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FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)como \ funci\[OAcute]n de\!\(\*\nStyleBox[\" \",\n\ FontSlant->\"Italic\"]\)\!\(\*SuperscriptBox[\n StyleBox[\"vT\",\nFontSlant->\ \"Italic\"], \n RowBox[{\"3\", \"/\", \"2\"}]]\) \n para \!\(\*\nStyleBox[\"n\ \",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\n\ FontSlant->\"Italic\"]\)= \!\(\*SuperscriptBox[\(10\), \(x\)]\) = ", ToString[ Round[10^$CellContext`x$$]]], 24], ImageSize -> 640, Background -> LightGray, ImageMargins -> 20, TicksStyle -> Directive[16, FontFamily -> "Arial"], AxesLabel -> { Style[ "\!\(TraditionalForm\`\(\(\\ \)\(v\\ \*SuperscriptBox[\(T\), \ \(3/2\)]\)\)\)", 24], None}], "Specifications" :> {{{$CellContext`x$$, 2}, 0, 4, Appearance -> "Open"}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{731., {288., 293.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({$CellContext`sol1[ Pattern[$CellContext`n, Blank[]], Pattern[$CellContext`a, Blank[]]] := (-2 - 3 $CellContext`n - 2 $CellContext`a $CellContext`n + Sqrt[4 + 4 $CellContext`n + 8 $CellContext`a $CellContext`n + $CellContext`n^2 - 4 $CellContext`a $CellContext`n^2 + 4 $CellContext`a^2 $CellContext`n^2])/( 2 (-1 - $CellContext`n - 2 $CellContext`a $CellContext`n)), $CellContext`sol2[ Pattern[$CellContext`n, Blank[]], Pattern[$CellContext`a, Blank[]]] := (2 + 3 $CellContext`n + 2 $CellContext`a $CellContext`n + Sqrt[4 + 4 $CellContext`n + 8 $CellContext`a $CellContext`n + $CellContext`n^2 - 4 $CellContext`a $CellContext`n^2 + 4 $CellContext`a^2 $CellContext`n^2])/( 2 (1 + $CellContext`n + 2 $CellContext`a $CellContext`n))}; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output"], Cell[TextData[{ "La soluci\[OAcute]n f\[IAcute]sica es la funci\[OAcute]n antes llamada \ sol1. Notar c\[OAcute]mo la soluci\[OAcute]n tiende a 1 de manera abrupta por \ debajo del valor cr\[IAcute]tico ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["a", "crit"], " ", "=", " ", RowBox[{"1", "/", "2"}]}], TraditionalForm]]], ". Cuanto mayor es ", Cell[BoxData[ FormBox["n", TraditionalForm]]], ", m\[AAcute]s marcada es la transici\[OAcute]n." }], "Text", FontSize->16], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"zeta", "[", RowBox[{"n_", ",", " ", "a_"}], "]"}], ":=", " ", RowBox[{"sol1", "[", RowBox[{"n", ",", " ", "a"}], "]"}]}], ";"}]], "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "La fracci\[OAcute]n de part\[IAcute]culas ", Cell[BoxData[ FormBox[ SubscriptBox["n", "0"], TraditionalForm]]], " en el nivel fundamental como funci\[OAcute]n de la temperatura para ", Cell[BoxData[ FormBox[ RowBox[{"v", " ", "=", " ", "1."}], TraditionalForm]]] }], "Section"], Cell[TextData[{ "La barra del gr\[AAcute]fico de abajo permite variar el n\[UAcute]mero de \ part\[IAcute]culas, escrito aqu\[IAcute] como ", Cell[BoxData[ FormBox[ SuperscriptBox["10", "x"], TraditionalForm]]], ". " }], "Text", FontSize->16], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"n0", "[", RowBox[{"z_", ",", " ", "n_"}], "]"}], ":=", RowBox[{ FractionBox["1", "n"], " ", FractionBox["z", RowBox[{"1", "-", "z"}]]}]}], ";"}]], "Input"], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`x$$ = 2, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`x$$], 2}, 0, 6}}, Typeset`size$$ = { 680., {251., 254.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`x$689$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`x$$ = 2}, "ControllerVariables" :> { Hold[$CellContext`x$$, $CellContext`x$689$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Plot[{ $CellContext`n0[ $CellContext`zeta[10^$CellContext`x$$, $CellContext`T^(3/2)], 10^$CellContext`x$$]}, {$CellContext`T, 0, 2}, PlotRange -> {0, 1}, PlotLabel -> Style[ StringJoin[ "\!\(\*SubscriptBox[\(n\), \(0\)]\) como funci\[OAcute]n de \!\(\*\n\ StyleBox[\"T\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\nFontSlant->\ \"Italic\"]\)\n para \!\(\*\nStyleBox[\"n\",\nFontSlant->\"Italic\"]\)\!\(\*\n\ StyleBox[\" \",\nFontSlant->\"Italic\"]\)= \!\(\*SuperscriptBox[\(10\), \ \(x\)]\) = ", ToString[ Round[10^$CellContext`x$$]]], 24], ImageSize -> 640, Background -> LightGray, TicksStyle -> Directive[16, FontFamily -> "Arial"], ImageMargins -> 20, TicksStyle -> Directive[16, FontFamily -> "Arial"], AxesLabel -> { Style["T", 24, Italic], None}], "Specifications" :> {{{$CellContext`x$$, 2}, 0, 6, Appearance -> "Open"}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{731., {310., 315.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({$CellContext`n0[ Pattern[$CellContext`z, Blank[]], Pattern[$CellContext`n, Blank[]]] := (1/$CellContext`n) ($CellContext`z/( 1 - $CellContext`z)), $CellContext`zeta[ Pattern[$CellContext`n, Blank[]], Pattern[$CellContext`a, Blank[]]] := $CellContext`sol1[$CellContext`n, $CellContext`a], \ $CellContext`sol1[ Pattern[$CellContext`n, Blank[]], Pattern[$CellContext`a, Blank[]]] := (-2 - 3 $CellContext`n - 2 $CellContext`a $CellContext`n + Sqrt[4 + 4 $CellContext`n + 8 $CellContext`a $CellContext`n + $CellContext`n^2 - 4 $CellContext`a $CellContext`n^2 + 4 $CellContext`a^2 $CellContext`n^2])/( 2 (-1 - $CellContext`n - 2 $CellContext`a $CellContext`n))}; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output"] }, Open ]], Cell[TextData[{ "Dado que el valor cr\[IAcute]tico de ", Cell[BoxData[ FormBox[ RowBox[{"a", " ", "=", " ", RowBox[{"v", " ", SuperscriptBox["T", RowBox[{"3", "/", "2"}]]}]}], TraditionalForm]]], " es 1/2, el valor cr\[IAcute]tico de la temperatura para ", Cell[BoxData[ FormBox[ RowBox[{"v", " ", "=", " ", "1"}], TraditionalForm]]], " es ", Cell[BoxData[ FormBox[ RowBox[{"T", " ", "=", " ", RowBox[{ RowBox[{"1", "/", SuperscriptBox["2", RowBox[{"2", "/", "3"}]]}], "=", " "}]}], TraditionalForm]]], "0.6299... Notar lo que ocurre con n0 al aumentar n." }], "Text", FontSize->16] }, Open ]], Cell[CellGroupData[{ Cell["\<\ La presi\[OAcute]n de las part\[IAcute]culas en el nivel fundamental, p0[z, \ T, n, v].\ \>", "Section"], Cell[TextData[{ "Se grafica ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["p", "0"], " ", "v"}], TraditionalForm]]], " para ", Cell[BoxData[ FormBox[ RowBox[{" ", RowBox[{"T", " ", "=", " ", "1."}]}], TraditionalForm]]], " En tal caso la variable independiente es el par\[AAcute]metro ", Cell[BoxData[ FormBox[ RowBox[{"a", " ", "=", " ", "v"}], TraditionalForm]]], ". Por comodidad, el n\[UAcute]mero de part\[IAcute]culas est\[AAcute] \ escrito como ", Cell[BoxData[ FormBox[ SuperscriptBox["10", "x"], TraditionalForm]]], "." }], "Text", FontSize->16], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`x$$ = 2, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`x$$], 2}, 0, 6}}, Typeset`size$$ = { 680., {236., 241.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`x$729$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`x$$ = 2}, "ControllerVariables" :> { Hold[$CellContext`x$$, $CellContext`x$729$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Plot[{$CellContext`a $CellContext`p0[ $CellContext`zeta[10^$CellContext`x$$, $CellContext`a], 1, 10^$CellContext`x$$, $CellContext`a]}, {$CellContext`a, 0, 3}, PlotRange -> All, PlotLabel -> Style[ StringJoin[ "\!\(\*\nStyleBox[SubscriptBox[\"p\", \"0\"],\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"v\",\nFontSlant->\"Italic\"]\)\!\(\ \*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)como funci\[OAcute]n de\!\(\*\n\ StyleBox[\" \",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"v\",\nFontSlant->\ \"Italic\"]\) \n para \!\(\*\nStyleBox[\"n\",\nFontSlant->\"Italic\"]\)\!\(\*\ \nStyleBox[\" \",\nFontSlant->\"Italic\"]\)= \!\(\*SuperscriptBox[\(10\), \ \(x\)]\) = ", ToString[ Round[10^$CellContext`x$$]]], 24], ImageSize -> 640, Background -> LightGray, TicksStyle -> Directive[16, FontFamily -> "Arial"], ImageMargins -> 20, TicksStyle -> Directive[16, FontFamily -> "Arial"], AxesLabel -> { Style["\!\(\*\nStyleBox[\"v\",\nFontSlant->\"Italic\"]\)", 24], None}], "Specifications" :> {{{$CellContext`x$$, 2}, 0, 6, Appearance -> "Open"}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{731., {296., 301.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({$CellContext`p0[ Pattern[$CellContext`z, Blank[]], Pattern[$CellContext`T, Blank[]], Pattern[$CellContext`n, Blank[]], Pattern[$CellContext`v, Blank[]]] := (-($CellContext`T/($CellContext`n $CellContext`v))) Log[1 - $CellContext`z], $CellContext`zeta[ Pattern[$CellContext`n, Blank[]], Pattern[$CellContext`a, Blank[]]] := $CellContext`sol1[$CellContext`n, $CellContext`a], \ $CellContext`sol1[ Pattern[$CellContext`n, Blank[]], Pattern[$CellContext`a, Blank[]]] := (-2 - 3 $CellContext`n - 2 $CellContext`a $CellContext`n + Sqrt[4 + 4 $CellContext`n + 8 $CellContext`a $CellContext`n + $CellContext`n^2 - 4 $CellContext`a $CellContext`n^2 + 4 $CellContext`a^2 $CellContext`n^2])/( 2 (-1 - $CellContext`n - 2 $CellContext`a $CellContext`n))}; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output"], Cell[TextData[{ "Notar como al aumentar ", Cell[BoxData[ FormBox["n", TraditionalForm]]], " el valor m\[AAcute]ximo de la presi\[OAcute]n de las part\[IAcute]culas en \ el nivel fundamental decrece fuertemente. (Prestar antenci\[OAcute]n a la \ escala vertical.) Adem\[AAcute]s, notar que se est\[AAcute] graficando ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["p", "0"], "v"}], TraditionalForm]]], ". Ustedes pueden graficar ", Cell[BoxData[ FormBox[ SubscriptBox["p", "0"], TraditionalForm]]], " por separado. Les va a convenir usar escala logar\[IAcute]tmica." }], "Text", FontSize->16] }, Open ]], Cell[CellGroupData[{ Cell["\<\ La presi\[OAcute]n total p[z, T, v, n] \ \>", "Section"], Cell[TextData[{ "Se grafican ", Cell[BoxData[ FormBox[ RowBox[{"p", " ", "v"}], TraditionalForm]]], " y ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["p", "0"], "v"}], TraditionalForm]]], " para ", Cell[BoxData[ FormBox[ RowBox[{" ", RowBox[{"T", " ", "=", " ", "1."}]}], TraditionalForm]]], " En tal caso, la variable independiente es el par\[AAcute]metro ", Cell[BoxData[ FormBox[ RowBox[{"a", " ", "=", " ", "v"}], TraditionalForm]]], ". El valor cr\[IAcute]tico del volumen por part\[IAcute]cula es 1/2." }], "Text", FontSize->16], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`x$$ = 1., Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`x$$], 1.}, 0, 6}}, Typeset`size$$ = { 680., {238., 243.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`x$770$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`x$$ = 1.}, "ControllerVariables" :> { Hold[$CellContext`x$$, $CellContext`x$770$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Plot[{$CellContext`a $CellContext`p[ $CellContext`zeta[10^$CellContext`x$$, $CellContext`a], 1, 10^$CellContext`x$$, $CellContext`a], $CellContext`a \ $CellContext`p0[ $CellContext`zeta[10^$CellContext`x$$, $CellContext`a], 1, 10^$CellContext`x$$, $CellContext`a]}, {$CellContext`a, 0.01, 3}, PlotRange -> All, PlotLabel -> Style[ StringJoin[ "\!\(\*\nStyleBox[SubscriptBox[\"vp\", \"total\"],\n\ FontSlant->\"Italic\"]\) y \!\(\*\nStyleBox[SubscriptBox[\"vp\", \"0\"],\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\n\ FontSlant->\"Italic\"]\)como funciones de\!\(\*\nStyleBox[\" \",\nFontSlant->\ \"Italic\"]\)\!\(\*\nStyleBox[\"v\",\nFontSlant->\"Italic\"]\)\n\!\(\*\n\ StyleBox[\" \",\nFontSlant->\"Italic\"]\)para \!\(\*\nStyleBox[\"n\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)\!\(\ \*\nStyleBox[\"=\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\n\ FontSlant->\"Italic\"]\)\!\(\*SuperscriptBox[\(10\), \(x\)]\) =", ToString[ Round[10^$CellContext`x$$]]], 24], ImageSize -> 640, Background -> LightGray, TicksStyle -> Directive[16, FontFamily -> "Arial"], ImageMargins -> 20, TicksStyle -> Directive[16, FontFamily -> "Arial"], AxesLabel -> { Style["\!\(\*\nStyleBox[\"v\",\nFontSlant->\"Italic\"]\)", 24], None}], "Specifications" :> {{{$CellContext`x$$, 1.}, 0, 6, Appearance -> "Open"}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{731., {298., 303.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({$CellContext`p[ Pattern[$CellContext`z, Blank[]], Pattern[$CellContext`T, Blank[]], Pattern[$CellContext`n, Blank[]], Pattern[$CellContext`v, Blank[]]] := (-($CellContext`T/($CellContext`n $CellContext`v))) Log[1 - $CellContext`z] + 2 $CellContext`T^(5/2) Log[2/(2 - $CellContext`z)], $CellContext`zeta[ Pattern[$CellContext`n, Blank[]], Pattern[$CellContext`a, Blank[]]] := $CellContext`sol1[$CellContext`n, $CellContext`a], \ $CellContext`sol1[ Pattern[$CellContext`n, Blank[]], Pattern[$CellContext`a, Blank[]]] := (-2 - 3 $CellContext`n - 2 $CellContext`a $CellContext`n + Sqrt[4 + 4 $CellContext`n + 8 $CellContext`a $CellContext`n + $CellContext`n^2 - 4 $CellContext`a $CellContext`n^2 + 4 $CellContext`a^2 $CellContext`n^2])/( 2 (-1 - $CellContext`n - 2 $CellContext`a $CellContext`n)), $CellContext`p0[ Pattern[$CellContext`z, Blank[]], Pattern[$CellContext`T, Blank[]], Pattern[$CellContext`n, Blank[]], Pattern[$CellContext`v, Blank[]]] := (-($CellContext`T/($CellContext`n $CellContext`v))) Log[1 - $CellContext`z]}; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output"], Cell[TextData[{ "Notar que a medida que crece ", StyleBox["n", FontSlant->"Italic"], ", el cambio en la derivada de la presi\[OAcute]n cerca del valor \ cr\[IAcute]tico del volumen se hace cada vez m\[AAcute]s abrupto. Abajo se \ grafica la derivada de ", Cell[BoxData[ FormBox[ RowBox[{"p", " ", "v"}], TraditionalForm]]], " respecto de ", Cell[BoxData[ FormBox["v", TraditionalForm]]], "." }], "Text", FontSize->16], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"derivada", "[", RowBox[{"x_", ",", " ", "a_"}], "]"}], ":=", " ", RowBox[{"Evaluate", "[", RowBox[{"D", "[", RowBox[{ RowBox[{"a", " ", RowBox[{"p", "[", RowBox[{ RowBox[{"zeta", "[", RowBox[{ SuperscriptBox["10", "x"], ",", " ", "a"}], "]"}], ",", "1", ",", " ", SuperscriptBox["10", "x"], ",", " ", "a"}], "]"}]}], ",", "a"}], "]"}], "]"}]}]], "Input"], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`x$$ = 2, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`x$$], 2}, 0, 6}}, Typeset`size$$ = { 680., {236., 241.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`x$810$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`x$$ = 2}, "ControllerVariables" :> { Hold[$CellContext`x$$, $CellContext`x$810$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Plot[ $CellContext`derivada[$CellContext`x$$, $CellContext`a], \ {$CellContext`a, 0, 3}, PlotRange -> All, PlotLabel -> Style[ StringJoin[ "\!\(\*FractionBox[\n StyleBox[\"dpv\",\nFontSlant->\"Italic\"], \n \ StyleBox[\"dv\",\nFontSlant->\"Italic\"]]\)\!\(\*\nStyleBox[\" \",\n\ FontSlant->\"Italic\"]\)para \!\(\*\nStyleBox[\"n\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)\!\(\ \*\nStyleBox[\"=\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\n\ FontSlant->\"Italic\"]\)\!\(\*SuperscriptBox[\(10\), \(x\)]\) =", ToString[ Round[10^$CellContext`x$$]]], 24], ImageSize -> 640, Background -> LightGray, TicksStyle -> Directive[16, FontFamily -> "Arial"], ImageMargins -> 20, TicksStyle -> Directive[16, FontFamily -> "Arial"], AxesLabel -> { Style["\!\(\*\nStyleBox[\"v\",\nFontSlant->\"Italic\"]\)", 24], None}], "Specifications" :> {{{$CellContext`x$$, 2}, 0, 6, Appearance -> "Open"}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{731., {296., 301.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({$CellContext`derivada[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`a, Blank[]]] := -( Log[1 - 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10^$CellContext`x - 2^(1 + $CellContext`x) 5^$CellContext`x $CellContext`a)))]}; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output"] }, Open ]], Cell[TextData[{ "Esto est\[AAcute] relacionado con la compresibilidad. No es directamente el \ inverso de la compresibilidad porque se calcula la derivada de ", Cell[BoxData[ FormBox[ RowBox[{"p", " ", "v"}], TraditionalForm]]], " respecto de ", Cell[BoxData[ FormBox["v", TraditionalForm]]], ". Piensen que en el caso de un gas ideal cl\[AAcute]sico, eso da cero, y es \ lo que se ve en el gr\[AAcute]fico de arriba para valores grandes de ", Cell[BoxData[ FormBox["v", TraditionalForm]]], " donde todas las cosas tienden a ser cl\[AAcute]sicas." }], "Text", FontSize->16] }, Open ]], Cell[CellGroupData[{ Cell["\<\ La energ\[IAcute]a por part\[IAcute]cula u[z, T, v].\ \>", "Section"], Cell[TextData[{ "Se grafica como funci\[OAcute]n de la temperatura para ", Cell[BoxData[ FormBox[ RowBox[{"v", " ", "=", " ", "1"}], TraditionalForm]]], ". La barra permite variar el n\[UAcute]mero de part\[IAcute]culas, definido \ como ", Cell[BoxData[ FormBox[ SuperscriptBox["10", "x"], TraditionalForm]]], ". Ustedes pueden encontrar f\[AAcute]cilmente el comportamiento para ", StyleBox["T", FontSlant->"Italic"], " grandes." }], "Text", FontSize->16], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`x$$ = 2, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`x$$], 2}, 0, 8}}, Typeset`size$$ = { 680., {223., 227.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`x$850$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`x$$ = 2}, "ControllerVariables" :> { Hold[$CellContext`x$$, $CellContext`x$850$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Plot[{ $CellContext`u[ $CellContext`zeta[ 10^$CellContext`x$$, $CellContext`a], $CellContext`a^(2/3), 1]}, {$CellContext`a, 0, 2}, PlotRange -> All, PlotLabel -> Style[ StringJoin[ "\!\(\*\nStyleBox[\"u\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\ \"(\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"T\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\")\",\nFontSlant->\"Italic\"]\)\!\(\ \*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)para \!\(\*\nStyleBox[\"n\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)\!\(\ \*\nStyleBox[\"=\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\n\ FontSlant->\"Italic\"]\)\!\(\*SuperscriptBox[\(10\), \(x\)]\) =", ToString[ Round[10^$CellContext`x$$]]], 24], ImageSize -> 640, Background -> LightGray, TicksStyle -> Directive[16, FontFamily -> "Arial"], ImageMargins -> 20, TicksStyle -> Directive[16, FontFamily -> "Arial"], AxesLabel -> { Style["\!\(\*\nStyleBox[\"T\",\nFontSlant->\"Italic\"]\)", 24], None}], "Specifications" :> {{{$CellContext`x$$, 2}, 0, 8, Appearance -> "Open"}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{731., {282., 287.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({$CellContext`u[ Pattern[$CellContext`z, Blank[]], Pattern[$CellContext`T, Blank[]], Pattern[$CellContext`v, Blank[]]] := 3 $CellContext`v $CellContext`T^(5/2) Log[2/(2 - $CellContext`z)], $CellContext`zeta[ Pattern[$CellContext`n, Blank[]], Pattern[$CellContext`a, Blank[]]] := $CellContext`sol1[$CellContext`n, $CellContext`a], \ $CellContext`sol1[ Pattern[$CellContext`n, Blank[]], Pattern[$CellContext`a, Blank[]]] := (-2 - 3 $CellContext`n - 2 $CellContext`a $CellContext`n + Sqrt[4 + 4 $CellContext`n + 8 $CellContext`a $CellContext`n + $CellContext`n^2 - 4 $CellContext`a $CellContext`n^2 + 4 $CellContext`a^2 $CellContext`n^2])/( 2 (-1 - $CellContext`n - 2 $CellContext`a $CellContext`n))}; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output"], Cell[TextData[{ "Notar que al aumentar ", StyleBox["n", FontSlant->"Italic"], ", el cambio en la derivada de u respecto de la temperatura se hace cada vez \ m\[AAcute]s marcado. Esa derivada es el calor espec\[IAcute]fico, que en el l\ \[IAcute]mite en que ", Cell[BoxData[ FormBox[ RowBox[{"n", "\[Rule]", " ", "\[Infinity]"}], TraditionalForm]]], " tiene una discontinuidad." }], "Text", FontSize->16] }, Open ]], Cell[CellGroupData[{ Cell["El calor espec\[IAcute]fico", "Section"], Cell[TextData[{ "El gr\[AAcute]fico muestra el calor espec\[IAcute]fico como funci\[OAcute]n \ de ", Cell[BoxData[ FormBox["T", TraditionalForm]]], " para ", Cell[BoxData[ FormBox[ RowBox[{"v", " ", "=", " ", "1."}], TraditionalForm]]] }], "Text", FontSize->16], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"cv", "[", RowBox[{"x_", ",", " ", "T_", ",", " ", "v_"}], "]"}], ":=", " ", RowBox[{"Evaluate", "[", RowBox[{"D", "[", RowBox[{ RowBox[{"u", "[", RowBox[{ RowBox[{"zeta", "[", RowBox[{"x", ",", " ", RowBox[{"v", " ", SuperscriptBox["T", RowBox[{"3", "/", "2"}]]}]}], "]"}], ",", " ", "T", ",", " ", "v"}], "]"}], ",", " ", "T"}], "]"}], "]"}]}], ";"}]], "Input"], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`x$$ = 2, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`x$$], 2}, 0, 8}}, Typeset`size$$ = { 680., {240., 245.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`x$891$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`x$$ = 2}, "ControllerVariables" :> { Hold[$CellContext`x$$, $CellContext`x$891$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Plot[{ $CellContext`cv[ 10^$CellContext`x$$, $CellContext`T, 1]}, {$CellContext`T, 0, 1.5}, PlotRange -> All, PlotLabel -> Style[ StringJoin[ "el calor espec\[IAcute]fico para \!\(\*\nStyleBox[\"v\",\n\ FontSlant->\"Italic\"]\) y \!\(\*\nStyleBox[\"n\",\n\ FontSlant->\"Italic\"]\) constante\!\(\*\nStyleBox[\" \",\n\ FontSlant->\"Italic\"]\)\n\!\(\*\nStyleBox[\" \",\n\ FontSlant->\"Italic\"]\)con \!\(\*\nStyleBox[\"n\",\nFontSlant->\"Italic\"]\)\ \!\(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"=\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)\!\(\ \*SuperscriptBox[\(10\), \(x\)]\) =", ToString[ Round[10^$CellContext`x$$]]], 24], ImageSize -> 640, Background -> LightGray, TicksStyle -> Directive[16, FontFamily -> "Arial"], ImageMargins -> 20, TicksStyle -> Directive[16, FontFamily -> "Arial"], AxesLabel -> { Style["\!\(\*\nStyleBox[\"T\",\nFontSlant->\"Italic\"]\)", 24], None}], "Specifications" :> {{{$CellContext`x$$, 2}, 0, 8, Appearance -> "Open"}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{731., {300., 305.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({$CellContext`cv[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`T, Blank[]], Pattern[$CellContext`v, Blank[]]] := ((-3) $CellContext`T^(5/ 2) $CellContext`v (-((-3) Sqrt[$CellContext`T] $CellContext`v $CellContext`x + ( 12 Sqrt[$CellContext`T] $CellContext`v $CellContext`x - 6 Sqrt[$CellContext`T] $CellContext`v $CellContext`x^2 + 12 $CellContext`T^2 $CellContext`v^2 $CellContext`x^2)/(2 Sqrt[4 + 4 $CellContext`x + 8 $CellContext`T^(3/ 2) $CellContext`v $CellContext`x + $CellContext`x^2 - 4 $CellContext`T^(3/2) $CellContext`v $CellContext`x^2 + 4 $CellContext`T^3 $CellContext`v^2 $CellContext`x^2]))/( 2 (-1 - $CellContext`x - 2 $CellContext`T^(3/2) $CellContext`v $CellContext`x)) - (3 Sqrt[$CellContext`T] $CellContext`v $CellContext`x (-2 - 3 $CellContext`x - 2 $CellContext`T^(3/2) $CellContext`v $CellContext`x + Sqrt[4 + 4 $CellContext`x + 8 $CellContext`T^(3/ 2) $CellContext`v $CellContext`x + $CellContext`x^2 - 4 $CellContext`T^(3/2) $CellContext`v $CellContext`x^2 + 4 $CellContext`T^3 $CellContext`v^2 $CellContext`x^2]))/( 2 (-1 - $CellContext`x - 2 $CellContext`T^(3/2) $CellContext`v $CellContext`x)^2)))/( 2 - (-2 - 3 $CellContext`x - 2 $CellContext`T^(3/2) $CellContext`v $CellContext`x + Sqrt[4 + 4 $CellContext`x + 8 $CellContext`T^(3/ 2) $CellContext`v $CellContext`x + $CellContext`x^2 - 4 $CellContext`T^(3/2) $CellContext`v $CellContext`x^2 + 4 $CellContext`T^3 $CellContext`v^2 $CellContext`x^2])/( 2 (-1 - $CellContext`x - 2 $CellContext`T^(3/2) $CellContext`v $CellContext`x))) + ( 15 $CellContext`T^(3/2) $CellContext`v Log[2/(2 - (-2 - 3 $CellContext`x - 2 $CellContext`T^(3/2) $CellContext`v $CellContext`x + Sqrt[4 + 4 $CellContext`x + 8 $CellContext`T^(3/ 2) $CellContext`v $CellContext`x + $CellContext`x^2 - 4 $CellContext`T^(3/2) $CellContext`v $CellContext`x^2 + 4 $CellContext`T^3 $CellContext`v^2 $CellContext`x^2])/( 2 (-1 - $CellContext`x - 2 $CellContext`T^(3/2) $CellContext`v $CellContext`x)))])/2}; 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