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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]], FormatType->"TraditionalForm"], ". 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Notar lo que ocurre con n0 al aumentar n." }], "Text", CellChangeTimes->{{3.6112411412298*^9, 3.6112413004846*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["\<\ La presi\[OAcute]n de las part\[IAcute]culas en el nivel fundamental, p0[z, \ T, n, v].\ \>", "Section", CellChangeTimes->{{3.6112413217806*^9, 3.6112413292966003`*^9}, 3.6112415026921997`*^9, {3.6112415732414*^9, 3.6112415830854*^9}}], 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", "n"], TraditionalForm]]], "." }], "Text", CellChangeTimes->{{3.6112415073852*^9, 3.6112415553304*^9}, { 3.611242148139*^9, 3.6112421614432*^9}, {3.622833845822*^9, 3.62283384937*^9}, {3.6228351830018*^9, 3.6228351846338*^9}}], Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{"a", " ", RowBox[{"p0", "[", RowBox[{ RowBox[{"zeta", "[", RowBox[{ SuperscriptBox["10", "n"], ",", " ", "a"}], "]"}], ",", "1", ",", " ", SuperscriptBox["10", "n"], ",", " ", "a"}], "]"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"a", ",", " ", "0", ",", " ", "3"}], "}"}], ",", " ", RowBox[{"PlotRange", "\[Rule]", " ", "All"}], ",", " ", RowBox[{"PlotLabel", "\[Rule]", " ", RowBox[{"Style", "[", RowBox[{"\"\<\!\(\* StyleBox[SubscriptBox[\"p\", \"0\"], FontSlant->\"Italic\"]\)\!\(\* StyleBox[\"v\", FontSlant->\"Italic\"]\)\>\"", ",", " ", "20"}], "]"}]}], ",", " ", RowBox[{"Background", "\[Rule]", "LightGray"}], ",", RowBox[{"AxesLabel", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"Style", "[", RowBox[{"\"\<\!\(\* StyleBox[\"v\", FontSlant->\"Italic\"]\)\>\"", ",", " ", "20"}], "]"}], ",", " ", "None"}], "}"}]}]}], "]"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n", ",", "2"}], "}"}], ",", " ", "0", ",", " ", "6", ",", " ", RowBox[{"Appearance", "\[Rule]", " ", "\"\\""}]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.6109790161698*^9, 3.6109790162946*^9}, { 3.6109791676442003`*^9, 3.6109791977911997`*^9}, {3.6109792446828003`*^9, 3.6109792449217997`*^9}, {3.6112414001415997`*^9, 3.6112414006986*^9}, 3.6112416038254004`*^9, {3.6112430822236*^9, 3.6112430823736*^9}, { 3.6228332882466*^9, 3.6228333116736*^9}, {3.62283381362*^9, 3.6228338294904003`*^9}, {3.6228341568136*^9, 3.6228341570408*^9}, { 3.6228342919494*^9, 3.6228342957214003`*^9}}], 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]], FormatType->"TraditionalForm"], ". Ustedes pueden graficar ", Cell[BoxData[ FormBox[ SubscriptBox["p", "0"], TraditionalForm]], FormatType->"TraditionalForm"], " por separado. Les va a convenir usar escala logar\[IAcute]tmica." }], "Text", CellChangeTimes->{{3.6112416327494*^9, 3.6112416693733997`*^9}, { 3.6228333388212*^9, 3.6228333444622*^9}, {3.6228342614898*^9, 3.6228343585774*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["\<\ La presi\[OAcute]n total p[z, T, v, n] \ \>", "Section", CellChangeTimes->{{3.6112416907684*^9, 3.611241716755*^9}}], Cell[TextData[{ "Se grafica ", Cell[BoxData[ FormBox[ RowBox[{"p", " ", "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. Por \ comparaci\[OAcute]n tambi\[EAcute]n se muestra la presi\[OAcute]n del \ fundamental. 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Abajo se grafica la derivada de ", Cell[BoxData[ FormBox[ RowBox[{"p", " ", "v"}], TraditionalForm]], FormatType->"TraditionalForm"], " respecto de ", Cell[BoxData[ FormBox["v", TraditionalForm]], FormatType->"TraditionalForm"], "." }], "Text", CellChangeTimes->{{3.611241757615*^9, 3.6112418136806*^9}, { 3.6112428232262*^9, 3.6112428288732*^9}, {3.6228338794258003`*^9, 3.6228339087390003`*^9}, {3.6228343681616*^9, 3.6228345331274*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"derivada", "[", RowBox[{"n_", ",", " ", "a_"}], "]"}], ":=", " ", RowBox[{"Evaluate", "[", RowBox[{"D", "[", RowBox[{ RowBox[{"a", " ", RowBox[{"p", "[", RowBox[{ RowBox[{"zeta", "[", RowBox[{ SuperscriptBox["10", "n"], ",", " ", "a"}], "]"}], ",", "1", ",", " ", SuperscriptBox["10", "n"], ",", " ", "a"}], "]"}]}], ",", "a"}], "]"}], "]"}]}]], "Input", CellChangeTimes->{{3.6112419563887997`*^9, 3.6112420105564003`*^9}}], Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{"derivada", "[", RowBox[{"n", ",", " ", "a"}], "]"}], ",", " ", RowBox[{"{", RowBox[{"a", ",", " ", "0", ",", " ", "3"}], "}"}], ",", " ", RowBox[{"PlotRange", "\[Rule]", " ", "All"}], ",", " ", RowBox[{"PlotLabel", "\[Rule]", " ", RowBox[{"Style", "[", RowBox[{"\"\<\!\(\*FractionBox[ RowBox[{ StyleBox[ RowBox[{\"d\", StyleBox[\"pv\", FontSlant->\"Italic\"]}]], StyleBox[\" \", FontSlant->\"Italic\"]}], StyleBox[ RowBox[{\"d\", StyleBox[\"v\", FontSlant->\"Italic\"]}]]]\)\>\"", ",", " ", "20"}], "]"}]}], ",", " ", RowBox[{"Background", "\[Rule]", "LightGray"}], ",", RowBox[{"AxesLabel", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"Style", "[", RowBox[{"\"\<\!\(\* StyleBox[\"v\", FontSlant->\"Italic\"]\)\>\"", ",", " ", "20"}], "]"}], ",", " ", "None"}], "}"}]}]}], "]"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n", ",", " ", "2"}], "}"}], ",", " ", "0", ",", " ", "6", ",", " ", RowBox[{"Appearance", "\[Rule]", " ", "\"\\""}]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{ 3.6109792823866*^9, {3.6109793283668003`*^9, 3.6109793288972*^9}, { 3.6112414041566*^9, 3.6112414047785997`*^9}, {3.611241746198*^9, 3.6112417499960003`*^9}, {3.6112418369035997`*^9, 3.6112419470758*^9}, { 3.6112420258873997`*^9, 3.6112420487674*^9}, {3.6112433319406*^9, 3.6112433320936003`*^9}, {3.6228335019484*^9, 3.6228335162106*^9}, { 3.6228335646654*^9, 3.6228335664336*^9}, {3.6228345757648*^9, 3.6228346064245996`*^9}, {3.6228346873394003`*^9, 3.6228346875594*^9}, 3.6228352660123997`*^9}], 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]], FormatType->"TraditionalForm"], " respecto de ", Cell[BoxData[ FormBox["v", TraditionalForm]], FormatType->"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]], FormatType->"TraditionalForm"], " donde todas las cosas tienden a ser cl\[AAcute]sicas." }], "Text", CellChangeTimes->{{3.6228345452518*^9, 3.6228345557408*^9}, { 3.622834618076*^9, 3.6228346412525997`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["\<\ La energ\[IAcute]a por part\[IAcute]cula u[z, T, v].\ \>", "Section", CellChangeTimes->{{3.6112420601344*^9, 3.6112420893894*^9}}], Cell[TextData[{ "Se grafica como funci\[OAcute]n de la temperatura para ", Cell[BoxData[ FormBox[ RowBox[{"v", " ", "=", " ", "1"}], TraditionalForm]], FormatType->"TraditionalForm"], ". La barra permite variar el n\[UAcute]mero de part\[IAcute]culas, definido \ como ", Cell[BoxData[ FormBox[ SuperscriptBox["10", "n"], TraditionalForm]], FormatType->"TraditionalForm"] }], "Text", CellChangeTimes->{{3.6112420916684*^9, 3.6112421306464*^9}}], Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", " ", RowBox[{"u", "[", RowBox[{ RowBox[{"zeta", "[", RowBox[{ SuperscriptBox["10", "n"], ",", " ", "a"}], "]"}], ",", SuperscriptBox["a", RowBox[{"2", "/", "3"}]], ",", " ", "1"}], "]"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"a", ",", " ", "0", ",", " ", ".8"}], "}"}], ",", " ", RowBox[{"PlotRange", "\[Rule]", " ", "All"}], ",", RowBox[{"PlotLabel", "\[Rule]", " ", RowBox[{"Style", "[", RowBox[{"\"\\"", ",", " ", "20"}], "]"}]}], ",", " ", RowBox[{"Background", "\[Rule]", "LightGray"}], ",", RowBox[{"AxesLabel", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"Style", "[", RowBox[{"\"\<\!\(\* StyleBox[\"T\", FontSlant->\"Italic\"]\)\>\"", ",", " ", "20"}], "]"}], ",", " ", "None"}], "}"}]}]}], "]"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n", ",", " ", "2"}], "}"}], ",", " ", "0", ",", " ", "8", ",", " ", RowBox[{"Appearance", "\[Rule]", " ", "\"\\""}]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.6109820414776*^9, 3.6109820933732*^9}, { 3.6112414074566*^9, 3.6112414080716*^9}, {3.611242168451*^9, 3.6112421962251997`*^9}, {3.6112433461015997`*^9, 3.6112433504116*^9}, { 3.6228346638176003`*^9, 3.6228346986717997`*^9}, {3.6228347573904*^9, 3.6228348557328*^9}, {3.623251067281*^9, 3.623251070256*^9}}], Cell[TextData[{ "Notar que al aumentar n, 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]], FormatType->"TraditionalForm"], " tiene una discontinuidad." }], "Text", CellChangeTimes->{{3.6112422068712*^9, 3.6112422759172*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["El calor espec\[IAcute]fico", "Section", CellChangeTimes->{{3.6112422797272*^9, 3.6112422844712*^9}}], Cell[TextData[{ "El gr\[AAcute]fico muestra el calor espec\[IAcute]fico como funci\[OAcute]n \ de ", Cell[BoxData[ FormBox["T", TraditionalForm]], FormatType->"TraditionalForm"], " para ", Cell[BoxData[ FormBox[ RowBox[{"v", " ", "=", " ", "1."}], TraditionalForm]], FormatType->"TraditionalForm"] }], "Text", CellChangeTimes->{{3.6112425244611998`*^9, 3.6112425455692*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"cv", "[", RowBox[{"n_", ",", " ", "T_", ",", " ", "v_"}], "]"}], ":=", " ", RowBox[{"Evaluate", "[", RowBox[{"D", "[", RowBox[{ 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