Otto Cycle
The Otto cycle is an idealized thermodynamic cycle of a typical spark ignition piston engine. It is the thermodynamic cycle most commonly found in automobile engines.
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LaTeX
otto-cycle.tex (37 lines)
\documentclass[tikz, svgnames]{standalone}
\usepackage{mathtools}
\usetikzlibrary{decorations.markings}
\def\V{10}
\def\p{7}
\tikzset{decoration={markings, mark=at position 0.5 with {\arrow{stealth}}}}
\begin{document}
\begin{tikzpicture}[thick]
\draw[->] (0, 0) -- (0, \p) node[right] {$p$};
\draw[->] (0, 0) -- (\V, 0) node[right] {$V$};
\draw[dashed] (0, 0.9*\p) node[left] {$p_\text{max}$} -| (0.2*\V, 0) node[below] {$V_\text{min}$};
\draw[dashed] (0, 0.2*\p) node[left] {$p_\text{min}$} -| (0.9*\V, 0) node[below] {$V_\text{max}$};
\coordinate[label=above:1] (a) at (0.2*\V, 0.9*\p);
\coordinate[label=right:2] (b) at (0.9*\V, 0.5*\p);
\coordinate[label=right:3] (c) at (0.9*\V, 0.2*\p);
\coordinate[label=left:4] (d) at (0.2*\V, 0.45*\p);
\foreach \point in {a, b, c, d}
\fill (\point) circle (3pt);
\draw[ultra thick, DarkBlue] (a) edge[out=-40, in=180, looseness=0.7, postaction={decorate}]
node[midway, above=2px] {$\Delta Q = 0$} (b) (b) -- (c)
node[midway, right, blue] {$\Rightarrow Q_\text{out}$} (c)
edge[out=180, in=-40, looseness=0.7, postaction={decorate}]
node[midway, above=2px] {$\Delta Q = 0$} (d) (d) -- (a)
node[midway, left, red] {$Q_\text{in} \Rightarrow$};
\end{tikzpicture}
\end{document}
Typst
otto-cycle.typ (151 lines)
#import "@preview/cetz:0.3.4": canvas, draw
#import draw: line, content, circle, bezier, set-style
#set page(width: auto, height: auto, margin: 8pt)
#let (V, p) = (9, 6)
#set-style(line: (mark: (scale: .5)))
#canvas({
// Draw axes
line((0, 0), (0, p), mark: (end: "stealth", fill: black), name: "y-axis")
content((rel: (0.2, 0), to: "y-axis.end"), $p$, name: "p-label")
line((0, 0), (V, 0), mark: (end: "stealth", fill: black), name: "x-axis")
content((rel: (0.2, 0), to: "x-axis.end"), $V$, name: "V-label")
// Define key values
let (p-min, p-max) = (0.2 * p, 0.9 * p)
let (V-min, V-max) = (0.2 * V, 0.9 * V)
// Create reference points for min/max values
content((0, p-max), name: "p-max-ref", [])
content((0, p-min), name: "p-min-ref", [])
content((V-min, 0), name: "V-min-ref", [])
content((V-max, 0), name: "V-max-ref", [])
// Horizontal dashed line for p-max
line(
"p-max-ref",
(rel: (V-min, 0), to: "p-max-ref"),
stroke: (dash: "dashed", thickness: 0.8pt),
name: "p-max-line",
)
// Vertical dashed line for V-min
line(
"V-min-ref",
(rel: (0, p-max), to: "V-min-ref"),
stroke: (dash: "dashed", thickness: 0.8pt),
name: "V-min-line",
)
// Labels for p-max and V-min
content((rel: (-0.5, 0), to: "p-max-ref"), $p_"max"$, name: "p-max-label")
content((rel: (0, -0.5), to: "V-min-ref"), $V_"min"$, name: "V-min-label")
// Horizontal dashed line for p-min
line(
"p-min-ref",
(rel: (V-max, 0), to: "p-min-ref"),
stroke: (dash: "dashed", thickness: 0.8pt),
name: "p-min-line",
)
// Vertical dashed line for V-max
line(
"V-max-ref",
(rel: (0, p-min), to: "V-max-ref"),
stroke: (dash: "dashed", thickness: 0.8pt),
name: "V-max-line",
)
// Labels for p-min and V-max
content((rel: (-0.5, 0), to: "p-min-ref"), $p_"min"$, name: "p-min-label")
content((rel: (0, -0.5), to: "V-max-ref"), $V_"max"$, name: "V-max-label")
// Define cycle points
circle((V-min, p-max), radius: 3pt, fill: black, name: "point-a")
circle((V-max, 0.5 * p), radius: 3pt, fill: black, name: "point-b")
circle((V-max, p-min), radius: 3pt, fill: black, name: "point-c")
circle((V-min, 0.45 * p), radius: 3pt, fill: black, name: "point-d")
// Add point labels
content("point-a", [1], anchor: "south", padding: (bottom: 5pt), name: "label-a")
content("point-b", [2], anchor: "west", padding: (left: 5pt), name: "label-b")
content("point-c", [3], anchor: "north-west", padding: (left: 5pt), name: "label-c")
content("point-d", [4], anchor: "east", padding: (right: 5pt), name: "label-d")
// Define styles for paths
let arrow_style = (end: "stealth", fill: black, scale: .5)
let stroke_style = (paint: rgb("#00008b"), thickness: 1.5pt)
// Draw cycle paths with arrows and labels
// a -> b (adiabatic expansion)
bezier(
"point-a",
"point-b",
(rel: (-5, 1), to: "point-b"),
stroke: stroke_style,
mark: arrow_style,
name: "path-ab",
)
// Calculate midpoint for label using relative positioning
// Create a midpoint reference
content(
((V-min + V-max) / 2, (p-max + 0.5 * p) / 2 - 0.35),
text(fill: blue.darken(25%), $Delta Q = 0$),
name: "label-ab",
anchor: "south",
padding: (bottom: 5pt),
)
// b -> c (heat rejection)
line("point-b", "point-c", mark: arrow_style, stroke: stroke_style, name: "path-bc")
content(
(rel: (0.1, 0), to: "path-bc"),
text(fill: blue.darken(5%), $arrow.double.r Q_"out"$),
name: "label-bc",
anchor: "west",
)
// c -> d (adiabatic compression)
bezier(
"point-c",
"point-d",
(rel: (2.4, -1.3), to: "point-d"),
stroke: stroke_style,
mark: arrow_style,
name: "path-cd",
)
content(
((V-max + V-min) / 2, (p-min + 0.45 * p) / 2 - 0.35),
text(fill: blue.darken(15%), $Delta Q = 0$),
name: "label-cd",
anchor: "south",
padding: (bottom: 5pt),
)
// d -> a (heat addition)
line(
"point-d",
"point-a",
mark: arrow_style,
stroke: stroke_style,
name: "path-da",
)
content(
(rel: (-0.1, 0), to: "path-da"),
text(fill: red)[$Q_"in" arrow.double.r$],
name: "label-da",
anchor: "east",
)
})