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+149,13 @@ Fall 3: Wrg und Geschwindigkeit $m dot s^'' eq F_1(s, s^') plus F_2(s, s^') plus [Induktivität], [ #zap.circuit({ import zap: * - capacitor("c1", (0, 0), (3, 0)) + inductor("i2", (0, 0), (3, 0), variant: "ieee") }) ], [$U_L eq L dot I^'$], [Kapazität], [ #zap.circuit({ import zap: * - inductor("i2", (0, 0), (3, 0), variant: "ieee") + capacitor("c1", (0, 0), (3, 0)) }) ], [$U_C eq frac(Q, C)$ mit $I eq Q^'$], ) @@ -208,7 +208,7 @@ $ D eq b^2 minus 4 dot a dot c $ $ C_2 eq v_0 minus lambda dot y_0 $ ], -[Fall 2 $D < 0$], [ +[Fall 3 $D < 0$], [ $ underline(underline(lambda_(1, 2)))) eq frac(minus b plus.minus root(, D), 2 dot a) eq frac(minus b, 2 dot a) plus.minus i dot frac(root(, abs(D)), 2 dot abs(a)) eq @@ -230,3 +230,6 @@ $ D eq b^2 minus 4 dot a dot c $ ], ) +==== Schwingungen + +=== Fourir diff --git a/src/physik_3.typ b/src/physik_3.typ index 2d4c358..9b58ea6 100644 --- a/src/physik_3.typ +++ b/src/physik_3.typ @@ -1,5 +1,4 @@ #import "@preview/cetz:0.4.1" -#import "@preview/cetz-venn:0.1.4" == Physik 3 === Physik des Lichts @@ -9,7 +8,7 @@ ==== Temperatur ===== Temperatur-Skalen -#table(columns: (0.5fr, 1fr, 1fr, 1fr), +#table(columns: (0.4fr, 1fr, 1fr, 1fr), [], [Fahrenheit], [Celsius], [Kelvin], [Definition], [willkürlich], [willkürlich], ["Bewusst"], [Bestimmung], [0 ℉ kälteste bekannte Temperatur. \ 32 ℉ Gefrierpunkt von Wasser. \ 96 ℉ Körpertemperatur eines gesunden Menschen.], @@ -25,9 +24,9 @@ Umrechnungsformeln ===== Thermische Ausdehnung #table(columns: (0.7fr, 0.8fr, 1fr), stroke: (x: none), align: horizon, -[Länge], [#box(stroke: 1pt + red, inset: (x: 1em, y: 0.5em), [$Delta l eq alpha dot l_(alpha) dot Delta T$])], [], -[Fläche], [#box(stroke: 1pt + red, inset: (x: 1em, y: 0.5em), [$Delta A eq beta dot A_0 dot Delta T$])], [$beta approx 2 dot alpha$], -[Volumen], [#box(stroke: 1pt + red, inset: (x: 1em, y: 0.5em), [$Delta V eq gamma dot V_0 dot Delta T$])], [$gamma approx 3 dot alpha$], +[Länge], [#box(width: 110pt, stroke: 1pt + red, inset: (x: 1em, y: 0.5em), [$Delta l eq alpha dot l_(alpha) dot Delta T$])], [], +[Fläche], [#box(width: 110pt, stroke: 1pt + red, inset: (x: 1em, y: 0.5em), [$Delta A eq beta dot A_0 dot Delta T$])], [$beta approx 2 dot alpha$], +[Volumen], [#box(width: 110pt, stroke: 1pt + red, inset: (x: 1em, y: 0.5em), [$Delta V eq gamma dot V_0 dot Delta T$])], [$gamma approx 3 dot alpha$], ) Volumenausdenung: #table(columns: (1fr, 1fr), @@ -39,12 +38,42 @@ Volumenausdenung: isotherme -> die Temperatur bleibt während des Prozesses immer konstant ==== Wärme-Energie - ===== Phasendiagramme +#image("../img/physik3/phasendiagramm.png") + +#grid(columns: (1fr, 1fr), gutter: 10pt, +[Phasendiagramm von Kohlendioxid $"CO"_2$.],[Phasendiagramm von Wasser $H_2O$.], +[#image("../img/physik3/phasendiagramm_CO2.png")],[#image("../img/physik3/phasendiagramm_H2O.png")], +[Unter Normaldruck existiert keine flüssige Phase. Festes CO2 kann also nicht +schmelzen sondern nur sublimieren, weshalb es Trockeneis genannt wird.], [Bei Temperaturen in der Nähe des Tripelpunktes kann festes Wasser durch Erhöhung des Druckes in flüssiges Wasser überführt werden. Zudem hat Eis eine geringere Dichte als flüssiges Wasser. Dieses Verhalten ist eine Ausnahme und wird als Anomalie des Wassers bezeichnet.], +) ===== Wärmekapazität +#cetz.canvas({ + import cetz.draw: * + line((-3, 0), (0.8, 0), mark: (end: ">"), fill: black) + circle((2, 0), radius: 1) + content((-1.1, 0.3), [Heizen]) + content((-1.1, -0.4), [$Delta Q eq.triple "Energiezufuhr"$]) + content((2, 0), [Objekt]) + content((3.5, 0), anchor: "west", [ + $T eq.triple$ Temperatur \ + $m eq.triple$ Masse \ + $N eq.triple$ Teilchenzahl \ + $n :eq frac(N,N_A) eq.triple$ Stoffmenge \ + ]) +}) + +#table(columns: (1fr, 1.5fr, 0.5fr), stroke: (x: none), align: horizon, +[Wärmekapazität:], [#box(width: 110pt, stroke: 1pt + white, inset: (x: 1em, y: 0.5em), [$c^* :eq frac(Delta Q, Delta T)$])], [$[c^*] eq frac(J,K)$], +[Spezifische Wärmekapazität:], [#box(width: 110pt, stroke: 1pt + white, inset: (x: 1em, y: 0.5em), [$c :eq frac(1, m) dot frac(Delta Q, Delta T)$])], [$[c] eq frac(J, "kg" dot K)$], +[Molare Wärmekapazität:], [#box(width: 110pt, stroke: 1pt + white, inset: (x: 1em, y: 0.5em), [$C :eq frac(1, n) dot frac(Delta Q, Delta T)$])], [$[C] eq frac(J, "mol" dot K)$], +[Wärme-Energie:], [#box(width: 250pt, stroke: 1pt + white, inset: (x: 1em, y: 0.5em), [$Delta Q eq c^* dot Delta T eq m dot c dot Delta T eq n dot C dot Delta T$])], [], +[Beziehungen:], [#box(width: 110pt, stroke: 1pt + white, inset: (x: 1em, y: 0.5em), [$c^* eq m dot c eq n dot C$])], [], +) ==== Latenz-Wärme +*Q-T-Diagramm* #cetz.canvas({ import cetz.draw: * line((-0.5, 0), (15, 0), mark: (end: ">"), fill: black) @@ -73,6 +102,87 @@ isotherme -> die Temperatur bleibt während des Prozesses immer konstant content((13.5, 0.5), [gas]) }) +Bezeichnungen bei Phasenübergang +#table(columns: (1fr, 0.5fr, 1fr), +[$Q_b$], [$J$], [Sublimationswärme], +[$Q_s$], [$J$], [Schmelzwärme], +[$Q_v$], [$J$], [Verdampfungswärme], +[$b :eq frac(1, m) dot Q_b$], [$frac(J, "kg")$], [spezifische Sublimationswärme], +[$s :eq frac(1, m) dot Q_s$], [$frac(J, "kg")$], [spezifische Schmelzwärme], +[$v :eq frac(1, m) dot Q_v$], [$frac(J, "kg")$], [spezifische Verdampfungswärme], +) + +==== Kalorimetrie +#cetz.canvas({ + import cetz.draw: * + // polygon((0,0), 7) + + hobby( + (0, 0.7), (1.4, 1.3), (0.7, 0.9), (1.0, 0.4), (0.2, -1), + close: true, + fill: gray, + stroke: 1pt + ) + + rect((4, 1.5), (8, -1.5), stroke: 0pt, fill: aqua) + bezier((4, 1.5), (8, 1.5), (5.5, 2.1), (6.5, 1.0), stroke: 0.7pt, fill: aqua) + line( + (4, 2), (4, -1.5), (8, -1.5), (8, 2), + stroke: gray.darken(60%) + 20pt, + ) + + content((10.5, 1.3), [Mischen]) + line((9, 1), (12, 1), mark: (end: ">"), fill: black) + + rect((13, 1.5), (17, -1.5), stroke: 0pt, fill: aqua) + bezier((13, 1.5), (17, 1.5), (14.5, 2.1), (15.5, 1.0), stroke: 0.7pt, fill: aqua) + line( + (13, 2), (13, -1.5), (17, -1.5), (17, 2), + stroke: gray.darken(60%) + 20pt, + ) + + hobby( + (14, 0.7), (15.4, 1.3), (14.7, 0.9), (15.0, 0.4), (14.2, -1), + close: true, + fill: gray, + stroke: 1pt + ) + + content((1, 2.5), [Objekt]) + content((1.8, 0), anchor: "west", [ + $m_"k"$ \ + $n_"k"$ \ + $T_"k"$ \ + $c_"k", C_"k"$ \ + ]) + + content((6, 2.5), [Wasser gefülltes Kalorimeter]) + content((4.8, 0), anchor: "west", [ + $m_"w"$ \ + $n_"w"$ \ + $T_"w"$ \ + $c_"w", C_"w"$ \ + ]) + + content((8.8, -1), anchor: "west", [#text(fill: orange)[ + Kalorimeter (Gehäuse) \ + $T_"kal" eq T_"w"$ \ + $c^* eq W_"kal"$ \ + $c^* eq "Wasserwert"$ \ + ]]) + line((8.7, -0.9), (8, -1.5), mark: (end: ">"), fill: orange, stroke: orange) + + content((15, 2.5), [$T_m :eq.triple "Mischtemperatur"$]) + content((16, 0.5), [$T_m$]) +}) + +*Energie-Erhaltung* +$ 0 &eq Delta Q_"zu" plus Delta Q_"ab" \ + 0 &eq Delta Q_"k" plus Delta Q_"w" plus Delta Q_"kal" \ + 0 &eq m_"k" dot c_"k" dot (T_"m" minus T_"k") plus m_"w" dot c_"w" dot (T_"m" minus T_"w") plus w_"kal" dot (T_"kal" minus T_"k") \ + 0 &eq n_"k" dot C_"k" dot (T_"m" minus T_"k") plus n_"w" dot C_"w" dot (T_"m" minus T_"w") plus w_"kal" dot (T_"kal" minus T_"k") $ + + ==== Ideale Gase ===== Makrozustand #cetz.canvas({ @@ -98,8 +208,37 @@ isotherme -> die Temperatur bleibt während des Prozesses immer konstant content((14.5, -2.5), [$approx m dot v$]) }) +#table(columns: (2fr, 1fr), +[$p eq.triple "Druck"$], [$["Pa"] arrow frac(N, m^2)$ (1 bar = 100'000Pa)], +[$V eq.triple "Volumen"$], [$[m^3]$], +[$T eq.triple "Temperatur"$], [$[K]$ (in Kelvin)], +[$N eq.triple "Teilchenzahl"$], [(Einheitslos)], +[$n :eq frac(N, N_A) eq.triple "Stoffmenge"$], [$["mol"]$ (in Mol)], +[$m eq.triple "Molekül-Masse"$], [[kg]], +[$v eq.triple "mittlere quadratische Molekül-Geschwindigkeit"$], [$[m^2/s^2]$ ], +[$c_"kin" eq.triple "mittlere kinetische Molekül-Energie"$], [[J] (Joule) oder [eV] (Elektronenvolt)], +) + +Thermische Zustandsgleichung des idealen Gases +$ p dot V eq n dot R dot T $ +$ p dot V eq N dot frac(R, N_A) dot T eq N dot k_B dot T $ +Bemerkungen: \ +R ist die universelle Gaskonstante \ +$R eq N_A dot k_B eq 8.314′462′618′153'24 frac(J, "mol" dot K)$ \ +$N_A$ Avogadro-Konstante: \ +$N_A eq 6.022 dot 10^23 frac(1,"mol")$ \ +$k_B eq frac(R, N_A)$ \ + ===== Universelle Gasgleichung +#align(center)[#box(width: 130pt, stroke: 1pt + red, inset: (x: 1em, y: 0.5em), [$ frac(p_0 dot V_0, T_0 dot n_0) eq frac(p_E dot V_E, T_E dot n_E) eq R $])] + ===== Allgemeine Gasgleichung +#align(center)[#box(width: 130pt, stroke: 1pt + red, inset: (x: 1em, y: 0.5em), [$ frac(p_0 dot V_0, T_0) eq frac(p_E dot V_E, T_E) $])] + +#table(columns: (1fr,)*3, align: horizon, +[Boyle-Mariotte-Gesetz], [Amonton-Gesetz ], [Charles-Gay-Lussa-Gesetz], +[$ p_0 dot V_0 eq p_E dot V_E $], [$ frac(p_0, T_0) eq frac(p_E, T_E) $], [$ frac(V_0, T_0) eq frac(V_E, T_E) $], +) ==== Kalorische Zustandsgleichung