(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 11.2' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 30873, 852] NotebookOptionsPosition[ 26783, 781] NotebookOutlinePosition[ 27163, 798] CellTagsIndexPosition[ 27120, 795] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"ClearAll", "[", "\"\\"", "]"}], " "}], "\[IndentingNewLine]", RowBox[{ RowBox[{"kB", "=", RowBox[{"1.38064852", "\[Times]", RowBox[{"10", "^", RowBox[{"(", RowBox[{"-", "23"}], ")"}]}], "*", " ", RowBox[{"m", "^", "2"}], "*", " ", RowBox[{ RowBox[{"kg", "/", RowBox[{"s", "^", "2"}]}], "/", "K"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Troom", "=", RowBox[{"300", "*", "K"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"hbar", "=", RowBox[{ RowBox[{"6.626176", "/", RowBox[{"(", RowBox[{"2", "*", "Pi"}], ")"}]}], "*", RowBox[{"10", "^", RowBox[{"(", RowBox[{"-", "34"}], ")"}]}], "*", "kg", "*", RowBox[{ RowBox[{"m", "^", "2"}], "/", "s"}]}]}]}], "Input", CellChangeTimes->{{3.7602722922224216`*^9, 3.7602723117985067`*^9}, { 3.760272540497641*^9, 3.760272563073134*^9}, {3.760272599283039*^9, 3.760272614641878*^9}, {3.763208645016173*^9, 3.7632086489510098`*^9}},ExpressionUUID->"6b6e588f-9f92-4a45-a1d1-\ cd464e22abcd"], Cell[BoxData[ FractionBox[ RowBox[{"1.0545886641968829`*^-34", " ", "kg", " ", SuperscriptBox["m", "2"]}], "s"]], "Output", CellChangeTimes->{3.760272583271785*^9, 3.760272616863406*^9, 3.761217657629534*^9, 3.761217704661766*^9, 3.76121774698207*^9, 3.7632086595117292`*^9, 3.763208899040555*^9},ExpressionUUID->"474fbea4-6fe1-4d0f-958c-\ 31d45502b820"] }, Open ]], Cell[BoxData[ RowBox[{"(*", " ", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"problem", " ", "1"}], " ", "**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**", "**", "**"}], "*", "8"}], "*)"}]], "Input", CellChangeTimes->{{3.760272340586644*^9, 3.760272346118238*^9}, { 3.76121719709226*^9, 3.7612171974389343`*^9}, {3.761217235855322*^9, 3.7612172383112793`*^9}},ExpressionUUID->"0cd82088-d241-4966-bc30-\ 24410bb35948"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"me", "=", RowBox[{"9.10938356", "*", RowBox[{"10", "^", RowBox[{"(", RowBox[{"-", "31"}], ")"}]}], "*", "kg"}]}], "\[IndentingNewLine]", RowBox[{"mcarrier", "=", RowBox[{"0.04", "*", "me"}]}], "\[IndentingNewLine]", RowBox[{"nquant", "=", RowBox[{ RowBox[{"(", RowBox[{"mcarrier", "*", "kB", "*", RowBox[{ RowBox[{ RowBox[{"Troom", "/", "2"}], "/", "Pi"}], "/", RowBox[{"hbar", "^", "2"}]}]}], ")"}], "^", RowBox[{"(", RowBox[{"3", "/", "2"}], ")"}]}]}]}], "Input", CellChangeTimes->{{3.7602723510676394`*^9, 3.7602723700064793`*^9}, { 3.760272406562043*^9, 3.760272491368141*^9}, {3.760272634130557*^9, 3.760272662202285*^9}},ExpressionUUID->"2d670ce4-007c-41cb-ba6c-\ 043388f5f929"], Cell[BoxData[ RowBox[{"9.10938356`*^-31", " ", "kg"}]], "Output", CellChangeTimes->{{3.760272622939793*^9, 3.7602726634902277`*^9}, 3.7612176577395487`*^9, 3.761217704759759*^9, 3.761217747063332*^9, 3.7632086596121483`*^9, 3.763208899143836*^9},ExpressionUUID->"bca8cc25-c77d-4904-905b-\ 6a275487a34d"], Cell[BoxData[ RowBox[{"3.643753424`*^-32", " ", "kg"}]], "Output", CellChangeTimes->{{3.760272622939793*^9, 3.7602726634902277`*^9}, 3.7612176577395487`*^9, 3.761217704759759*^9, 3.761217747063332*^9, 3.7632086596121483`*^9, 3.7632088991504593`*^9},ExpressionUUID->"05e01f1b-ea2a-4efa-953c-\ c7fa74a17dee"], Cell[BoxData[ RowBox[{"1.0037162400452657`*^23", " ", SuperscriptBox[ RowBox[{"(", FractionBox["1", SuperscriptBox["m", "2"]], ")"}], RowBox[{"3", "/", "2"}]]}]], "Output", CellChangeTimes->{{3.760272622939793*^9, 3.7602726634902277`*^9}, 3.7612176577395487`*^9, 3.761217704759759*^9, 3.761217747063332*^9, 3.7632086596121483`*^9, 3.763208899154995*^9},ExpressionUUID->"9f73b2bc-c079-4ebf-9790-\ 373356906235"] }, Open ]], Cell[BoxData[ RowBox[{"(*", " ", RowBox[{ RowBox[{"so", " ", "for", " ", "original", " ", "n", RowBox[{"<<", " ", "nquant"}]}], ",", " ", RowBox[{ "as", " ", "needed", " ", "for", " ", "ieal", " ", "gas", " ", "treatment"}], ",", " ", RowBox[{ "but", " ", "not", " ", "true", " ", "for", " ", "maximally", " ", "doped"}]}], " ", "*)"}]], "Input", CellChangeTimes->{{3.760272699328738*^9, 3.7602727230512114`*^9}, { 3.76027285135878*^9, 3.760272851748673*^9}, {3.763209055509379*^9, 3.7632090722997303`*^9}, {3.763209104716425*^9, 3.763209106756274*^9}},ExpressionUUID->"944fe96b-d64e-422e-bafc-\ 7bb17246e3bf"], Cell[BoxData[ RowBox[{"(*", " ", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"problem", " ", "2"}], " ", "**"}], "**"}], "*", "\[IndentingNewLine]", "the", " ", "mass", " ", "times", " ", "the", " ", "centrifugal", " ", "acceleration", " ", RowBox[{"Omega", "^", "2"}], "*", "L", " ", "is", " ", "the", " ", "force"}], ",", " ", RowBox[{"times", " ", "l", " ", "is", " ", RowBox[{"energy", "\[IndentingNewLine]", "**", "**", "**"}], "*", RowBox[{ "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**"}]}]}], "*******)"}]], "Input", CellChangeTimes->{{3.761217227351325*^9, 3.7612172549922047`*^9}, { 3.7632089891076107`*^9, 3.76320902054712*^9}, {3.763209119708539*^9, 3.7632091205562763`*^9}, {3.7632091709501467`*^9, 3.763209171325656*^9}},ExpressionUUID->"4b849dee-311a-4d9d-8826-\ 459020c7edf9"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{"Exp", "[", RowBox[{ RowBox[{"-", "M"}], "*", RowBox[{"Omega", "^", "2"}], "*", "L", "*", RowBox[{ RowBox[{"l", "/", "kB"}], "/", "T"}]}], "]"}], "\[Equal]", "0.01"}], ",", "Omega"}], "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"kB", "=", RowBox[{"1.38064852", "\[Times]", RowBox[{"10", "^", RowBox[{"(", RowBox[{"-", "23"}], ")"}]}], "*", " ", RowBox[{"m", "^", "2"}], "*", " ", RowBox[{ RowBox[{"kg", "/", RowBox[{"s", "^", "2"}]}], "/", "K"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"T", "=", RowBox[{"300", " ", "K"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"L", "=", RowBox[{"1", "*", "m"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"l", "=", RowBox[{"0.05", "*", "m"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"mN", "=", RowBox[{"1.67", "*", RowBox[{"10", "^", RowBox[{"(", RowBox[{"-", "27"}], ")"}]}], "*", "kg"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"M", "=", RowBox[{ RowBox[{"10", "^", "6"}], "*", "mN"}]}], ";"}]}], "Input", CellChangeTimes->{{3.761217259237185*^9, 3.761217372585341*^9}, { 3.76121741884202*^9, 3.7612174258578587`*^9}, {3.761217570356443*^9, 3.761217596300112*^9}, {3.761217686502467*^9, 3.761217700261508*^9}, { 3.7618485792302628`*^9, 3.761848606679039*^9}, {3.761848641046855*^9, 3.7618486697510967`*^9}},ExpressionUUID->"2ac37010-1e6a-49fa-8cff-\ c0d4b27a157a"], Cell[BoxData[ TemplateBox[{ "Solve","ifun", "\"Inverse functions are being used by \ \\!\\(\\*RowBox[{\\\"Solve\\\"}]\\), so some solutions may not be found; use \ Reduce for complete solution information.\"",2,278,18,21638358103321692052, "Local"}, "MessageTemplate"]], "Message", "MSG", CellChangeTimes->{ 3.761217375978776*^9, 3.7612176578532*^9, 3.7612177048514833`*^9, 3.761217747165525*^9, {3.761848553199595*^9, 3.761848579746348*^9}, { 3.76184861233051*^9, 3.761848676535746*^9}, 3.7632086597372637`*^9, 3.763208899245722*^9},ExpressionUUID->"1e7aaedd-6c8f-497e-9697-\ 5ddc3673131b"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"Omega", "\[Rule]", RowBox[{"-", FractionBox[ RowBox[{"7.973782917557125`*^-12", " ", SqrtBox["kg"], " ", "m", " ", SqrtBox["T"]}], RowBox[{ SqrtBox["K"], " ", SqrtBox["l"], " ", SqrtBox["L"], " ", SqrtBox["M"], " ", "s"}]]}]}], "}"}], ",", RowBox[{"{", RowBox[{"Omega", "\[Rule]", FractionBox[ RowBox[{"7.973782917557125`*^-12", " ", SqrtBox["kg"], " ", "m", " ", SqrtBox["T"]}], RowBox[{ SqrtBox["K"], " ", SqrtBox["l"], " ", SqrtBox["L"], " ", SqrtBox["M"], " ", "s"}]]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{ 3.761217375981262*^9, 3.761217657872511*^9, 3.761217704869772*^9, 3.7612177471857567`*^9, {3.761848553204372*^9, 3.761848579752364*^9}, { 3.761848612334334*^9, 3.761848676538015*^9}, 3.763208659755793*^9, 3.763208899261958*^9},ExpressionUUID->"8c378ed5-dec2-47d2-9a27-\ fefe8c832124"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Assuming", "[", RowBox[{ RowBox[{ RowBox[{"m", ">", "0"}], "&&", RowBox[{"s", ">", "0"}], "&&", RowBox[{"kg", ">", "0"}], "&&", RowBox[{"K", ">", "0"}]}], ",", RowBox[{"Simplify", "[", RowBox[{"Omega", "=", FractionBox[ RowBox[{"2.145966026289347`", " ", SqrtBox["kB"], " ", SqrtBox["T"]}], RowBox[{ SqrtBox["L"], SqrtBox["l"], SqrtBox["M"]}]]}], "]"}]}], "]"}]], "Input", CellChangeTimes->{{3.761217440690776*^9, 3.7612174410021763`*^9}, { 3.7612176073643093`*^9, 3.761217650164907*^9}, {3.761217720398162*^9, 3.76121774147888*^9}},ExpressionUUID->"29f66a98-88b2-42fa-b5b9-\ ff93749678c6"], Cell[BoxData[ FractionBox["15.11408281900868`", "s"]], "Output", CellChangeTimes->{{3.761217651946313*^9, 3.761217657935017*^9}, 3.761217704936837*^9, 3.76121774724726*^9, 3.763208659809759*^9, 3.763208899337183*^9},ExpressionUUID->"d7f22cf3-69b4-4787-a6bc-\ 436f788517c0"] }, Open ]], Cell[BoxData[ RowBox[{"(*", " ", RowBox[{ RowBox[{ "centrifuge", " ", "acceleration", " ", "about", " ", "20", " ", "times", " ", "g"}], "=", RowBox[{"9.8", " ", RowBox[{"m", "/", RowBox[{"s", "^", "2"}]}]}]}], " ", "*)"}]], "Input", CellChangeTimes->{{3.761217763395772*^9, 3.761217778998456*^9}, { 3.7612178462640343`*^9, 3.7612178784156303`*^9}},ExpressionUUID->"db628070-6fb9-426f-8890-\ bf6e579f7d7f"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"gcentri", "=", RowBox[{ RowBox[{ RowBox[{"(", FractionBox["15.11408281900868`", "s"], ")"}], "^", "2"}], "*", "L"}]}]], "Input", CellChangeTimes->{{3.76121779427136*^9, 3.761217817255039*^9}},ExpressionUUID->"82651076-58e4-4545-807d-\ 30f7064b17a6"], Cell[BoxData[ FractionBox[ RowBox[{"228.43549945985336`", " ", "m"}], SuperscriptBox["s", "2"]]], "Output", CellChangeTimes->{{3.7612178086849613`*^9, 3.761217818867424*^9}, 3.761849680053776*^9, 3.763208659861596*^9, 3.763208899404262*^9},ExpressionUUID->"b55959ab-3c98-4f1a-9f06-\ 6d1e198e9586"] }, Open ]], Cell[BoxData[ RowBox[{"(*", " ", RowBox[{"problem", " ", RowBox[{ "3", " ", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**"}]}], "*******)"}]], "Input", CellChangeTimes->{{3.761217895136801*^9, 3.761217895383738*^9}},ExpressionUUID->"d9d2882f-cf86-4d42-8a32-\ 1e1649b84df2"], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ RowBox[{"triangular", " ", "cycle"}], ",", " ", RowBox[{ RowBox[{"(", "a", ")"}], " ", "V0"}], ",", RowBox[{"2", "T0"}], ",", " ", RowBox[{"p", "=", RowBox[{"R", " ", "2", RowBox[{"T0", "/", "V0"}], "\[IndentingNewLine]", RowBox[{"(", "b", ")"}], " ", "2", "V0"}]}], ",", RowBox[{"2", "T0"}], ",", " ", RowBox[{ RowBox[{"p", "=", RowBox[{"R", " ", "2", RowBox[{"T0", "/", "V0"}]}]}], " ", ";", " ", RowBox[{ RowBox[{"(", "c", ")"}], " ", "V0"}]}], ",", "T0", ",", " ", RowBox[{ RowBox[{"p", "=", RowBox[{"R", " ", RowBox[{"T0", "/", "V0"}]}]}], " ", ";", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"the", " ", "line", " ", "bc", " ", "is", " ", "p"}], "=", RowBox[{"const", " ", "isobar"}]}]}], ",", " ", RowBox[{ RowBox[{ RowBox[{"so", " ", "in", " ", "the", " ", "plot", " ", "in", " ", "p"}], "-", RowBox[{ "V", " ", "plot", " ", "bc", " ", "is", " ", "horizontal", "\[IndentingNewLine]", "S"}]}], "=", RowBox[{ RowBox[{ RowBox[{"R", "*", "log", RowBox[{"(", RowBox[{"V", "*", RowBox[{"T", "^", RowBox[{"(", RowBox[{"3", "/", "2"}], ")"}]}]}], ")"}]}], "+", RowBox[{"const", " ", "so", " ", "Sa"}]}], "=", RowBox[{"Rlog", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"V0", "*", RowBox[{ RowBox[{"(", RowBox[{"2", "T0"}], ")"}], "^", RowBox[{"(", RowBox[{"3", "/", "2"}], ")"}]}]}], "+", RowBox[{"const", "\[IndentingNewLine]", "Sb"}]}], "=", RowBox[{"Rlog", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"2", "V0", "*", RowBox[{ RowBox[{"(", RowBox[{"2", "T0"}], ")"}], "^", RowBox[{"(", RowBox[{"3", "/", "2"}], ")"}]}]}], "+", "const"}], ",", " ", RowBox[{"Sc", "=", RowBox[{"Rlog", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"V0", "*", RowBox[{ RowBox[{"(", "T0", ")"}], "^", RowBox[{"(", RowBox[{"3", "/", "2"}], ")"}]}]}], "+", RowBox[{ "const", "\[IndentingNewLine]", "\[IndentingNewLine]", "Heat", " ", "in", " ", "is", " ", "heat", " ", "on", " ", RowBox[{"(", "ab", ")"}]}]}], "=", RowBox[{ RowBox[{"integral", " ", "T", " ", "dS"}], "=", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"2", "T0"}], ")"}], "*", RowBox[{"(", RowBox[{"Sb", "-", "Sa"}], ")"}]}], "=", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"2", "T_", "0"}], ")"}], "R", "*", RowBox[{"log", "[", "2", "]"}], "\[IndentingNewLine]", "Work", " ", "on", " ", RowBox[{"(", "ab", ")"}]}], "=", RowBox[{ RowBox[{"integral", " ", "p", " ", "dV"}], "=", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"2", "T0", " ", "R"}], ")"}], " ", "integral", " ", RowBox[{"dV", "/", "V"}]}], "=", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"2", "T0", " ", "R"}], ")"}], "log", RowBox[{"(", "2", ")"}], "\[IndentingNewLine]", "work", " ", "on", " ", "cycle", " ", "is", " ", "work", " ", "on", " ", RowBox[{"(", "ab", ")"}]}], " ", "-", RowBox[{ RowBox[{"(", "bc", ")"}], " ", "since", " ", "no", " ", "work", " ", "on", " ", RowBox[{"(", "ca", ")"}], " ", "\[IndentingNewLine]", "\[IndentingNewLine]", "Work", " ", "on", " ", "cycle", " ", RowBox[{"(", RowBox[{"ab", "-", "bc"}], ")"}]}]}], "=", RowBox[{ RowBox[{ RowBox[{"2", "*", "T0", "*", "R", "*", "log", RowBox[{"(", "2", ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{"RT0", "/", "V0"}], ")"}], "*", "V0", "\[IndentingNewLine]", "eta"}]}], "=", RowBox[{"work", " ", "on", " ", RowBox[{"cycle", "/", "heat"}]}]}]}]}]}]}]}]}]}], " "}]}]}]}]}]}]}]}]}]}]}]}], "*)"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.7612179170619993`*^9, 3.761217918240087*^9}, { 3.761217954768869*^9, 3.7612180571141453`*^9}, {3.76121814769204*^9, 3.76121817161138*^9}, {3.761218274853692*^9, 3.761218426999812*^9}, { 3.761218563168717*^9, 3.7612187823314247`*^9}, {3.7612188326206923`*^9, 3.7612188894288473`*^9}, {3.7612189670702877`*^9, 3.7612191339120827`*^9}, { 3.761219186352943*^9, 3.761219188800913*^9}, {3.761219365995181*^9, 3.761219386931295*^9}, {3.763208871938508*^9, 3.76320887532957*^9}},ExpressionUUID->"c45377ef-adc1-484e-b4b5-\ bad791cd5dbd"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"eta", "=", RowBox[{"1", "-", RowBox[{ RowBox[{"(", RowBox[{"R", "*", RowBox[{"T0", "/", "V0"}]}], ")"}], "*", RowBox[{"V0", "/", RowBox[{"(", RowBox[{"2", "*", "T0", "*", "R", "*", RowBox[{"Log", "[", "2", "]"}]}], ")"}]}]}]}]}]], "Input", CellChangeTimes->{{3.761219199630184*^9, 3.761219251081481*^9}},ExpressionUUID->"e5fb98be-b663-449e-94dd-\ 432a44c45625"], Cell[BoxData[ RowBox[{"1", "-", FractionBox["1", RowBox[{"2", " ", RowBox[{"Log", "[", "2", "]"}]}]]}]], "Output", CellChangeTimes->{{3.761219232882025*^9, 3.761219255988452*^9}, 3.763208659926434*^9, 3.763208899482072*^9},ExpressionUUID->"443eb419-055f-4e8e-937c-\ f52026d0a0cb"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"1", "-", FractionBox["1", RowBox[{"2", " ", RowBox[{"Log", "[", "2.", "]"}]}]]}]], "Input", CellChangeTimes->{ 3.761219277482585*^9},ExpressionUUID->"293e4252-0d82-45bb-bf25-\ 82df9dd68f2a"], Cell[BoxData["0.2786524795555183`"], "Output", CellChangeTimes->{3.761219278438047*^9, 3.763208659967092*^9, 3.763208899549572*^9},ExpressionUUID->"182654ae-ed45-48dc-b415-\ b2ace1b4b5ab"] }, Open ]], Cell[BoxData[""], "Input", CellChangeTimes->{{3.7612190120438766`*^9, 3.761219020110962*^9}},ExpressionUUID->"2dc7329b-8704-4dff-88f7-\ 9992509a6edd"], Cell[BoxData[ RowBox[{"(*", " ", RowBox[{"problem", " ", RowBox[{ "4", " ", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**"}]}], "*******)"}]], "Input", CellChangeTimes->{{3.76121934803544*^9, 3.761219348618671*^9}},ExpressionUUID->"f2f5ba62-220f-496e-8b7d-\ d0c03a5f39dc"], Cell[BoxData[ RowBox[{"(*", " ", RowBox[{ RowBox[{ RowBox[{"Maxwell", " ", "relation", " ", RowBox[{"(", RowBox[{"partial", " ", RowBox[{"S", "/", "partial"}], " ", "V"}], ")"}], "_T"}], "=", RowBox[{ RowBox[{"N", "*", RowBox[{"KB", "/", "V"}], "\[IndentingNewLine]", RowBox[{"(", RowBox[{"partial", " ", RowBox[{"p", "/", "partial"}], " ", "T"}], ")"}], "_V"}], "=", " ", RowBox[{ RowBox[{"(", RowBox[{"partial", " ", RowBox[{ RowBox[{"(", RowBox[{"N", "*", "kB", "*", RowBox[{"T", "/", "V"}]}], ")"}], "/", "partial"}], " ", "T"}], ")"}], "=", RowBox[{"N", "*", RowBox[{"KB", "/", "V"}]}]}]}]}], ",", " ", RowBox[{"the", " ", "same"}]}], " ", "*)"}]], "Input", CellChangeTimes->{{3.761219427489176*^9, 3.761219613342154*^9}},ExpressionUUID->"5f0ded68-28f6-4e38-9c01-\ bcf2551507bc"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{" ", RowBox[{"Derivatives", " ", "in", " ", "Jacobian", " "}]}]], "Input", CellChangeTimes->{{3.761219602668085*^9, 3.761219642822579*^9}},ExpressionUUID->"d4d8c334-1587-46aa-8b10-\ 54f03a08c21b"], Cell[BoxData[ RowBox[{"Derivatives", " ", "in", " ", "Jacobian"}]], "Output", CellChangeTimes->{3.763208660057355*^9, 3.763208899656521*^9},ExpressionUUID->"e5e440cf-eebe-436f-89c0-\ 20875eb985e2"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"partial", " ", RowBox[{"T", "/", "partial"}], " ", "p"}], ")"}], "_V"}], "=", RowBox[{ RowBox[{"V", "/", "N"}], "/", "KB"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"partial", " ", RowBox[{"T", "/", "partial"}], " ", "V"}], ")"}], "_p"}], "=", RowBox[{ RowBox[{"p", "/", "N"}], "/", "KB"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"partial", " ", RowBox[{"S", "/", "partial"}], " ", "p"}], ")"}], "_V"}], "=", RowBox[{"N", "*", "kB", "*", RowBox[{ RowBox[{"(", RowBox[{"3", "/", "2"}], ")"}], "/", "p"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"partial", " ", RowBox[{"S", "/", "partial"}], " ", "V"}], ")"}], "_p"}], "=", RowBox[{"N", "*", "kB", "*", RowBox[{ RowBox[{"(", RowBox[{"5", "/", "2"}], ")"}], "/", "V"}]}]}], ";"}]}], "Input", CellChangeTimes->{{3.761219950875325*^9, 3.761220130372796*^9}, { 3.763208887747074*^9, 3.7632088944095592`*^9}},ExpressionUUID->"8e5aeec8-5ae0-44d3-8343-\ c18b7af10eb0"], Cell[BoxData[ TemplateBox[{ "Set","write", "\"Tag \\!\\(\\*RowBox[{\\\"Times\\\"}]\\) in \ \\!\\(\\*RowBox[{RowBox[{\\\"(\\\", RowBox[{\\\"300\\\", \\\" \\\", \ \\\"K\\\", \\\" \\\", \\\"p\\\"}], \\\")\\\"}], \\\" \\\", \\\"_V\\\"}]\\) is \ Protected.\"",2,296,19,21638358103321692052,"Local"}, "MessageTemplate"]], "Message", "MSG", CellChangeTimes->{3.763208660109291*^9, 3.763208899720004*^9},ExpressionUUID->"c3d2e042-037d-4ad1-b470-\ 21e3cd78a4f8"], Cell[BoxData[ TemplateBox[{ "Set","write", "\"Tag \\!\\(\\*RowBox[{\\\"Times\\\"}]\\) in \ \\!\\(\\*RowBox[{RowBox[{\\\"(\\\", RowBox[{\\\"300\\\", \\\" \\\", \ \\\"K\\\", \\\" \\\", \\\"V\\\"}], \\\")\\\"}], \\\" \\\", \\\"_p\\\"}]\\) is \ Protected.\"",2,297,20,21638358103321692052,"Local"}, "MessageTemplate"]], "Message", "MSG", CellChangeTimes->{3.763208660109291*^9, 3.763208899736476*^9},ExpressionUUID->"f19e745b-bf00-4c1c-b6a4-\ 3e06362f6ca8"], Cell[BoxData[ TemplateBox[{ "Set","write", "\"Tag \\!\\(\\*RowBox[{\\\"Times\\\"}]\\) in \ \\!\\(\\*RowBox[{RowBox[{\\\"(\\\", RowBox[{\\\"p\\\", \\\" \\\", \ \\\"S\\\"}], \\\")\\\"}], \\\" \\\", \\\"_V\\\"}]\\) is Protected.\"",2,298, 21,21638358103321692052,"Local"}, "MessageTemplate"]], "Message", "MSG", CellChangeTimes->{3.763208660109291*^9, 3.763208899750552*^9},ExpressionUUID->"e4a1a9e6-2ce2-41fa-b641-\ 666af61a076b"], Cell[BoxData[ TemplateBox[{ "Set","write", "\"Tag \\!\\(\\*RowBox[{\\\"Times\\\"}]\\) in \ \\!\\(\\*RowBox[{RowBox[{\\\"(\\\", RowBox[{\\\"S\\\", \\\" \\\", \ \\\"V\\\"}], \\\")\\\"}], \\\" \\\", \\\"_p\\\"}]\\) is Protected.\"",2,299, 22,21638358103321692052,"Local"}, "MessageTemplate"]], "Message", "MSG", CellChangeTimes->{3.763208660109291*^9, 3.763208899764447*^9},ExpressionUUID->"54910a6f-7eaa-4e6a-906f-\ 91ab68ddf9b1"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"partial", " ", RowBox[{"T", "/", "partial"}], " ", "p"}], ")"}]}], "_V", "*", RowBox[{"(", RowBox[{"partial", " ", RowBox[{"S", "/", "partial"}], " ", "V"}], ")"}], "_p"}], "+", RowBox[{ RowBox[{"(", RowBox[{"partial", " ", RowBox[{"T", "/", "partial"}], " ", "V"}], ")"}], "_p", "*", RowBox[{"(", RowBox[{"partial", " ", RowBox[{"S", "/", "partial"}], " ", "p"}], ")"}], "_V"}]}], "=", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "5"}], "/", "2"}], "+", RowBox[{"3", "/", "2"}]}], "=", RowBox[{"-", "1"}]}]}]], "Input", CellChangeTimes->{{3.7612201656137943`*^9, 3.761220216734192*^9}, { 3.7618611760407467`*^9, 3.7618612007863398`*^9}},ExpressionUUID->"73d91965-9918-47db-a421-\ 3f38b9c39309"], Cell[BoxData[ TemplateBox[{ "Set","write", "\"Tag \\!\\(\\*RowBox[{\\\"Plus\\\"}]\\) in \ \\!\\(\\*RowBox[{RowBox[{\\\"-\\\", FractionBox[\\\"5\\\", \\\"2\\\"]}], \ \\\"+\\\", FractionBox[\\\"3\\\", \\\"2\\\"]}]\\) is Protected.\"",2,300,23, 21638358103321692052,"Local"}, "MessageTemplate"]], "Message", "MSG", CellChangeTimes->{3.763208660243018*^9, 3.763208899855818*^9},ExpressionUUID->"5310bf2a-7815-4865-aff5-\ 057eee15df27"], Cell[BoxData[ TemplateBox[{ "Set","write", "\"Tag \\!\\(\\*RowBox[{\\\"Plus\\\"}]\\) in \ \\!\\(\\*RowBox[{RowBox[{RowBox[{\\\"-\\\", \\\"300\\\"}], \\\" \\\", \\\"K\\\ \", \\\" \\\", \\\"p\\\", \\\" \\\", \\\"S\\\", \\\" \\\", \\\"V\\\", \\\" \\\ \", \\\"_p\\\", \\\" \\\", \\\"_V\\\"}], \\\"+\\\", RowBox[{\\\"300\\\", \\\" \ \\\", \\\"K\\\", \\\" \\\", \\\"p\\\", \\\" \\\", \\\"S\\\", \\\" \\\", \\\"V\ \\\", \\\" \\\", \\\"_p\\\", \\\" \\\", \\\"_V\\\"}]}]\\) is Protected.\"",2, 300,24,21638358103321692052,"Local"}, "MessageTemplate"]], "Message", "MSG", CellChangeTimes->{3.763208660243018*^9, 3.763208899871738*^9},ExpressionUUID->"05e91c7d-1da6-422b-a17e-\ f0414c7f6544"], Cell[BoxData[ RowBox[{"-", "1"}]], "Output", CellChangeTimes->{3.7632086602690697`*^9, 3.763208899885891*^9},ExpressionUUID->"bf13e0e0-cacf-4bd3-945c-\ e3b8fcdd1cb5"] }, Open ]] }, WindowSize->{975, 962}, WindowMargins->{{Automatic, 376}, {0, Automatic}}, Magnification->1.25, FrontEndVersion->"11.2 for Mac OS X x86 (32-bit, 64-bit Kernel) (September \ 10, 2017)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[580, 22, 1092, 31, 116, "Input",ExpressionUUID->"6b6e588f-9f92-4a45-a1d1-cd464e22abcd"], Cell[1675, 55, 371, 8, 64, "Output",ExpressionUUID->"474fbea4-6fe1-4d0f-958c-31d45502b820"] }, Open ]], Cell[2061, 66, 1238, 37, 37, "Input",ExpressionUUID->"0cd82088-d241-4966-bc30-24410bb35948"], Cell[CellGroupData[{ Cell[3324, 107, 786, 21, 90, "Input",ExpressionUUID->"2d670ce4-007c-41cb-ba6c-043388f5f929"], Cell[4113, 130, 317, 6, 43, "Output",ExpressionUUID->"bca8cc25-c77d-4904-905b-6a275487a34d"], Cell[4433, 138, 320, 6, 43, "Output",ExpressionUUID->"05e01f1b-ea2a-4efa-953c-c7fa74a17dee"], Cell[4756, 146, 445, 11, 61, "Output",ExpressionUUID->"9f73b2bc-c079-4ebf-9790-373356906235"] }, Open ]], Cell[5216, 160, 655, 15, 64, "Input",ExpressionUUID->"944fe96b-d64e-422e-bafc-7bb17246e3bf"], Cell[5874, 177, 891, 20, 116, "Input",ExpressionUUID->"4b849dee-311a-4d9d-8826-459020c7edf9"], Cell[CellGroupData[{ Cell[6790, 201, 1585, 46, 194, "Input",ExpressionUUID->"2ac37010-1e6a-49fa-8cff-c0d4b27a157a"], Cell[8378, 249, 616, 13, 50, "Message",ExpressionUUID->"1e7aaedd-6c8f-497e-9697-5ddc3673131b"], Cell[8997, 264, 1045, 31, 77, "Output",ExpressionUUID->"8c378ed5-dec2-47d2-9a27-fefe8c832124"] }, Open ]], Cell[CellGroupData[{ Cell[10079, 300, 712, 21, 71, "Input",ExpressionUUID->"29f66a98-88b2-42fa-b5b9-ff93749678c6"], Cell[10794, 323, 283, 5, 60, "Output",ExpressionUUID->"d7f22cf3-69b4-4787-a6bc-436f788517c0"] }, Open ]], Cell[11092, 331, 442, 12, 37, "Input",ExpressionUUID->"db628070-6fb9-426f-8890-bf6e579f7d7f"], Cell[CellGroupData[{ Cell[11559, 347, 297, 9, 58, "Input",ExpressionUUID->"82651076-58e4-4545-807d-30f7064b17a6"], Cell[11859, 358, 312, 7, 62, "Output",ExpressionUUID->"b55959ab-3c98-4f1a-9f06-6d1e198e9586"] }, Open ]], Cell[12186, 368, 353, 8, 37, "Input",ExpressionUUID->"d9d2882f-cf86-4d42-8a32-1e1649b84df2"], Cell[12542, 378, 5695, 137, 350, "Input",ExpressionUUID->"c45377ef-adc1-484e-b4b5-bad791cd5dbd"], Cell[CellGroupData[{ Cell[18262, 519, 439, 13, 37, "Input",ExpressionUUID->"e5fb98be-b663-449e-94dd-432a44c45625"], Cell[18704, 534, 302, 8, 63, "Output",ExpressionUUID->"443eb419-055f-4e8e-937c-f52026d0a0cb"] }, Open ]], Cell[CellGroupData[{ Cell[19043, 547, 229, 7, 60, "Input",ExpressionUUID->"293e4252-0d82-45bb-bf25-82df9dd68f2a"], Cell[19275, 556, 192, 3, 42, "Output",ExpressionUUID->"182654ae-ed45-48dc-b415-b2ace1b4b5ab"] }, Open ]], Cell[19482, 562, 154, 3, 37, "Input",ExpressionUUID->"2dc7329b-8704-4dff-88f7-9992509a6edd"], Cell[19639, 567, 352, 8, 37, "Input",ExpressionUUID->"f2f5ba62-220f-496e-8b7d-d0c03a5f39dc"], Cell[19994, 577, 949, 27, 90, "Input",ExpressionUUID->"5f0ded68-28f6-4e38-9c01-bcf2551507bc"], Cell[CellGroupData[{ Cell[20968, 608, 226, 5, 37, "Input",ExpressionUUID->"d4d8c334-1587-46aa-8b10-54f03a08c21b"], Cell[21197, 615, 202, 4, 42, "Output",ExpressionUUID->"e5e440cf-eebe-436f-89c0-20875eb985e2"] }, Open ]], Cell[CellGroupData[{ Cell[21436, 624, 1259, 41, 116, "Input",ExpressionUUID->"8e5aeec8-5ae0-44d3-8343-c18b7af10eb0"], Cell[22698, 667, 465, 10, 29, "Message",ExpressionUUID->"c3d2e042-037d-4ad1-b470-21e3cd78a4f8"], Cell[23166, 679, 465, 10, 29, "Message",ExpressionUUID->"f19e745b-bf00-4c1c-b6a4-3e06362f6ca8"], Cell[23634, 691, 443, 10, 29, "Message",ExpressionUUID->"e4a1a9e6-2ce2-41fa-b641-666af61a076b"], Cell[24080, 703, 443, 10, 29, "Message",ExpressionUUID->"54910a6f-7eaa-4e6a-906f-91ab68ddf9b1"] }, Open ]], Cell[CellGroupData[{ Cell[24560, 718, 885, 27, 64, "Input",ExpressionUUID->"73d91965-9918-47db-a421-3f38b9c39309"], Cell[25448, 747, 446, 10, 47, "Message",ExpressionUUID->"5310bf2a-7815-4865-aff5-057eee15df27"], Cell[25897, 759, 696, 13, 29, "Message",ExpressionUUID->"05e91c7d-1da6-422b-a17e-f0414c7f6544"], Cell[26596, 774, 171, 4, 42, "Output",ExpressionUUID->"bf13e0e0-cacf-4bd3-945c-e3b8fcdd1cb5"] }, Open ]] } ] *)