9}, 3.561142329327742*^9, {
   3.561142364245804*^9, 3.561142382045435*^9}}]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["Fermion <n>", "Subsubsection",
 CellChangeTimes->{{3.561476774678748*^9, 3.5614767841479645`*^9}, {
  3.5616466092451725`*^9, 3.5616466119251456`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", 
   RowBox[{"Aven", ",", "mu"}], "]"}], "  ", 
  RowBox[{"(*", " ", 
   RowBox[{
    RowBox[{
    "be", " ", "sure", " ", "to", " ", "clear", " ", "things", " ", "as", " ",
      "you", " ", "re"}], "-", 
    RowBox[{"do", " ", "the", " ", "graphs"}]}], " ", "*)"}], 
  " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Aven", "=", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      RowBox[{"Exp", "[", 
       RowBox[{"B", "*", 
        RowBox[{"(", 
         RowBox[{"Es", "-", "mu"}], ")"}]}], "]"}], "+", "1"}], ")"}], "^", 
    RowBox[{"(", 
     RowBox[{"-", "1"}], ")"}]}]}], "  ", 
  RowBox[{"(*", " ", 
   RowBox[{"<", "n", ">", " ", 
    RowBox[{"for", " ", "Fermions"}]}], " ", "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Aven1", "=", 
   RowBox[{"Aven", "/.", 
    RowBox[{"{", 
     RowBox[{"B", "\[Rule]", 
      RowBox[{"1", "/", 
       RowBox[{"(", 
        RowBox[{"k", "*", "T"}], ")"}]}]}], "}"}]}]}], "    ", 
  RowBox[{"(*", " ", "stustitutions", " ", "*)"}], 
  " "}], "\[IndentingNewLine]", 
 RowBox[{"Aven2", "=", 
  RowBox[{"Aven1", "/.", 
   RowBox[{"{", 
    RowBox[{"k", "\[Rule]", 
     RowBox[{"8.6174", "*", 
      RowBox[{"10", "^", 
       RowBox[{"(", 
        RowBox[{"-", "5"}], ")"}]}]}]}], "}"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"mu", "=", "4"}], "  ", 
  RowBox[{"(*", " ", 
   RowBox[{"chemical", " ", "potential", " ", "in", " ", "eV"}], " ", 
   "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Aven4000", "=", 
   RowBox[{"Aven2", "/.", 
    RowBox[{"{", 
     RowBox[{"T", "\[Rule]", "4000"}], "}"}]}]}], ";", "   ", 
  RowBox[{"(*", " ", 
   RowBox[{"set", " ", "a", " ", "temperature"}], " ", "*)"}], 
  "\[IndentingNewLine]", 
  RowBox[{"Plot", "[", 
   RowBox[{
    RowBox[{"{", "Aven40000", "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"Es", ",", "0", ",", "13"}], "}"}], ",", 
    RowBox[{"PlotRange", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{"0", ",", "1"}], "}"}]}]}], "]"}]}]}], "Input",
 CellChangeTimes->{{3.5614768155748186`*^9, 3.561476938955633*^9}, {
  3.5614769884371185`*^9, 3.5614770992273083`*^9}, {3.5614771594534087`*^9, 
  3.561477167503023*^9}, {3.5614776985217457`*^9, 3.5614777361601706`*^9}, {
  3.5614779766382904`*^9, 3.561478118588354*^9}, {3.5614781636590357`*^9, 
  3.5614781647038813`*^9}, {3.561646649079875*^9, 3.561646731518875*^9}}],

Cell[BoxData[
 FractionBox["1", 
  RowBox[{"1", "+", 
   SuperscriptBox["\[ExponentialE]", 
    RowBox[{"B", " ", 
     RowBox[{"(", 
      RowBox[{"Es", "-", "mu"}], ")"}]}]]}]]], "Output",
 CellChangeTimes->{{3.5614768632449017`*^9, 3.561476991680524*^9}, 
   3.5614770347107954`*^9, {3.561477093049698*^9, 3.5614771008497114`*^9}, 
   3.561477169905427*^9, {3.5614777305129147`*^9, 3.5614777368494945`*^9}, {
   3.561478022478691*^9, 3.5614781193213053`*^9}, 3.561478165390048*^9}],

Cell[BoxData[
 FractionBox["1", 
  RowBox[{"1", "+", 
   SuperscriptBox["\[ExponentialE]", 
    FractionBox[
     RowBox[{"Es", "-", "mu"}], 
     RowBox[{"k", " ", "T"}]]]}]]], "Output",
 CellChangeTimes->{{3.5614768632449017`*^9, 3.561476991680524*^9}, 
   3.5614770347107954`*^9, {3.561477093049698*^9, 3.5614771008497114`*^9}, 
   3.561477169905427*^9, {3.5614777305129147`*^9, 3.5614777368494945`*^9}, {
   3.561478022478691*^9, 3.5614781193213053`*^9}, 3.561478165390048*^9}],

Cell[BoxData[
 FractionBox["1", 
  RowBox[{"1", "+", 
   SuperscriptBox["\[ExponentialE]", 
    FractionBox[
     RowBox[{"11604.42824982013`", " ", 
      RowBox[{"(", 
       RowBox[{"Es", "-", "mu"}], ")"}]}], "T"]]}]]], "Output",
 CellChangeTimes->{{3.5614768632449017`*^9, 3.561476991680524*^9}, 
   3.5614770347107954`*^9, {3.561477093049698*^9, 3.5614771008497114`*^9}, 
   3.561477169905427*^9, {3.5614777305129147`*^9, 3.5614777368494945`*^9}, {
   3.561478022478691*^9, 3.5614781193213053`*^9}, 3.561478165390048*^9}],

Cell[BoxData["4"], "Output",
 CellChangeTimes->{{3.5614768632449017`*^9, 3.561476991680524*^9}, 
   3.5614770347107954`*^9, {3.561477093049698*^9, 3.5614771008497114`*^9}, 
   3.561477169905427*^9, {3.5614777305129147`*^9, 3.5614777368494945`*^9}, {
   3.561478022478691*^9, 3.5614781193213053`*^9}, 3.561478165390048*^9}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJw91Hk0Vd//MHAJoTude8kUXbMbyZzhnnPeRCjKlKQoyZCQmVTGRElIqSSZ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     "]]}, 
   {Hue[0.9060679774997897, 0.6, 0.6], LineBox[CompressedData["
1:eJwV13c8V10YAHB7k733XilJku49j5HKSlGRESKRzEJWslJWJCGrSBJlRklZ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     "]]}, 
   {Hue[0.1421359549995791, 0.6, 0.6], LineBox[CompressedData["
1:eJwdy3k4lAkcwPHRqmZ266nNJLYix5jezWa3mg7J7zexFZHK8DB2ypHoKXI1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     "]]}, 
   {Hue[0.37820393249936934`, 0.6, 0.6], LineBox[CompressedData["
1:eJwdz2lQUwcUBeAgqICllFWiyL49I7hQbEHkXhZxQUcmhAhqKIu4YpRgwUpK
HRFpRYmsCoK4tYgBpMWySBVCaZRSMMqiBXnvUSKKEqC4sCXaN/1x58w3Z86P
axt9iBs7h8VibWHu/3x85uZIe5YPP3TlwIKvaDjCN8uYG3oYXiReuPomgobt
Wt5jA7zj4K7UxPQxbudvtVXwzkHdtd+HbjJO1wr3us+7DOXNXiMbGSt7+uXN
vCrIHHjyPl1AQ7avzdkmXhN4Vir0dXbSMJzoe7iRpwBuX5erOoyGCxbVmTk6
A6AuEjzdx6VhTQkxW7BhGHyeaQ0FbqZh9Iqvq+Tncdi9t7zSL5AG2WREdYP5
O1iQdqS7AWjgRQtPPloxDXUjrvuve9KwN3hU+uiqBrZN+wv03Wm4N3Roty5L
C2viuowky2i4cSuqyFJPG394oe+T6kRDyJ0MjaPPXByUO7e9taZB8NBN5/qW
+WiTt6K7m03DC+npdBlXD3P01km7TWhY9afV6q7UBejMm3rONaChf4JzeofE
ANWqf6/DfBo2CuL1nsoNMcv6ZlsZi4bC+7VzZqY/Q3c5mRH7loKm2ISQZo0R
jlZDHv8lBXKHNs+0hSb4gcM95tdHgXovJTphZYpEll2ywUMKjDskvsfWmKGN
609RnTIKhvOLOnxDzNFMfUP7yW0KxpSxlf5hC1EgjGutv0FBT0ibPSZY4LCJ
Iu38RQpU61WvE5PZGDJatZ8noaCl5IDo25RFWGOZZ7o1lYJki1OZKecXI3va
4kFAIgXR5gJNfbElPsitKGXvp4DwUGiN1y/BLxeVXB7eSUFVbUnLO4UVlrEC
4ie3UrCnkdPr0W2N5RF/C5X+FHx8U+ZXl2SDR80UxX+tpmBwU5FMNGuDMdnt
MzlLKSjt/M06T2yLtwxqVhZYUdAXJ31wW9cOL10arC4wYvoNU4XxGXaoMrwX
+c1cZv+5SR2HbY/RsE7ImyKhNubMhxPF9ugl2f3jpyMkHGhxd/CzdsDvwntl
82gSJB5luR+kDmjqKBLMPCYhaFjsFrbcEXOzFi1ul5OQVGFlcuuuI7qwDOMv
1pOQem205+BGJ/TPvdJcWk6C8zPLltY2J1ziJePkXCbB25Gttgt3xj3GQ8HH
ckh4WZUgYPc7Y+gY9T2mk3BEqC5OinDByefG1QHJJMR7hxCdr1yQcyD/XoCQ
hHlbdMm2gwRqKsUd9tEkTEniKk0PE6jNF5Sqokh4/ViRIhAReDdw/fFaxoqw
AuuxRAJt9b9YFcS4cNfSKOPjBKZ5ncoXRZKwXLxZGZZN4L5gZaQsgoQw6blX
z2sI7PyjVB2xg4RNo2/vuNUTWD5T3ePCeO3K8IykBgIHSlqrJraTYFdru0yv
icC1aBR7irGq+ZeDy1oJPDlj1FERTsKJ3q5xUR+B/8T0XlFvY/5b4ilr6Ccw
c3mKWM54T2Rxlg5N4HgKZ9s5xpuHYlflKwk8X3H1EwfG5hPvE+pVBEbFaR8N
4pOg67EjYM44gcKkN1wzxrNJjaZBEwR2G6pcqVASaE36r8/eE3hWpR4UMe7E
kTTHaQLXeZg0ejOWpwbzhbMEuhm6F85jXCe/7VSrIVAs3vm1gkeCVI89+fEj
gbtSJMGFjP8DSftW2Q==
     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{{0, 13}, {0, 1}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], Automatic}]], "Output",
 CellChangeTimes->{{3.5614768632449017`*^9, 3.561476991680524*^9}, 
   3.5614770347107954`*^9, {3.561477093049698*^9, 3.5614771008497114`*^9}, 
   3.561477169905427*^9, {3.5614777305129147`*^9, 3.5614777368494945`*^9}, {
   3.561478022478691*^9, 3.5614781193213053`*^9}, 3.5614781654056425`*^9}]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["\<\
Boltzmann distribution: N2 at T=295K; what fraction less than 300 m/s?\
\>", "Subsubsection",
 CellChangeTimes->{{3.5629533154733944`*^9, 3.5629533275477943`*^9}, {
  3.562954401912794*^9, 3.562954417980794*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "m", "]"}], "\[IndentingNewLine]", 
 RowBox[{"Dv", "=", 
  RowBox[{
   RowBox[{
    RowBox[{"(", 
     RowBox[{"m", "/", 
      RowBox[{"(", 
       RowBox[{"2", "*", "Pi", "*", "k", "*", "T"}], ")"}]}], ")"}], "^", 
    RowBox[{"(", 
     RowBox[{"3", "/", "2"}], ")"}]}], "*", "4", "*", "Pi", "*", 
   RowBox[{"v", "^", "2"}], "*", 
   RowBox[{"Exp", "[", 
    RowBox[{
     RowBox[{"-", "B"}], "*", 
     RowBox[{"(", 
      RowBox[{"1", "/", "2"}], ")"}], "*", "m", "*", 
     RowBox[{"v", "^", "2"}]}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{"Dv1", "=", 
  RowBox[{"Dv", "/.", 
   RowBox[{"B", "\[Rule]", 
    RowBox[{"1", "/", 
     RowBox[{"(", 
      RowBox[{"k", "*", "T"}], ")"}]}]}]}]}], "\[IndentingNewLine]", 
 RowBox[{"Dv2", "=", 
  RowBox[{"Dv1", "/.", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"m", "\[Rule]", 
      RowBox[{"4.653", "*", 
       RowBox[{"10", "^", 
        RowBox[{"(", 
         RowBox[{"-", "26"}], ")"}]}]}]}], ",", 
     RowBox[{"k", "\[Rule]", 
      RowBox[{"1.38066", "*", 
       RowBox[{"10", "^", 
        RowBox[{"(", 
         RowBox[{"-", "23"}], ")"}]}]}]}], ",", 
     RowBox[{"T", "\[Rule]", "295"}]}], "}"}]}]}], "\[IndentingNewLine]", 
 RowBox[{"ans", "=", 
  RowBox[{"NIntegrate", "[", 
   RowBox[{"Dv2", ",", 
    RowBox[{"{", 
     RowBox[{"v", ",", "0", ",", "300"}], "}"}]}], "]"}]}]}], "Input",
 CellChangeTimes->{{3.5629533324305944`*^9, 3.5629535041397943`*^9}}],

Cell[BoxData[
 RowBox[{
  SuperscriptBox["\[ExponentialE]", 
   RowBox[{
    RowBox[{"-", 
     FractionBox["1", "2"]}], " ", "B", " ", "m", " ", 
    SuperscriptBox["v", "2"]}]], " ", 
  SqrtBox[
   FractionBox["2", "\[Pi]"]], " ", 
  SuperscriptBox[
   RowBox[{"(", 
    FractionBox["m", 
     RowBox[{"k", " ", "T"}]], ")"}], 
   RowBox[{"3", "/", "2"}]], " ", 
  SuperscriptBox["v", "2"]}]], "Output",
 CellChangeTimes->{
  3.562953389448594*^9, {3.562953436076994*^9, 3.5629534602257943`*^9}, {
   3.562953497899794*^9, 3.562953504982194*^9}}],

Cell[BoxData[
 RowBox[{
  SuperscriptBox["\[ExponentialE]", 
   RowBox[{"-", 
    FractionBox[
     RowBox[{"m", " ", 
      SuperscriptBox["v", "2"]}], 
     RowBox[{"2", " ", "k", " ", "T"}]]}]], " ", 
  SqrtBox[
   FractionBox["2", "\[Pi]"]], " ", 
  SuperscriptBox[
   RowBox[{"(", 
    FractionBox["m", 
     RowBox[{"k", " ", "T"}]], ")"}], 
   RowBox[{"3", "/", "2"}]], " ", 
  SuperscriptBox["v", "2"]}]], "Output",
 CellChangeTimes->{
  3.562953389448594*^9, {3.562953436076994*^9, 3.5629534602257943`*^9}, {
   3.562953497899794*^9, 3.562953504982194*^9}}],

Cell[BoxData[
 RowBox[{"3.080892195974834`*^-8", " ", 
  SuperscriptBox["\[ExponentialE]", 
   RowBox[{
    RowBox[{"-", "5.712080221029146`*^-6"}], " ", 
    SuperscriptBox["v", "2"]}]], " ", 
  SuperscriptBox["v", "2"]}]], "Output",
 CellChangeTimes->{
  3.562953389448594*^9, {3.562953436076994*^9, 3.5629534602257943`*^9}, {
   3.562953497899794*^9, 3.562953504982194*^9}}],

Cell[BoxData["0.20556498801029183`"], "Output",
 CellChangeTimes->{
  3.562953389448594*^9, {3.562953436076994*^9, 3.5629534602257943`*^9}, {
   3.562953497899794*^9, 3.562953505060194*^9}}]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["\<\
Plotting some made-up \[OpenCurlyDoubleQuote]energy density distribution\
\[CloseCurlyDoubleQuote] function u(\[CurlyEpsilon]) \
\>", "Subsubsection",
 CellChangeTimes->{{3.5631232164231925`*^9, 3.563123265032878*^9}, {
  3.56329505045504*^9, 3.563295080413887*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"u", "=", 
  RowBox[{"8", "*", 
   RowBox[{"Pi", "/", 
    RowBox[{"(", 
     RowBox[{"h", "*", "c"}], ")"}]}], "*", 
   RowBox[{"\[CurlyEpsilon]", "/", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"Exp", "[", 
       RowBox[{"\[Beta]", "*", "\[CurlyEpsilon]"}], "]"}], "-", "1"}], 
     ")"}]}]}]}], "\[IndentingNewLine]", 
 RowBox[{"u1", "=", 
  RowBox[{"u", "/.", 
   RowBox[{"\[Beta]", "\[Rule]", 
    RowBox[{"1", "/", 
     RowBox[{"(", 
      RowBox[{"k", "*", "T"}], ")"}]}]}]}]}], "\[IndentingNewLine]", 
 RowBox[{"D", "[", 
  RowBox[{"u1", ",", "\[CurlyEpsilon]"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"Simplify", "[", 
  RowBox[{"D", "[", 
   RowBox[{"u1", ",", "\[CurlyEpsilon]"}], "]"}], 
  "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"NSolve", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"D", "[", 
      RowBox[{"u1", ",", "\[CurlyEpsilon]"}], "]"}], "\[Equal]", "0"}], ",", 
    "\[CurlyEpsilon]"}], "]"}], "  ", 
  RowBox[{"(*", " ", 
   RowBox[{
    RowBox[{"numerically", " ", "solve", " ", "du1", 
     RowBox[{
      RowBox[{"(", "\[CurlyEpsilon]", ")"}], "/", "d\[CurlyEpsilon]"}]}], "=", 
    RowBox[{"0", " ", "for", " ", "\[CurlyEpsilon]"}]}], " ", "*)"}], 
  " "}], "\[IndentingNewLine]", 
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"15", "*", 
    RowBox[{"Sin", "[", 
     RowBox[{"2", "*", 
      RowBox[{"\[CurlyEpsilon]", "^", "2"}]}], "]"}], "*", 
    RowBox[{"Exp", "[", 
     RowBox[{"-", "\[CurlyEpsilon]"}], "]"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"\[CurlyEpsilon]", ",", 
     RowBox[{"10", "^", 
      RowBox[{"-", "25"}]}], ",", 
     RowBox[{"10", "^", "1"}]}], "}"}], ",", 
   RowBox[{"PlotRange", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "10"}], ",", "10"}], "}"}]}], ",", 
   RowBox[{"AxesLabel", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
     "\"\<\[CurlyEpsilon]\>\"", ",", 
      "\"\<sin(\[CurlyEpsilon])*Exp[-\[CurlyEpsilon]]\>\""}], "}"}]}]}], 
  "]"}]}], "Input",
 CellChangeTimes->{{3.5631206549688396`*^9, 3.5631206995577393`*^9}, {
  3.56312074868414*^9, 3.563121049238723*^9}, {3.563121079564746*^9, 
  3.5631211012181034`*^9}, {3.5631211338468523`*^9, 3.563121134253854*^9}, {
  3.563121552401471*^9, 3.5631215528538713`*^9}, {3.563121609653571*^9, 
  3.5631216952841215`*^9}, {3.5631218075629196`*^9, 3.5631218423509808`*^9}, {
  3.5631218771234417`*^9, 3.5631219854968324`*^9}, {3.5631222138344336`*^9, 
  3.563122233677668*^9}, {3.563122278746147*^9, 3.5631224912547207`*^9}, {
  3.563291408228191*^9, 3.5632914237624164`*^9}, {3.563291552588825*^9, 
  3.563291564194642*^9}, {3.5632916805052257`*^9, 3.563291680875226*^9}, {
  3.5632917257672987`*^9, 3.5632917594313507`*^9}, {3.563291847735492*^9, 
  3.5632918486002936`*^9}, {3.5632947047828755`*^9, 3.5632948885639763`*^9}, {
  3.5632949236398335`*^9, 3.563295029947806*^9}}],

Cell[BoxData[
 FractionBox[
  RowBox[{"8", " ", "\[Pi]", " ", "\[CurlyEpsilon]"}], 
  RowBox[{"c", " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"-", "1"}], "+", 
     SuperscriptBox["\[ExponentialE]", 
      RowBox[{"\[Beta]", " ", "\[CurlyEpsilon]"}]]}], ")"}], " ", 
   "h"}]]], "Output",
 CellChangeTimes->{
  3.563120694907362*^9, {3.5631207684943833`*^9, 3.563120771930978*^9}, 
   3.563120824316681*^9, 3.56312085547856*^9, {3.563120901134364*^9, 
   3.563120987968956*^9}, {3.5631210245601482`*^9, 3.5631210504127655`*^9}, {
   3.5631210890520124`*^9, 3.563121156658437*^9}, 3.563121554725875*^9, {
   3.563121624941598*^9, 3.563121692585317*^9}, {3.5631218204017425`*^9, 
   3.563121843037382*^9}, {3.563121894127472*^9, 3.5631219862924337`*^9}, {
   3.5631222960465775`*^9, 3.563122322597824*^9}, 3.56312235435948*^9, {
   3.56312239427995*^9, 3.5631224091935763`*^9}, {3.5632914138817997`*^9, 
   3.5632914290104246`*^9}, {3.5632915544688277`*^9, 3.5632915659106455`*^9}, 
   3.5632916829584293`*^9, {3.563291729677705*^9, 3.5632917602513514`*^9}, {
   3.5632918319702673`*^9, 3.5632918497234955`*^9}, {3.563294862033332*^9, 
   3.5632950305562067`*^9}}],

Cell[BoxData[
 FractionBox[
  RowBox[{"8", " ", "\[Pi]", " ", "\[CurlyEpsilon]"}], 
  RowBox[{"c", " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"-", "1"}], "+", 
     SuperscriptBox["\[ExponentialE]", 
      FractionBox["\[CurlyEpsilon]", 
       RowBox[{"k", " ", "T"}]]]}], ")"}], " ", "h"}]]], "Output",
 CellChangeTimes->{
  3.563120694907362*^9, {3.5631207684943833`*^9, 3.563120771930978*^9}, 
   3.563120824316681*^9, 3.56312085547856*^9, {3.563120901134364*^9, 
   3.563120987968956*^9}, {3.5631210245601482`*^9, 3.5631210504127655`*^9}, {
   3.5631210890520124`*^9, 3.563121156658437*^9}, 3.563121554725875*^9, {
   3.563121624941598*^9, 3.563121692585317*^9}, {3.5631218204017425`*^9, 
   3.563121843037382*^9}, {3.563121894127472*^9, 3.5631219862924337`*^9}, {
   3.5631222960465775`*^9, 3.563122322597824*^9}, 3.56312235435948*^9, {
   3.56312239427995*^9, 3.5631224091935763`*^9}, {3.5632914138817997`*^9, 
   3.5632914290104246`*^9}, {3.5632915544688277`*^9, 3.5632915659106455`*^9}, 
   3.5632916829584293`*^9, {3.563291729677705*^9, 3.5632917602513514`*^9}, {
   3.5632918319702673`*^9, 3.5632918497234955`*^9}, {3.563294862033332*^9, 
   3.5632950305562067`*^9}}],

Cell[BoxData[
 RowBox[{
  FractionBox[
   RowBox[{"8", " ", "\[Pi]"}], 
   RowBox[{"c", " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", "1"}], "+", 
      SuperscriptBox["\[ExponentialE]", 
       FractionBox["\[CurlyEpsilon]", 
        RowBox[{"k", " ", "T"}]]]}], ")"}], " ", "h"}]], "-", 
  FractionBox[
   RowBox[{"8", " ", 
    SuperscriptBox["\[ExponentialE]", 
     FractionBox["\[CurlyEpsilon]", 
      RowBox[{"k", " ", "T"}]]], " ", "\[Pi]", " ", "\[CurlyEpsilon]"}], 
   RowBox[{"c", " ", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "1"}], "+", 
       SuperscriptBox["\[ExponentialE]", 
        FractionBox["\[CurlyEpsilon]", 
         RowBox[{"k", " ", "T"}]]]}], ")"}], "2"], " ", "h", " ", "k", " ", 
    "T"}]]}]], "Output",
 CellChangeTimes->{
  3.563120694907362*^9, {3.5631207684943833`*^9, 3.563120771930978*^9}, 
   3.563120824316681*^9, 3.56312085547856*^9, {3.563120901134364*^9, 
   3.563120987968956*^9}, {3.5631210245601482`*^9, 3.5631210504127655`*^9}, {
   3.5631210890520124`*^9, 3.563121156658437*^9}, 3.563121554725875*^9, {
   3.563121624941598*^9, 3.563121692585317*^9}, {3.5631218204017425`*^9, 
   3.563121843037382*^9}, {3.563121894127472*^9, 3.5631219862924337`*^9}, {
   3.5631222960465775`*^9, 3.563122322597824*^9}, 3.56312235435948*^9, {
   3.56312239427995*^9, 3.5631224091935763`*^9}, {3.5632914138817997`*^9, 
   3.5632914290104246`*^9}, {3.5632915544688277`*^9, 3.5632915659106455`*^9}, 
   3.5632916829584293`*^9, {3.563291729677705*^9, 3.5632917602513514`*^9}, {
   3.5632918319702673`*^9, 3.5632918497234955`*^9}, {3.563294862033332*^9, 
   3.5632950305562067`*^9}}],

Cell[BoxData[
 FractionBox[
  RowBox[{"8", " ", "\[Pi]", " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      RowBox[{"(", 
       RowBox[{
        RowBox[{"-", "1"}], "+", 
        SuperscriptBox["\[ExponentialE]", 
         FractionBox["\[CurlyEpsilon]", 
          RowBox[{"k", " ", "T"}]]]}], ")"}], " ", "k", " ", "T"}], "-", 
     RowBox[{
      SuperscriptBox["\[ExponentialE]", 
       FractionBox["\[CurlyEpsilon]", 
        RowBox[{"k", " ", "T"}]]], " ", "\[CurlyEpsilon]"}]}], ")"}]}], 
  RowBox[{"c", " ", 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", "1"}], "+", 
      SuperscriptBox["\[ExponentialE]", 
       FractionBox["\[CurlyEpsilon]", 
        RowBox[{"k", " ", "T"}]]]}], ")"}], "2"], " ", "h", " ", "k", " ", 
   "T"}]]], "Output",
 CellChangeTimes->{
  3.563120694907362*^9, {3.5631207684943833`*^9, 3.563120771930978*^9}, 
   3.563120824316681*^9, 3.56312085547856*^9, {3.563120901134364*^9, 
   3.563120987968956*^9}, {3.5631210245601482`*^9, 3.5631210504127655`*^9}, {
   3.5631210890520124`*^9, 3.563121156658437*^9}, 3.563121554725875*^9, {
   3.563121624941598*^9, 3.563121692585317*^9}, {3.5631218204017425`*^9, 
   3.563121843037382*^9}, {3.563121894127472*^9, 3.5631219862924337`*^9}, {
   3.5631222960465775`*^9, 3.563122322597824*^9}, 3.56312235435948*^9, {
   3.56312239427995*^9, 3.5631224091935763`*^9}, {3.5632914138817997`*^9, 
   3.5632914290104246`*^9}, {3.5632915544688277`*^9, 3.5632915659106455`*^9}, 
   3.5632916829584293`*^9, {3.563291729677705*^9, 3.5632917602513514`*^9}, {
   3.5632918319702673`*^9, 3.5632918497234955`*^9}, {3.563294862033332*^9, 
   3.563295030587407*^9}}],

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"NSolve", "::", "ifun"}], "MessageName"], 
  RowBox[{
  ":", " "}], "\<\"Inverse functions are being used by \[NoBreak]\\!\\(NSolve\
\\)\[NoBreak], so some solutions may not be found; use Reduce for complete \
solution information. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \
ButtonStyle->\\\"Link\\\", ButtonFrame->None, \
ButtonData:>\\\"paclet:ref/NSolve\\\", ButtonNote -> \\\"NSolve::ifun\\\"]\\)\
\"\>"}]], "Message", "MSG",
 CellChangeTimes->{{3.563122394482751*^9, 3.5631224092871766`*^9}, {
   3.5632914143810005`*^9, 3.563291429182025*^9}, {3.563291554588828*^9, 
   3.5632915660530453`*^9}, 3.5632916830984297`*^9, {3.5632917298181047`*^9, 
   3.5632917603913517`*^9}, {3.563291832105868*^9, 3.5632918498638954`*^9}, {
   3.5632948623601327`*^9, 3.5632950308838077`*^9}}],

Cell[BoxData[
 RowBox[{"{", "}"}]], "Output",
 CellChangeTimes->{
  3.563120694907362*^9, {3.5631207684943833`*^9, 3.563120771930978*^9}, 
   3.563120824316681*^9, 3.56312085547856*^9, {3.563120901134364*^9, 
   3.563120987968956*^9}, {3.5631210245601482`*^9, 3.5631210504127655`*^9}, {
   3.5631210890520124`*^9, 3.563121156658437*^9}, 3.563121554725875*^9, {
   3.563121624941598*^9, 3.563121692585317*^9}, {3.5631218204017425`*^9, 
   3.563121843037382*^9}, {3.563121894127472*^9, 3.5631219862924337`*^9}, {
   3.5631222960465775`*^9, 3.563122322597824*^9}, 3.56312235435948*^9, {
   3.56312239427995*^9, 3.5631224091935763`*^9}, {3.5632914138817997`*^9, 
   3.5632914290104246`*^9}, {3.5632915544688277`*^9, 3.5632915659106455`*^9}, 
   3.5632916829584293`*^9, {3.563291729677705*^9, 3.5632917602513514`*^9}, {
   3.5632918319702673`*^9, 3.5632918497234955`*^9}, {3.563294862033332*^9, 
   3.5632950308838077`*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJwUV3c8lu8Xfr3ma77LKkmlrDLaou7T0DD6yqoQpUlSKrKipJQiRBSJqBDZ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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesLabel->{
    FormBox["\"\[CurlyEpsilon]\"", TraditionalForm], 
    FormBox[
    "\"sin(\[CurlyEpsilon])*Exp[-\[CurlyEpsilon]]\"", TraditionalForm]},
  AxesOrigin->{0, 0},
  PlotRange->NCache[{{
      Rational[1, 10000000000000000000000000], 10}, {-10, 10}}, {{
     9.999999999999999*^-26, 10}, {-10, 10}}],
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], Automatic}]], "Output",
 CellChangeTimes->{
  3.563120694907362*^9, {3.5631207684943833`*^9, 3.563120771930978*^9}, 
   3.563120824316681*^9, 3.56312085547856*^9, {3.563120901134364*^9, 
   3.563120987968956*^9}, {3.5631210245601482`*^9, 3.5631210504127655`*^9}, {
   3.5631210890520124`*^9, 3.563121156658437*^9}, 3.563121554725875*^9, {
   3.563121624941598*^9, 3.563121692585317*^9}, {3.5631218204017425`*^9, 
   3.563121843037382*^9}, {3.563121894127472*^9, 3.5631219862924337`*^9}, {
   3.5631222960465775`*^9, 3.563122322597824*^9}, 3.56312235435948*^9, {
   3.56312239427995*^9, 3.5631224091935763`*^9}, {3.5632914138817997`*^9, 
   3.5632914290104246`*^9}, {3.5632915544688277`*^9, 3.5632915659106455`*^9}, 
   3.5632916829584293`*^9, {3.563291729677705*^9, 3.5632917602513514`*^9}, {
   3.5632918319702673`*^9, 3.5632918497234955`*^9}, {3.563294862033332*^9, 
   3.5632950309150076`*^9}}]
}, Open  ]]
}, Open  ]]
},
CellGrouping->Manual,
WindowSize->{698, 645},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
FrontEndVersion->"8.0 for Microsoft Windows (64-bit) (February 23, 2011)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[579, 22, 282, 8, 27, "Subsubsection",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}],
Cell[864, 32, 1046, 31, 132, "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}],
Cell[1913, 65, 346, 7, 48, "Output",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}],
Cell[2262, 74, 372, 8, 48, "Output",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}],
Cell[2637, 84, 373, 8, 48, "Output",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}],
Cell[3013, 94, 399, 9, 47, "Output",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}],
Cell[3415, 105, 459, 13, 73, "Output",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}],
Cell[3877, 120, 297, 4, 30, "Output",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}]
}, Closed]],
Cell[CellGroupData[{
Cell[4211, 129, 343, 8, 21, "Subsubsection",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}],
Cell[CellGroupData[{
Cell[4579, 141, 3437, 100, 192, "Input"],
Cell[8019, 243, 391, 9, 48, "Output"],
Cell[8413, 254, 321, 6, 47, "Output"],
Cell[8737, 262, 444, 11, 60, "Output"],
Cell[9184, 275, 489, 13, 52, "Output"],
Cell[9676, 290, 461, 11, 60, "Output"],
Cell[10140, 303, 476, 14, 73, "Output"],
Cell[10619, 319, 331, 6, 30, "Output"],
Cell[10953, 327, 331, 6, 30, "Output"],
Cell[11287, 335, 313, 5, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[11637, 345, 1569, 47, 132, "Input"],
Cell[13209, 394, 200, 5, 30, "Output"],
Cell[13412, 401, 253, 7, 50, "Output"],
Cell[13668, 410, 10417, 181, 234, 5284, 94, "CachedBoxData", "BoxData", \
"Output"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[24134, 597, 113, 1, 21, "Subsubsection"],
Cell[CellGroupData[{
Cell[24272, 602, 3149, 92, 212, "Input"],
Cell[27424, 696, 776, 20, 54, "Output"],
Cell[28203, 718, 794, 21, 54, "Output"],
Cell[29000, 741, 738, 17, 52, "Output"],
Cell[29741, 760, 608, 12, 35, "Output"],
Cell[30352, 774, 608, 12, 35, "Output"],
Cell[30963, 788, 607, 12, 35, "Output"],
Cell[31573, 802, 18028, 303, 315, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[49638, 1110, 1874, 52, 152, "Input"],
Cell[51515, 1164, 628, 18, 54, "Output"],
Cell[52146, 1184, 1060, 32, 54, "Output"],
Cell[53209, 1218, 853, 27, 74, "Output"],
Cell[54065, 1247, 253, 4, 30, "Output"],
Cell[54321, 1253, 266, 4, 30, "Output"],
Cell[54590, 1259, 314, 5, 30, "Output"],
Cell[54907, 1266, 464, 11, 44, "Output"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[55420, 1283, 157, 2, 21, "Subsubsection"],
Cell[CellGroupData[{
Cell[55602, 1289, 2400, 68, 152, "Input"],
Cell[58005, 1359, 484, 10, 47, "Output"],
Cell[58492, 1371, 481, 10, 56, "Output"],
Cell[58976, 1383, 527, 11, 55, "Output"],
Cell[59506, 1396, 322, 4, 30, "Output"],
Cell[59831, 1402, 32025, 533, 253, "Output"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[91905, 1941, 222, 4, 21, "Subsubsection"],
Cell[CellGroupData[{
Cell[92152, 1949, 1467, 44, 112, "Input"],
Cell[93622, 1995, 548, 17, 54, "Output"],
Cell[94173, 2014, 566, 18, 54, "Output"],
Cell[94742, 2034, 377, 9, 35, "Output"],
Cell[95122, 2045, 190, 3, 30, "Output"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[95361, 2054, 276, 5, 21, "Subsubsection"],
Cell[CellGroupData[{
Cell[95662, 2063, 2854, 72, 152, "Input"],
Cell[98519, 2137, 1168, 22, 52, "Output"],
Cell[99690, 2161, 1184, 22, 66, "Output"],
Cell[100877, 2185, 1654, 37, 77, "Output"],
Cell[102534, 2224, 1655, 37, 84, "Output"],
Cell[104192, 2263, 832, 15, 39, "Message"],
Cell[105027, 2280, 919, 14, 30, "Output"],
Cell[105949, 2296, 50039, 826, 239, "Output"]
}, Open  ]]
}, Open  ]]
}
]
*)

(* End of internal cache information *)