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Worksheet E02: The perfect gas equation of state

Goals

This worksheet examines the perfect gas equations of state, pV = nRT, and its applications. For Extensions, see Worksheet E03 on real gases.

Calculation

the gas constant

set the amount of substance (mol)

set the preasure (Pa)

set the volume (m3)

set the temperature (K)

1. Boyle's law

The pressure of a perfect gas is

 9303.8919 Pa *

P(Pa) vs. V(m3)

 x P

This graph corresponds to Fig. P7:1.5.

P(Pa) vs. 1/V(1/m3)

 x P1

This graph corresponds to Fig. P7:1.6.

Exploration E02.1 :Explore how the pressure of 1.5 mol CO2(g) varies with volume as it is compressed at (a) 273 K, (b) 373 K from 30 L to 15 L.

2. Charles's law

0.0927 m 3 ^ *

The volume as a function of temperature is

V(m3) vs. T(K)

 x V

This graph corresponds to Fig. P7:1.7.

The pressure as a function of temperature is similarly

P(Pa) vs. T(K)

 x P2

This graph corresponds to Fig. P7:1.8.

Exploration E02.2: Explore how the pressure of 1.5 mol CO2(g) in a container of volume (a) 30 L, (b) 15 L varies with temperature as it is cooled from 373 K to 273 K.

3. The surface of state

The equation of state defines the following surface, in the sense that the only permissible states of a perfect gas correspond to points on the surface. The isotherms, isobars, and isochores drawn above are slices through this surface. You can rotate the surface by dragging with your mouse. To set up the graph, we need to confine P and V to integer steps, so the following definitions redefine p and t.

 <p fontName="Arial">Draw-Descriptions (Maxima)</p> <p fontName="Arial">Draw-Descriptions (Maxima)</p>

Optionen

Options

[Maxima Draw] adapt_depth (=10): maximale Teilungstiefe der adaptive Kurvenabtastung

[Maxima Draw] adapt_depth (=10) maximum number of adaptive interval splits when drawing curves

 adapt_depth adapt_depth :

[Maxima Draw] axis_3d (=true): Achsen im 3D zeichnen, false: keine Achsen zeichnen

[Maxima Draw] axis_3d (=true): draw 3D axes, false: don't draw axes

 axis_3d axis_3d :

[Maxima Draw] axis_bottom (=true): untere Achse im 2D zeichnen, false: Achse nicht zeichnen

[Maxima Draw] axis_bottom (=true): draw bottom axis in 2D, false: don't draw axis

 axis_bottom axis_bottom :

[Maxima Draw] axis_top (=true): obere Achse im 2D zeichnen, false: Achse nicht zeichnen

[Maxima Draw] axis_top (=true): draw top axis in 2D, false: don't draw axis

 axis_top axis_top :

[Maxima Draw] axis_left (=true): linke Achse im 2D zeichnen, false: Achse nicht zeichnen

[Maxima Draw] axis_left (=true): draw left axis in 2D, false: don't draw axis

 axis_left axis_left :

[Maxima Draw] axis_right (=true): rechte Achse im 2D zeichnen, false: Achse nicht zeichnen

[Maxima Draw] axis_right (=true): draw right axis in 2D, false: don't draw axis

 axis_right axis_right :

[Maxima Draw] background_color (=white): Hintergrundfarbe des Diagramms

[Maxima Draw] background_color (=white): background color of the plot

 background_color background_color :

[Maxima Draw] border (=true): Ränder von polygon(), ellipse() oder rectangle() zeichnen

[Maxima Draw] border (=true): draw borders of polygon(), ellipse() or rectangle() objects

 border border :

[Maxima Draw] cbrange (=auto): Farbbereich (Liste min,max)

[Maxima Draw] cbrange (=auto): color bar range (list min,max)

 cbrange cbrange :

[Maxima Draw] cbtics (=auto): Marken an der Farblegende

[Maxima Draw] cbtics (=auto): color bar tick marks

 cbtics cbtics :

[Maxima Draw] color (=blue): Farbe für Linien, Punkte, Kanten und Text, als Namen oder hexadezimal in der Form "#rrggbb"

[Maxima Draw] color (=blue): color for lines, points, borders and text, given as name or as "#rrggbb"

 color color :

[Maxima Draw] colorbox (=true): Farblegende ohne Beschriftung zeichnen, false: keine Farblegende zeichnen, text: Farblegende mit text als Beschriftung zeichnen.

[Maxima Draw] colorbox (=true): draw color scale without label, false: no colorbar, string: draw colorbar with string as label.

 colorbox colorbox :

[Maxima Draw] contour (=none): Art der Höhenlinien. none: keine, base: auf der xy-Ebene, surface: auf der 3D-Fläche, both: auf xy-Ebene und Fläche, map: auf xy-Ebene und Blickrichtung senkrecht.

[Maxima Draw] contour (=none): contour lines. none: no contours, base: on xy plane, surface: on 3D surface, both: on xy plane and surface, map: on xy plane plus vertical view.

 contour contour :

[Maxima Draw] contour_levels (=5): Werte für die Höhenlinien. Anzahl oder Liste (min, Δ, max), oder set(L1, L2,...) mit Werten

[Maxima Draw] contour_levels (=5): contour levels. number oder list (min, Δ, max), or set(L1, L2,...) of values

 contour_levels contour_levels :

[Maxima Draw] data_file_name (="data.gnuplot"): Kurvendaten für Gnuplot

[Maxima Draw] data_file_name (="data.gnuplot"): internal data file name for gnuplot

 data_file_name data_file_name :

[Maxima Draw] delay (=5) Zeitschritt in animierten gif-Dateien

[Maxima Draw] delay (=5): time step in animted gif files

 delay delay :

[Maxima Draw] dimensions (= 600 x 500): Liste [Breite,Höhe]

[Maxima Draw] dimensions (= 600 x 500) list [width, height]

 dimensions dimensions :

[Maxima Draw] draw_realpart (=true) Realteil zur Darstellung komplexer Werte verwenden

[Maxima Draw] draw_realpart (=true) use real part for plotting complex values

 draw_realpart draw_realpart :

[Maxima Draw] enhanced3d (=none) Farbpalette, none: 3D Flächen als Gitter zeichnen (Steuerung mit color und surface_hide), true: Farbe anhand des z-Werts, Liste [f(x,y,z), x, y, z]: Farbe anhand der Funktion f, Liste [f(u,v),u,v]: Farbe anhand der Flächenparameter oder Liste [f(k), k ]: Farbe anhand der Punktnummer in points() Objekten

[Maxima Draw] enhanced3d (=none) don't use color palette, draw 3D surfaces as grid (control using color und surface_hide), true: coloring of surfaces by z-value, or list [f(x,y,z), x, y, z]: coloring according to function f or list [f(u,v),u,v] or list [f(k), k ] (k being the point counter in points() objects)

 enhanced3d enhanced3d :

[Maxima Draw] error_type (=y) Art der Fehlerbalken in errors(): x, y, xy oder boxes

[Maxima Draw] error_type (=y) type of error bars in errors(): x, y, xy or boxes

 error_type error_type :

[Maxima Draw] file_name (="maxima_out") Grafik-Ausgabedatei, Endung wird gemäß Ausgabeformat ergänzt

[Maxima Draw] file_name (="maxima_out") output file, extension is set according to format

 file_name file_name :

[Maxima Draw] fill_color (=red) Füllfarbe für Objejte polygon() und explicit() in 2D

[Maxima Draw] fill_color (=red) fill color for polygons and explicit functions y(x) in 2D

fill_color fill_color :

[Maxima Draw] fill_density (=0) Deckungsgrad der Füllfarbe in bars()-Objekten, zwischen 0 und 1

[Maxima Draw] fill_density (=0) opacity of the fill color in bars()-objects, 0..1

 fill_density fill_density :

[Maxima Draw] filled_func (=false): explizite Funktionen y(x) werden nicht gefüllt, true: Füllung bis zur Unterkante des Diagramms, g(x): Füllung zwischen g(x) und y(x)

[Maxima Draw] filled_func (=false): don't fill explicit functions y(x), true: fill between the next explicit() object and the bottom border of the diagram, g(x): fill between g(x) and the next explicit() object

 filled_func filled_func :

[Maxima Draw] gnuplot_file_name (="maxout.gnuplot"): Kommandodatei für Gnuplot

[Maxima Draw] gnuplot_file_name (="maxout.gnuplot"): name of the temporary gnuplot command file

 gnuplot_file_name gnuplot_file_name :

[Maxima Draw] gnuplot_term (): Ausgabe-Format-Spezifikation (Text nach "set terminal")

[Maxima Draw] gnuplot_term (): gnuplot terminal options (arguments of "set terminal")

 gnuplot_term gnuplot_term :

[Maxima Draw] gnuplot_out_file (=maxplot.xxx) Ausgabedateiname (xxx abhängig vom Format)

[Maxima Draw] gnuplot_out_file (=maxplot.xxx) output file name (xxx depends on terminal)

 gnuplot_out_file gnuplot_out_file :

[Maxima Draw] grid (=false): kein Gitterraster zeichnen, true: Gitter zeichnen

[Maxima Draw] grid (=false): don't draw xy grid, true: draw grid

 grid grid :

[Maxima Draw] head_angle (=45) Pfeilwinkel an vector()-Objekten (halber Öffnungswinkel in °)

[Maxima Draw] head_angle (=45): head angle of vector()-Objekten (angle between border and vector direction in °)

 head_angle head_angle :

[Maxima Draw] head_both (=false) oder true: ob bei vector()-Objekten zwei Pfeilspitzen gezeichnet werden.

[Maxima Draw] head_both (=false): don't draw a second head of vector() objects, true: draw a second head

 head_both head_both :

[Maxima Draw] head_length (=2) Länge der Pfeilspitze bei vector()-Objekten in Einheiten der x-Achse

[Maxima Draw] head_length (=2): head length of vector() objects in units of the x-axis

 head_length head_length :

[Maxima Draw] head_type (=filled) Spitzenform bei vector()-Objekten: filled, empty oder nonfilled

[Maxima Draw] head_type (=filled) head type of vector() objects: filled, empty or nonfilled

 head_type head_type :

[Maxima Draw] ip_grid (={50, 50): Primäres Gitter für die Darstellung impliziter Funktionen, als Liste angeben

[Maxima Draw] ip_grid (={50, 50): primary grid for sampling of implicit functions, two-element list

 ip_grid ip_grid :

[Maxima Draw] ip_grid_in (={5, 5 ): Sekundäres Gitter für die Darstellung impliziter Funktionen

[Maxima Draw] ip_grid_in (={5, 5 ): secondary grid for sampling of implicit functions

 ip_grid_in ip_grid_in :

[Maxima Draw] key (=""): Legendeneintrag für das nachfolgende Grafikobjekt.

[Maxima Draw] key (=""): legend key for subsequent graphics object.

 key key :

[Maxima Draw] key_pos (="", entspricht top_right): Legendenposition. Gültige Werte: top_left, top_center, top_right, center_left, center, center_right, bottom_left, bottom_center, bottom_right

[Maxima Draw] key_pos (="", equivalent to top_right): position of the legend. Valid options: top_left, top_center, top_right, center_left, center, center_right, bottom_left, bottom_center, bottom_right

 key_pos key_pos :

[Maxima Draw] label_alignment (=center), left oder right: horizontale Ausrichtung von Beschriftungen

[Maxima Draw] label_alignment (=center), left or right: alignment of text labels

 label_alignment label_alignment :

[Maxima Draw] label_orientation (=horizontal) oder vertical: Ausrichtung von Texten

[Maxima Draw] label_orientation (=horizontal) or vertical: orientation of text labels

 label_orientation label_orientation :

[Maxima Draw] line_type (=solid) Linienart. Alternativen: dots (für alle Formate) oder wenn von Gnuplot unterstützt: dashes, short_dashes, short_long_dashes, short_short_long_dashes

[Maxima Draw] line_type (=solid) line type. Other options: dots (for all formats) or if supported by Gnuplot: dashes, short_dashes, short_long_dashes, short_short_long_dashes

line_type line_type :

[Maxima Draw] line_width (=1) , >0

line_width line_width :

[Maxima Draw] logcb (=false) oder true: logarithmische Farbskale

[Maxima Draw] logcb (=false) or true: log scale of the colorbar

 logcb logcb :

[Maxima Draw] logx (=false) oder true: logarithmische x-Achse

[Maxima Draw] logx (=false) or true: log scale of x-axis

 logx logx :

[Maxima Draw] logx_secondary (=false) oder true: logarithmische zweite x-Achse

[Maxima Draw] logx_secondary (=false) or true: log scale of secondary x-axis

 logx_secondary logx_secondary :

[Maxima Draw] logy (=false) oder true: logarithmische y-Achse

[Maxima Draw] logy (=false) or true: log scale of y-axis

 logy logy :

[Maxima Draw] logy_secondary (=false) oder true: logarithmische zweite y-Achse

[Maxima Draw] logy_secondary (=false) or true: log scale of secondary y-axis

 logy_secondary logy_secondary :

[Maxima Draw] logz (=false) oder true: logarithmische z-Achse

[Maxima Draw] logz (=false) or true: log scale of z-axis

 logz logz :

[Maxima Draw] nticks (=29): Punktezahl für die Kurvenabtastung

[Maxima Draw] nticks (=29): number of points for curve sampling (explicit and parametric)

 nticks nticks :

[Maxima Draw] palette (=color) Standard-Farbpalette, gray: Graustufen, Liste { Farbe1, Farbe2... oder false: Flächen nicht färben

[Maxima Draw] palette (=color) default color palette, gray: gray levels, list { color1, color2... or false: don't color 3D objects

palette palette :

[Maxima Draw] point_size (=1) Größe von points()-Symbolen

[Maxima Draw] point_size (=1) size of points()-symbols

 point_size point_size :

[Maxima Draw] point_type (=1) Symbol für points()-Objekte, Name oder Kennzahl: none -1, dot 0, plus 1, multiply 2, asterisk 3, square 4, filled_square 5, circle 6, filled_circle 7, up_triangle 8, filled_up_triangle 9, down_triangle 10, filled_dwn_triangle 11, diamant 12, filled_diamant 13

[Maxima Draw] point_type (=1) type of points() objects, name or key number: none -1, dot 0, plus 1, multiply 2, asterisk 3, square 4, filled_square 5, circle 6, filled_circle 7, up_triangle 8, filled_up_triangle 9, down_triangle 10, filled_down_triangle 11, diamant 12, filled_diamant 13

 point_type point_type :

[Maxima Draw] points_joined (=false), true or impulses: how to join points()

points_joined points_joined :

[Maxima Draw] proportional_axes (=none), xy oder xyz: Achsen mit gleicher Skalierung)

[Maxima Draw] proportional_axes (=none), xy or xyz: set axes of equal scaling)

 proportional_axes proportional_axes :

[Maxima Draw] surface_hide (=false) oder true: Ausblendung verdeckter Flächen bei Linienrasterdarstellung

[Maxima Draw] surface_hide (=false) or true: handling of hidden lines in surface grids

 surface_hide surface_hide :

[Maxima Draw] terminal (=screen) separate interactive terminal window, png, jpg, gif, eps, svg, pdf, animated_gif: gnuplot output format

terminal terminal :

[Maxima Draw] title (="") Überschrift für das Diagramm

[Maxima Draw] title (="") headline for the plot

 title title :

[Maxima Draw] transform (=none) Koordinatentransformation, für 2D als Liste {f1(x,y), f2(x,y), x, y, für 3D als Liste {f1(x,y), f2(x,y), f3(x, y, z), x, y, z

[Maxima Draw] transform (=none) co-ordinate transformation, for 2D as list {f1(x,y), f2(x,y), x, y, for 3D as list {f1(x,y), f2(x,y), f3(x, y, z), x, y, z

 transform transform :

[Maxima Draw] transparent (=false) oder true: ob Rechtecke, Polygone oder Ellipsen transparent sein sollen (bei false werden sie gefüllt)

[Maxima Draw] transparent (=false) fill objects with border, true: don't fill (make them transparent)

 transparent transparent :

[Maxima Draw] tube_extremes (=(open, open) ), open oder closed: Endscheiben von tube()-Objekten.

[Maxima Draw] tube_extremes (=(open, open) ), open or closed: how tube() objects are terminated.

 tube_extremes tube_extremes :

[Maxima Draw] unit_vectors (=false) oder true: Vektoren in originaler Länge oder als Einheitsvektoren zeichnen.

[Maxima Draw] unit_vectors (=false) draw vectors in original length, true: draw unit vectors.

 unit_vectors unit_vectors :

[Maxima Draw] user_preamble (="") Zeichenkette oder Liste von Zeichenketten, die unmittelbar vor dem eigentlichen Diagrammbefehl an Gnuplot übergeben werden.

[Maxima Draw] user_preamble (="") string or list of strings, gnuplot commands placed immediately before the plot commands

 user_preamble user_preamble :

[Maxima Draw] view (=(60,30)) view direction

view view :

[Maxima Draw] wired_surface (=false) oder true: Gitternetz auf eingefärbten Flächen anzeigen oder nicht.

[Maxima Draw] wired_surface (=false) no grid on colored surfaces, true: draw grid on surfaces

 wired_surface wired_surface :

[Maxima Draw] x_voxel (=10) x-Bereichsteilung für den Marching-Cubes-Algorithmus bei implizit gegebenen Flächen

[Maxima Draw] x_voxel (=10) number of x steps for the Marching Cube algorithm (for implicit 3D functions)

 x_voxel x_voxel :

[Maxima Draw] y_voxel (=10) y-Bereichsteilung für den Marching-Cubes-Algorithmus bei implizit gegebenen Flächen

[Maxima Draw] y_voxel (=10) number of y steps for the Marching Cube algorithm (for implicit 3D functions)

 y_voxel y_voxel :

[Maxima Draw] z_voxel (=10) z-Bereichsteilung für den Marching-Cubes-Algorithmus bei implizit gegebenen Flächen

[Maxima Draw] z_voxel (=10) number of z steps for the Marching Cube algorithm (for implicit 3D functions)

 z_voxel z_voxel :

[Maxima Draw] xaxis (=false) oder true: Anzeige der x-Achse

[Maxima Draw] xaxis (=false) or true: draw x-axis

 xaxis xaxis :

[Maxima Draw] yaxis (=false) oder true: Anzeige der y-Achse

[Maxima Draw] yaxis (=false) or true: draw y-axis

 yaxis yaxis :

[Maxima Draw] zaxis (=false) oder true: Anzeige der z-Achse

[Maxima Draw] zaxis (=false) or true: draw z-axis

 zaxis zaxis :

[Maxima Draw] xaxis_color (=black) Farbe x-Achse

[Maxima Draw] xaxis_color (=black) color of the x-axis

 xaxis_color xaxis_color :

[Maxima Draw] yaxis_color (=black) Farbe y-Achse

[Maxima Draw] yaxis_color (=black) color of the y-axis

 yaxis_color yaxis_color :

[Maxima Draw] zaxis_color (=black) Farbe z-Achse

[Maxima Draw] zaxis_color (=black) color of the z-axis

 zaxis_color zaxis_color :

[Maxima Draw] xaxis_secondary (=false) oder true: Nutzung einer zweiten x-Achse (oben) für die nachfolgenden Objekte

[Maxima Draw] xaxis_secondary (=false) or true: use the secondary x-axis (top) for subsequent objects

 xaxis_secondary xaxis_secondary :

[Maxima Draw] yaxis_secondary (=false) oder true: Nutzung einer zweiten y-Achse (rechts) für die nachfolgenden Objekte

[Maxima Draw] yaxis_secondary (=false) or true: use the secondary y-axis (right) for subsequent objects

 yaxis_secondary yaxis_secondary :

[Maxima Draw] xaxis_type (=dots) oder solid: Linienart der x-Achse

[Maxima Draw] xaxis_type (=dots) or solid

 xaxis_type xaxis_type :

[Maxima Draw] yaxis_type (=dots) oder solid: Linienart der y-Achse

[Maxima Draw] yaxis_type (=dots) or solid

 yaxis_type yaxis_type :

[Maxima Draw] zaxis_type (=dots) oder solid: Linienart der z-Achse

[Maxima Draw] zaxis_type (=dots) or solid

 zaxis_type zaxis_type :

[Maxima Draw] xaxis_width (=1) Linienbreite der x-Achse

[Maxima Draw] xaxis_width (=1)

 xaxis_width xaxis_width :

[Maxima Draw] yaxis_width (=1) Linienbreite der y-Achse

[Maxima Draw] yaxis_width (=1)

 yaxis_width yaxis_width :

[Maxima Draw] zaxis_width (=1) Linienbreite der z-Achse

[Maxima Draw] zaxis_width (=1)

 zaxis_width zaxis_width :

[Maxima Draw] xlabel (="") x-Achsenbeschriftung

[Maxima Draw] xlabel (="") label of the x-axis

 xlabel xlabel :

[Maxima Draw] ylabel(="") y-Achsenbeschriftung

[Maxima Draw] ylabel (="") label of the y-axis

 ylabel ylabel :

[Maxima Draw] zlabel (="") z-Achsenbeschriftung

[Maxima Draw] zlabel (="") label of the z-axis

 zlabel zlabel :

[Maxima Draw] xrange (=auto) oder Liste {min,max: x-Achsenbereich

[Maxima Draw] xrange (=auto) or list {min,max: range of the x-axis

 xrange xrange :

[Maxima Draw] yrange (=auto) oder Liste {min,max: y-Achsenbereich

[Maxima Draw] yrange (=auto) or list {min,max: range of the y-axis

 yrange yrange :

[Maxima Draw] zrange (=auto) oder Liste {min,max: z-Achsenbereich

[Maxima Draw] zrange (=auto) or list {min,max: range of the z-axis

 zrange zrange :

[Maxima Draw] xrange_secondary (=auto) oder Liste {min,max: Bereich der zweiten (oberen) x-Achse

[Maxima Draw] xrange_secondary (=auto) or list {min,max: range of the secondary (top) x-axis

 xrange_secondary xrange_secondary :

[Maxima Draw] yrange_secondary (=auto) oder Liste {min,max: Bereich der zweiten (rechten) y-Achse

[Maxima Draw] yrange_secondary (=auto) or list {min,max: range of the secondary (right) y-axis

 yrange_secondary yrange_secondary :

[Maxima Draw] xtics (=auto): automatische x-Achsmarken, none: keine, Zahl: Schrittweite, Liste mit {min, Schritt, max, oder set() von Zahlen: explizite Vorgabe der Zahlenwerte, oder set() von Listen ("text",pos) mit Vorgabe von Beschriftung und Position.

[Maxima Draw] xtics (=auto): automatic x ticks, none: no x ticks, number: tick interval, list of {min, step, max, or set() of numbers: explicit tick values, or set() of lists ("text",pos) for spec of position and text.

 xtics xtics :

[Maxima Draw] ytics (=auto): automatische y-Achsmarken, none: keine, Zahl: Schrittweite, Liste mit {min, Schritt, max, oder set() von Zahlen: explizite Vorgabe der Zahlenwerte, oder set() von Listen {"text",pos mit Vorgabe von Beschriftung und Position.

[Maxima Draw] ytics (=auto): automatic y ticks, none: no y ticks, number: tick interval, list of {min, step, max, or set() of numbers: explicit tick values, or set() of lists ("text",pos) for spec of position and text.

 ytics ytics :

[Maxima Draw] ztics (=auto): automatische z-Achsmarken, none: keine, Zahl: Schrittweite, Liste mit {min, Schritt, max, oder set() von Zahlen: explizite Vorgabe der Zahlenwerte, oder set() von Listen {"text",pos mit Vorgabe von Beschriftung und Position.

[Maxima Draw] ztics (=auto): automatic z ticks, none: no x ticks, number: tick interval, list of {min, step, max, or set() of numbers: explicit tick values, or set() of lists ("text",pos) for spec of position and text.

 ztics ztics :

[Maxima Draw] xtics_secondary (=auto): automatische Marken an der sekundären (oberen) x-Achse, none: keine, Zahl: Schrittweite, Liste mit {min, Schritt, max, oder set() von Zahlen: explizite Vorgabe der Zahlenwerte, oder set() von Listen {"text",pos mit Vorgabe von Beschriftung und Position.

[Maxima Draw] xtics_secondary (=auto): automatic ticks on the secondary (top) x-axis, none: no ticks, number: tick interval, list of {min, step, max, or set() of numbers: explicit tick values, or set() of lists ("text",pos) for spec of position and text.

 xtics_secondary xtics_secondary :

[Maxima Draw] ytics_secondary (=auto): automatische Marken an der sekundären (rechten) y-Achse, none: keine, Zahl: Schrittweite, Liste mit {min, Schritt, max, oder set() von Zahlen: explizite Vorgabe der Zahlenwerte, oder set() von Listen {"text",pos mit Vorgabe von Beschriftung und Position.

[Maxima Draw] ytics_secondary (=auto): automatic ticks on the secondary (right) y-axis, none: no ticks, number: tick interval, list of {min, step, max, or set() of numbers: explicit tick values, or set() of lists ("text",pos) for spec of position and text.

 ytics_secondary ytics_secondary :

[Maxima Draw] xtics_axis (=false): x-Achsmarken am Rand, true: an der Achse

[Maxima Draw] xtics_axis (=false): ticks on the boundary, true: ticks on the axis

 xtics_axis xtics_axis :

[Maxima Draw] ytics_axis (=false): y-Achsmarken am Rand, true: an der Achse

[Maxima Draw] ytics_axis (=false): ticks on the boundary, true: ticks on the axis

 ytics_axis ytics_axis :

[Maxima Draw] ztics_axis (=false): z-Achsmarken am Rand, true: an der Achse

[Maxima Draw] ztics_axis (=false): ticks on the boundary, true: ticks on the axis

 ztics_axis ztics_axis :

[Maxima Draw] xtics_secondary_axis (=false): Marken an der sekundaren (oberen) x-Achse am Rand, true: an der Achse

[Maxima Draw] xtics_secondary_axis (=false): ticks on the secondary (top) boundary, true: ticks on the axis

 xtics_secondary_axis xtics_secondary_axis :

[Maxima Draw] ytics_secondary_axis (=false): Marken an der sekundaren (rechten) y-Achse am Rand, true: an der Achse

[Maxima Draw] ytics_secondary_axis (=false): ticks on the secondary (right) boundary, true: ticks on the axis

 ytics_secondary_axis ytics_secondary_axis :

[Maxima Draw] xtics_rotate (=false): x-Achsmarken nicht drehen, true: um 90° drehen

[Maxima Draw] xtics_rotate (=false): horizontal tick labels, true: vertical tick labels

 xtics_rotate xtics_rotate :

[Maxima Draw] ytics_rotate (=false): y-Achsmarken nicht drehen, true: um 90° drehen

[Maxima Draw] ytics_rotate (=false): horizontal tick labels, true: vertical tick labels

 ytics_rotate ytics_rotate :

[Maxima Draw] ztics_rotate (=false): z-Achsmarken nicht drehen, true: um 90° drehen

[Maxima Draw] ztics_rotate (=false): horizontal tick labels, true: vertical tick labels

 ztics_rotate ztics_rotate :

[Maxima Draw] xtics_rotate_secondary (=false): Marken an der sekundären (oberen) x-Achse nicht drehen, true: um 90° drehen

[Maxima Draw] xtics_rotate_secondary (=false): don't rotate ticks of the secondary (top) x-axis, true: rotate about 90°

 xtics_rotate_secondary xtics_rotate_secondary :

[Maxima Draw] ytics_rotate_secondary (=false): Marken an der sekundären (rechten) y-Achse nicht drehen, true: um 90° drehen

[Maxima Draw] ytics_rotate_secondary (=false): don't rotate ticks of the secondary (right) y-axis, true: rotate about 90°

 ytics_rotate_secondary ytics_rotate_secondary :

[Maxima Draw] xu_grid (=30) Abtastpunkte in x- oder u-Richtung

[Maxima Draw] xu_grid (=30) sampling points in x- or u-direction

xu_grid xu_grid :

[Maxima Draw] yv_grid (=30) Abtastpunkte in y- oder v-Richtung

[Maxima Draw] yv_grid (=30) sampling points in y- or v-direction

yv_grid yv_grid :

[Maxima Draw] xyplane (=false): xy-Koordinatenebene automatisch anordnen, Zahl: z-Koordinate

[Maxima Draw3D] xyplane (=false): automatic allocation of the xy-plane, reak number: xy-plane intersects the z-axis at this level

 xyplane xyplane :

Objekte

[Maxima Draw2D] bars(b1,b2...) Säulendiagramm, Säulen gegeben durch Listen (x,h,w). Optionen: key, color, fill_color, fill_density and line_

[Maxima Draw2D] bars(b1,b2...) vertical bars, given as lists (x,h,w). Options: key, color, fill_color, fill_density and line_width

 _ bars _ bars :

[Maxima Draw3D] elevation_grid(Matrix,x0,y0,w,h) Stellt eine Matrix in 3D dar. M_11 bei x=x0,y=y0+h, M_mn bei x=x0+w,y=y0. Optionem: xu_grid, yv_grid, line_type, key, wired_surface, enhanced3d and color

[Maxima Draw3D] elevation_grid(Matrix,x0,y0,w,h) Draws a m x n-matrix in 3D. M_11 at x=x0,y=y0+h, M_mn at x=x0+w,y=y0. Options: xu_grid, yv_grid, line_type, key, wired_surface, enhanced3d and color

 _1 _2 _3 _4 _5 elevation_grid _1 _2 _3 _4 _5 elevation_grid :

[Maxima Draw2D] ellipse(xc,yc,a,b,φ1,φ2) Ellipse, zentriert bei xc, yc mit den Halbachsen a und b, von Winkel φ1 bis Winkel φ2. Optionen nticks, transparent, fill_color, border, line_width, line_type, key and color.

[Maxima Draw2D] ellipse(xc,yc,a,b,φ1,φ2) plots an ellipse centered at [xc, yc] with horizontal and vertical semi axis a and b, respectively, starting at angle ang1 with an amplitude equal to angle ang2. Options: nticks, transparent, fill_color, border, line_width, line_type, key and color.

#1 #2 #3 #4 #5 #6 ellipse #1 #2 #3 #4 #5 #6 ellipse :

[Maxima Draw2D] errors(e1,e2...) Punkte mit Fehlerbalken, horizontal, vertical oder beide, abhängig von der Option error_type. Argumente für error_type = x: Listen [x, y, xdelta] oder [x, y, xlow, xhigh]. Argumente für error_type = y; Listen [x, y, ydelta] oder [x, y, ylow, yhigh]. Argumente für error_type = xy oder error_type = boxes: Listen [x, y, xdelta, ydelta] oder [x, y, xlow, xhigh, ylow, yhigh]. Optionen: error_type, points_joined, line_width, key, line_type, color, fill_density, xaxis_secondary, and yaxis_secondary

[Maxima Draw2D] errors(e1,e2...) Draws points with error bars, horizontally, vertically or both, depending on the value of option error_type. If error_type = x, arguments are lists [x, y, xdelta] or [x, y, xlow, xhigh]. If error_type = y, arguments are lists [x, y, ydelta] or [x, y, ylow, yhigh]. If error_type = xy or error_type = boxes, arguments are lists [x, y, xdelta, ydelta] or [x, y, xlow, xhigh, ylow, yhigh]. Options: error_type, points_joined, line_width, key, line_type, color, fill_density, xaxis_secondary, and yaxis_secondary

 _ errors _ errors :

[Maxima Draw2D] explicit(f,x,xmin,xmax) zeichnet eine Funktion f von x von xmin bis xmax. Optionen: nticks, adapt_depth, draw_realpart, line_width, line_type, key, filled_func, fill_color und color

[Maxima Draw2D] explicit(f,x,xmin,xmax) plots explicit function f, with variable x taking values from xmin to xmax. Options: nticks, adapt_depth, draw_realpart, line_width, line_type, key, filled_func, fill_color and color

 _1 _2 _3 _4 explicit _1 _2 _3 _4 explicit :

[Maxima Draw3D] explicit(f,x,xmin,xmax,y,ymin,ymax) zeichnet eine Funktion f von x und y im Bereich xmin bis xmax und ymin bis ymax Optionen: draw_realpart, xu_grid, yv_grid, line_type, line_width, key, wired_surface, enhanced3d und color.

[Maxima Draw3D] explicit(f,x,xmin,xmax,y,ymin,ymax) plots the explicit function f, with variable x taking values from xmin to xmax and variable y taking values from yminto ymax. Options: draw_realpart, xu_grid, yv_grid, line_type, line_width, key, wired_surface, enhanced3d, and color.

#1 #2 #3 #4 #5 #6 #7 explicit #1 #2 #3 #4 #5 #6 #7 explicit :

[Maxima Draw2D] image(Matrix,x0,y0,w,h) Farbdarstellung einer m x n Matrix entsprechend der Option palette

[Maxima Draw2D] image(matrix,x0,y0,w,h) plots matrix in the rectangular region from vertex (x0,y0) to (x0+w,y0+h) according to option palette.

 #1 #2 #3 #4 #5 image #1 #2 #3 #4 #5 image :

[Maxima Draw2D] implicit(f,x,xmin,xmax,y,ymin,ymax) 2D Darstellung einer implizit gegebenen Funktion im angegebenen Variablenbereich (marching squares Algorithmus). Optionen: ip_grid, ip_grid_in, line_width, line_type, key, color

[Maxima Draw2D] implicit(f,x,xmin,xmax,y,ymin,ymax) plots the implicit function defined by f, with variable x taking values from xmin to xmax, and variable y taking values from ymin to ymax. Options: ip_grid, ip_grid_in, line_width, line_type, key, color

 #1 #2 #3 #4 #5 #6 #7 implicit #1 #2 #3 #4 #5 #6 #7 implicit :

[Maxima Draw3D] implicit(f,x,xmin,xmax,y,ymin,ymax,z,zmin,zmax) 3D Darstellung einer implizit gegebenen Funktion im angegebenen Variablenbereich (Marching Cubes Algorithmus). Optionen: x_voxel, y_voxel, z_voxel, ip_grid_in, line_width, line_type, wired_surface, enhanced3D, color [Maxima Draw]

[Maxima Draw3D] implicit(f,x,xmin,xmax,y,ymin,ymax,z,zmin,zmax) plots the implicit surface defined by f, with variable x taking values from xmin to xmax, variable y taking values from ymin to ymax and variable z taking values from zmin to zmax. This object implements the marching cubes algorithm. Options: x_voxel, y_voxel, z_voxel, line_width, line_type, key, wired_surface, enhanced3d,and color

 #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 implicit #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 implicit :

[Maxima Draw2D and 3D] label(list) Beschriftung, im 2D gegeben als Liste (text,x,y), im 3D als Liste (text,x,y,z), spezielle Optionen: color, label_alignment, label_orientation

[Maxima Draw2D and 3D] label(list) text label specified in 2D as list [text,x,y], in 3D as list [text,x,y,z], Options: color, label_alignment, label_orientation

 _ label _ label :

[Maxima Draw2D] parametric(fx,fy,p,pmin,pmax) parametrisch gegebenen Funktion. Optionen: nticks, line_width, line_type, key, color, enhanced3d

[Maxima Draw2D] parametric(fx,fy,p,pmin,pmax) plots the parametric function fx, fy with parameter p taking values from pmin to pmax. Options nticks, line_width, line_type, key, color, enhanced3d

 #1 #2 #3 #4 #5 parametric #1 #2 #3 #4 #5 parametric :

[Maxima Draw3D] parametric(fx,fy,fz,p,pmin,pmax) parametrisch gegebene Kurve. Optionen: nticks, line_width, line_type, key, color, enhanced3d

#1 #2 #3 #4 #5 #6 parametric #1 #2 #3 #4 #5 #6 parametric :

points(matrix) Punkte, zeilenweise gegeben als n x 2 (2D) oder n x 3 (3D)-Matrix. Spezielle Optionen: points_joined, point_type, point_size [Maxima Draw2D/3D]

[Maxima Draw2D und 3D] points(matrix) 2D: n x 2, 3D: n x 3, plots points, given as the rows in a matrix. special options: points_joined, point_type, point_size

 #1 points #1 points :

points(vx,vy) Punkte, gegeben durch Vektoren der x- und y-Koordinaten. Spezielle Optionen: points_joined, point_type, point_size [Maxima Draw2D]

[Maxima Draw2D] points(vx,vy) points given by two vectors, special options: points_joined, point_type, point_size

 #1 #2 points #1 #2 points :

[Maxima Draw3D] points(vx,vy,vz) zeichnet Punkte, gegeben durch drei Vektoren, spezielle Optionen: points_joined, point_type, point_size

[Maxima Draw3D] points(vx,vy,vz) points given by three vectors, special options: points_joined, point_type, point_size

 #1 #2 #3 points #1 #2 #3 points :

polar() funktioniert nicht.

[Maxima Draw2D] polygon(matrix) Polygon durch die als n x 2 Matrix gegebenen Punkte. Spezielle Optionen: transparent, fill_color, border, line_width, key, line_type color

[Maxima Draw2D] polygon(matrix) polygon defined by matrix (each row one point). Special options: transparent, fill_color, border, line_width, key, line_type color

#1 polygon #1 polygon :

[Maxima Draw2D] polygon(vx,vy) Zeichnet ein Polygon durch die als x- und y-Vektoren gegebenen Punkte. Spezielle Optionen: transparent, fill_color, border, line_width, key, line_type color

[Maxima Draw2D] polygon(vx,vy) polygon defined by two vectors. Special options: transparent, fill_color, border, line_width, key, line_type color

#1 #2 polygon #1 #2 polygon :

[Maxima Draw2D/3D] quadrilateral(l1,l2,l3,l4) Viereck, gegeben durch Listen der Eckkoordinaten 2D: (x,y) oder 3D: (x,y,z). Spezielle Optionen: transparent, fill_color, border, line_width, key, line_type, color, enhanced3D (nur 3D)

[Maxima Draw2D/3D] quadrilateral(l1,l2,l3,l4) quadrilateral given by lists of vertex coordinates: [x,y] in 2D or [x,y,z] in 3D. Special options: transparent, fill_color, border, line_width, key, line_type, color, enhanced3D (3D only)

 #1 #2 #3 #4 quadrilateral #1 #2 #3 #4 quadrilateral :

[Maxima Draw2D] rectangle(l1,l2) Rechteck gegeben durch Koordinatenlisten (x,y) gegenüberliegender Ecken. Spezielle Optionen: transparent, fill_color, border, line_width, key, line_type, color

[Maxima Draw2D] rectangle(l1,l2) specified by lists (x,y) of opposite corners. Special options: transparent, fill_color, border, line_width, key, line_type, color

#1 #2 rectangle #1 #2 rectangle :

[Maxima Draw2D] region(expr,x,xmin,xmax,y,ymin,ymax) Füllt das Gebiet wo expr wahr (true) ist im Bereich von xmin, xmax, ymin, ymax. Optionen: fill_color, key, x_voxel, y_voxel

[Maxima Draw2D] region(expr,x,xmin,xmax,y,ymin,ymax) Fills the region where expr is true in the domain given by xmin, xmax, ymin, ymax. Options: fill_color, key, x_voxel, y_voxel

 #1 #2 #3 #4 #5 #6 #7 region #1 #2 #3 #4 #5 #6 #7 region :

spherical() funktioniert nicht

[Maxima Draw2D/3D] triangle(l1,l2,l3) Dreieck, gegeben durch Koordinatenlisten (x,y) (2D) oder (x,y,z) (3D) der Ecken. Spezielle Optionen: transparent, fill_color, border, line_width, key, line_type, color

[Maxima Draw2D/3D] triangle(l1,l2,l3) given by co-ordinate lists (x,y) (2D) or (x,y,z) (3D) of the corners Special options: transparent, fill_color, border, line_width, key, line_type, color

#1 #2 #3 triangle #1 #2 #3 triangle :

[Maxima Draw3D] tube(fx,fy,fz,fr,p,pmin,pmax) Röhre, gegeben durch Mittellinie mit fx,fy,fz und den Radius fr als Funktionen des Parameters p. Spezielle Optionen: xu_grid, yv_grid, line_type, line_width, key, wired_surface, enhanced3d, color,tube_extremes.

[Maxima Draw3D] tube(fx,fy,fz,fr,p,pmin,pmax) tube, given by functions fx,fy,fz of the centerline and radius function fr pf parameters p. Special options: xu_grid, yv_grid, line_type, line_width, key, wired_surface, enhanced3d, color,tube_extremes.

 #1 #2 #3 #4 #5 #6 #7 tube #1 #2 #3 #4 #5 #6 #7 tube :

[Maxima Draw2D/3D] vector(l1,l2) Pfeil, gegeben durch Koordinatenlisten (x,y) (2D) oder (x,y,z) (3D) der Endpunkte. Spezielle Optionen: head_both, head_length, head_angle, head_type, line_width, line_type, key color.

[Maxima Draw2D/3D] vector(l1,l2) given by co-ordinate lists (x,y) (2D) or (x,y,z) (3D) of the end points. Spezielle Optionen: head_both, head_length, head_angle, head_type, line_width, line_type, key color.

 #1 #2 vector #1 #2 vector :

[Maxima] set(e1, e2,...) Maxima set (Liste in geschweiften Klammern)

[Maxima] set(e1, e2,...) Maxima set (in Maxima this is a list in curly braces)

 _ set _ set :

[Maxima] args(expr) Liste der Argumente von expr

[Maxima] args(expr) list of the top level arguments of expr

 _ args _ args :

Sonstige

[Maxima]

true true :

[Maxima]

false false : 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 p Draw3D 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 p 400 300 2 1 sys Draw3D

Exploration E02.3: The following data (which have in fact been calculated from the van der Waals equation of state) are close to the experimental values for carbon dioxide. Confirm that the gas behaves like a perfect gas at low pressures. At what pressure does the deviation from perfect gas behaviour become greater than 10 per cent? You can explore this question for other gases by introducing the appropriate values of the van der Waals parameters a and b (see Worksheet E03): to do so, first expand the collapsed region below.

This collapsed region calculates the pressure of a van der Waals gas.

 <p fontName="Arial">6395</p>

For conversions, note that 1 L2 atm mol-2 = 0.101325 m6 Pa mol-2 and 1 L mol-1 = 10-3 m3 mol-1.