Some basic PV (pressure-volume) diagrams with isothermal, isochoric, isobaric or adiabatic processes, including the Otto cycle and Carnot cycle. For more figures related to thermodynamics, see the “thermodynamics” category.
PV diagram for a constant pressure P:
PV diagram for a constant volume V:
PV diagram with an isotherm (constant temperature T):
PV diagram of a simple, engine:
Connecting isotherms via different paths in PV by adding heat Q to the system:
Specific heat capacities for constant pressure (CP) or constant volume (CV):
Connecting isotherms with an adiabatic process:
The work done by an adiabatic process is given by the area:
PV diagram for the Otto cycle:
PV diagram for the Carnot cycle:
Edit and compile if you like:
% Author: Izaak Neutelings (June, 2018)
\documentclass[border=3pt,tikz]{standalone}
\usepackage{tikz}
\usepackage{amsmath} % for \text
\usepackage[outline]{contour} % glow around text
\usetikzlibrary{arrows.meta} % to control arrow size
\tikzset{>={Latex[length=4,width=4]}} % for LaTeX arrow head
\usetikzlibrary{calc,decorations.markings,arrows.meta}
\usepackage{xcolor} % for colored text
\contourlength{1.2pt}
\colorlet{mylightblue}{blue!20}
\colorlet{myblue}{blue!80!black}
\colorlet{mydarkblue}{blue!30!black}
\colorlet{mylightred}{red!10}
\colorlet{myred}{red!80!black}
\colorlet{mydarkred}{red!60!black}
\colorlet{mydarkgreen}{green!30!black}
%\tikzstyle{midarr}=[decoration={markings,mark=at position 0.5 with {\arrow{stealth}}},postaction={decorate}]
\tikzset{
midarr/.style={decoration={markings,mark=at position #1 with {\arrow{stealth}}},postaction={decorate}},
midarr/.default=0.5
}
\def\xtick#1#2{\draw[thick] (#1)++(0,.1) --++ (0,-.2) node[below=-.5pt,scale=0.9] {#2};}
\def\ytick#1#2{\draw[thick] (#1)++(.1,0) --++ (-.2,0) node[left=-.5pt,scale=0.9] {#2};}
\begin{document}
% PV diagram - constant P
\def\N{40} % number of plot samples
\def\xmax{3}
\def\ymax{2.5}
\begin{tikzpicture}
% AREA
\coordinate (A) at (.2*\xmax,.8*\ymax);
\coordinate (B) at (.8*\xmax,.8*\ymax);
\coordinate (C) at (.8*\xmax,.2*\ymax);
\fill[mylightblue] (A) rectangle (C|-0,0) node[midway,blue] {$W$};
% LINE
\draw[very thick,midarr=.55,myred] (A) -- (B);
\draw[very thick,midarr=.55,blue] (B) -- (C);
\fill (A) circle(0.07) node[right=5,above=2] {$P_1$, $V_1$};
\fill (B) circle(0.07);
\fill (C) circle(0.07) node[right=2] {$P_2$, $V_2$};
% AXIS
\draw[->,thick] (0,-0.1*\ymax) -- (0,\ymax) node[anchor=north east] {$P$};
\draw[->,thick] (-0.1*\xmax,0) -- (\xmax,0) node[anchor=north east] {$V$};
\end{tikzpicture}
% PV diagram - constant V
\begin{tikzpicture}
% AREA
\coordinate (A) at (.2*\xmax,.8*\ymax);
\coordinate (B) at (.2*\xmax,.2*\ymax);
\coordinate (C) at (.8*\xmax,.2*\ymax);
\fill[mylightblue] (B) rectangle (C|-0,0) node[below=-6,midway,blue] {$W$};
% LINE
\draw[very thick,midarr=.55,blue] (A) -- (B);
\draw[very thick,midarr=.55,myred] (B) -- (C);
\fill (A) circle(0.07) node[right=5,above=2] {$P_1$, $V_1$};
\fill (B) circle(0.07);
\fill (C) circle(0.07) node[right=2] {$P_2$, $V_2$};
% AXIS
\draw[->,thick] (0,-0.1*\ymax) -- (0,\ymax) node[anchor=north east] {$P$};
\draw[->,thick] (-0.1*\xmax,0) -- (\xmax,0) node[anchor=north east] {$V$};
\end{tikzpicture}
% PV diagram - isotherm
\begin{tikzpicture}
\def\isotherm{(A) to[out=-60,in=170] (B)}
\def\T{1.2}
\def\xa{.2*\xmax}
\def\xb{.8*\xmax}
\def\ya{{\T/(\xa)}}
\def\yb{{\T/(\xb)}}
% AREA
\coordinate (A) at (\xa,\ya);
\coordinate (B) at (\xb,\yb);
\fill[mylightblue,samples=\N,domain=\xa:\xb]
plot(\x,{\T/\x}) -- (B|-0,0) -- (A|-0,0) node[midway,left=4,above=5,blue] {$W$} -- cycle;
% LINE
\draw[myred,very thick,midarr=.58,samples=\N,domain={\xa}:{\xb}]
plot(\x,{\T/\x});
\fill (A) circle(0.07) node[right=5,above=2] {$P_1$, $V_1$};
\fill (B) circle(0.07) node[right=2] {$P_2$, $V_2$};
% AXIS
\draw[->,thick] (0,-0.1*\ymax) -- (0,\ymax) node[anchor=north east] {$P$};
\draw[->,thick] (-0.1*\xmax,0) -- (\xmax,0) node[anchor=north east] {$V$};
\end{tikzpicture}
% PV diagram - simple engine
\def\xmax{3.5}
\def\ymax{3.0}
\begin{tikzpicture}
% AREA
\coordinate (A) at (.2*\xmax,.8*\ymax);
\coordinate (B) at (.8*\xmax,.8*\ymax);
\coordinate (C) at (.8*\xmax,.2*\ymax);
\coordinate (D) at (.2*\xmax,.2*\ymax);
\fill[mylightblue] (A) rectangle (C) node[midway,blue] {$W$};
% LINE
\draw[very thick,myred,midarr=.25,midarr=.80]
(D) -- (A) -- (B);
\draw[very thick,blue,midarr=.25,midarr=.80]
(B) -- (C) -- (D);
% AXIS
\draw[->,thick] (0,-0.1*\ymax) -- (0,\ymax) node[above=2,anchor=north east] {$P$};
\draw[->,thick] (-0.1*\xmax,0) -- (\xmax,0) node[right=2,anchor=north east] {$V$};
% TICKS
\draw[dashed]
(A-|0,0) -- (A)
(D-|0,0) -- (D)
(D|-0,0) -- (D)
(C|-0,0) -- (C);
\xtick{A|-0,0}{$V_1$}
\xtick{B|-0,0}{$V_2$}
\ytick{D-|0,0}{$P_1$}
\ytick{A-|0,0}{$P_2$}
% HEAT
\fill[mydarkblue]
(A) circle (0.07)
(B) circle (0.07)
(C) circle (0.07)
(D) circle (0.07);
\draw[>={LaTeX[width=8,length=5]},->,line width=4,mydarkred]
($(D)!.26!(A)$)++(-.2,0) --++ (.6,0) node[pos=0,left=-4,scale=.9] {$Q_1$};
\draw[>={LaTeX[width=8,length=5]},->,line width=4,mydarkred]
($(A)!.27!(B)$)++(0,.2) --++ (0,-.6) node[near end,above=11,scale=.9] {$Q_2$};
\draw[>={LaTeX[width=8,length=5]},->,line width=4,mydarkblue]
($(B)!.25!(C)$)++(-.2,0) --++ (.6,0) node[right=-2,scale=.9] {$Q_3$};
\draw[>={LaTeX[width=8,length=5]},->,line width=4,mydarkblue]
($(C)!.30!(D)$)++(0,.2) --++ (0,-.6) node[right=-1,scale=.9] {$Q_4$};
\end{tikzpicture}
% PV diagram - different heat paths
\def\isotherm#1#2{{ #2/(#1) }}
\begin{tikzpicture}
\def\Th{2.7}
\def\Tc{.85}
\coordinate (A) at ({0.30*\xmax},{\isotherm{0.30*\xmax}{\Tc}});
\coordinate (B) at ({0.29*\xmax},{\isotherm{0.29*\xmax}{\Th}});
\coordinate (C) at ({0.58*\xmax},{\isotherm{0.58*\xmax}{\Th}});
\coordinate (D) at ({0.82*\xmax},{\isotherm{0.82*\xmax}{\Th}});
% AXIS
\draw[->,thick] (0,-0.1*\ymax) -- (0,\ymax+0.1)
node[anchor=north east,inner sep=4,scale=1] {$P$};
\draw[->,thick] (-0.1*\xmax,0) -- (\xmax+0.1,0)
node[anchor=north east,inner sep=4,scale=1] {$V$};
% ISOTHERMS
\draw[mydarkblue,thick,
domain={\isotherm{\ymax}{\Th}}:{.95*\xmax},samples=\N,smooth]
plot (\x,\isotherm{\x}{\Th});
\draw[mydarkblue,thick,
domain={\isotherm{\ymax}{\Tc}}:{.95*\xmax},samples=\N,smooth]
plot (\x,\isotherm{\x}{\Tc});
% PATHS
\draw[mydarkred,thick,midarr=.5] (A) to[out=100,in=-95] (B);
\draw[mydarkred,thick,midarr=.6] (A) to[out=50,in=-170] (C);
\draw[mydarkred,thick,midarr=.5] (A) to[out=10,in=175] (D);
\path (A) -- (B) node[mydarkred,scale=0.9,pos=0.70,left=-1] {$Q_1$};
\path (A) -- (C) node[mydarkred,scale=0.9,pos=0.40,above=4] {$Q_2$};
\path (A) -- (D) node[mydarkred,scale=0.9,pos=0.60,below=-3] {$Q_3$};
% POINTS
\node[mydarkblue,above=2,right=-5,scale=0.9]
at (\xmax,{\isotherm{\xmax}{\Th}}) {$T+\Delta T$};
\node[mydarkblue,above=1,right=-5,scale=0.9]
at (\xmax,{\isotherm{\xmax}{\Tc}}) {$T$};
\fill[mydarkblue]
(A) circle(0.05)
(B) circle(0.05)
(C) circle(0.05)
(D) circle(0.05); % node[right=5,above right=-2,scale=0.9] {$P_2$, $V_2$};
\end{tikzpicture}
% PV diagram - specific heat capacities
\begin{tikzpicture}
\def\Th{2.6}
\def\Tc{.85}
\def\Vc{0.28*\xmax}
\def\Vh{\Vc*\Th/\Tc}
\coordinate (A) at (\Vc,{\isotherm{\Vc}{\Tc}});
\coordinate (B) at (\Vc,{\isotherm{\Vc}{\Th}});
\coordinate (C) at (\Vh,{\isotherm{\Vh}{\Th}});
% AXIS
\draw[->,thick] (0,-0.1*\ymax) -- (0,\ymax+0.1)
node[anchor=north east,inner sep=4,scale=1] {$P$};
\draw[->,thick] (-0.1*\xmax,0) -- (\xmax+0.1,0)
node[anchor=north east,inner sep=4,scale=1] {$V$};
% ISOTHERMS
\draw[mydarkblue,thick,
domain={\isotherm{\ymax}{\Th}}:{.95*\xmax},samples=\N,smooth]
plot (\x,\isotherm{\x}{\Th});
\draw[mydarkblue,thick,
domain={\isotherm{\ymax}{\Tc}}:{.95*\xmax},samples=\N,smooth]
plot (\x,\isotherm{\x}{\Tc});
% PATHS
\path (A) -- (B) node[mydarkred,scale=0.85,pos=0.45,left=-1.5]
{\contour{white}{$C_\mathrm{V}\Delta T$}};
\path (A) -- (C) node[mydarkred,scale=0.85,pos=0.60,below=0]
{$C_\mathrm{P}\Delta T$};
\draw[mydarkred,thick,midarr=.48] (A) -- (B);
\draw[mydarkred,thick,midarr=.58] (A) -- (C);
% POINTS
\node[mydarkblue,above=2,right=-5,scale=0.9]
at (\xmax,{\isotherm{\xmax}{\Th}}) {$T+\Delta T$};
\node[mydarkblue,above=1,right=-5,scale=0.9]
at (\xmax,{\isotherm{\xmax}{\Tc}}) {$T$};
\fill[mydarkblue]
(A) circle(0.05)
(B) circle(0.05)
(C) circle(0.05);
\end{tikzpicture}
% PV diagram - adiabatic + isotherms
\def\gam{2}
\def\isotherm#1#2{{ #2/(#1) }}
\def\adiabatic#1#2{{ #2/(#1)^(\gam) }}
\begin{tikzpicture}
\def\Th{2.6}
\def\Tc{.85}
\def\Ch{2.5}
\def\A{ (\Th/\Ch)^(1/(1-\gam)) }
\def\B{ (\Tc/\Ch)^(1/(1-\gam)) }
%\def\intersect#1#2{ (#1/#2)^(1/(1-\gam) }
\coordinate (A) at ({\A},{\isotherm{\A}{\Th}});
\coordinate (B) at ({\B},{\isotherm{\B}{\Tc}});
% AXIS
\draw[->,thick] (0,-0.1*\ymax) -- (0,\ymax+0.1)
node[anchor=north east,inner sep=4,scale=1] {$P$};
\draw[->,thick] (-0.1*\xmax,0) -- (\xmax+0.1,0)
node[anchor=north east,inner sep=4,scale=1] {$V$};
% ISOTHERMS
\draw[mydarkblue,thick,
domain={\isotherm{\ymax}{\Th}}:{.95*\xmax},samples=\N,smooth]
plot (\x,\isotherm{\x}{\Th});
\draw[mydarkblue,thick,
domain={\isotherm{\ymax}{\Tc}}:{.95*\xmax},samples=\N,smooth]
plot (\x,\isotherm{\x}{\Tc});
% ADIABATIC
\draw[mydarkred,thick,midarr=.48,
domain={\A:\B},samples=\N]
plot (\x,\adiabatic{\x}{\Ch});
% POINTS
\node[mydarkblue,above right=-2] at (.48*\xmax,{\isotherm{.48*\xmax}{\Th}}) {$T_1$};
\node[mydarkblue,below left=-2] at (.30*\xmax,{\isotherm{.30*\xmax}{\Tc}}) {$T_2$};
\fill[mydarkblue]
(A) circle(0.05) node[right=2,scale=0.9] {$P_1$, $V_1$};
\fill[mydarkblue]
(B) circle(0.05) node[right=2,above right=-2,scale=0.9] {$P_2$, $V_2$};
\end{tikzpicture}
% PV diagram - adiabatic + isotherms + work
\begin{tikzpicture}
\def\Th{2.5}
\def\Tc{.8}
\def\Ch{2.4}
\def\A{ (\Th/\Ch)^(1/(1-\gam)) }
\def\B{ (\Tc/\Ch)^(1/(1-\gam)) }
%\def\intersect#1#2{ (#1/#2)^(1/(1-\gam) }
\coordinate (A) at ({\A},{\isotherm{\A}{\Th}});
\coordinate (B) at ({\B},{\isotherm{\B}{\Tc}});
% WORK
\fill[mylightblue,domain={\A:\B},samples=\N]
plot (\x,\adiabatic{\x}{\Ch}) |- (A|-0,0) -- cycle;
\node[blue] at ($(B-|A)!.25!(B)+(0,.14)$) {$W$};
% ISOTHERMS
\draw[mydarkblue,thick,
domain={\isotherm{\ymax}{\Th}}:{.96*\xmax},samples=\N,smooth]
plot (\x,\isotherm{\x}{\Th});
% ADIABATIC
\draw[mydarkred,thick,midarr=.48,
domain={\A:\B},samples=\N]
plot (\x,\adiabatic{\x}{\Ch});
% POINTS
\fill[mydarkblue] (A) circle(0.05);
\fill[mydarkblue] (B) circle(0.05);
% AXIS
\draw[->,thick] (0,-0.1*\ymax) -- (0,\ymax+0.1)
node[anchor=north east,inner sep=4,scale=1] {$P$};
\draw[->,thick] (-0.1*\xmax,0) -- (\xmax+0.1,0)
node[anchor=north east,inner sep=4,scale=1] {$V$};
\end{tikzpicture}
% PV diagram - Otto cycle
\begin{tikzpicture}
\def\Ch{2.5}
\def\Cc{0.9}
\def\N{40}
\def\gam{1.0}
\def\adiabatic#1#2{{ #2/(#1)^(\gam) }}
\def\xA{.24*\xmax}
\def\xB{.90*\xmax}
\coordinate (A) at ({\xA},{\adiabatic{\xA}{\Ch}});
\coordinate (B) at ({\xB},{\adiabatic{\xB}{\Ch}});
\coordinate (C) at ({\xB},{\adiabatic{\xB}{\Cc}});
\coordinate (D) at ({\xA},{\adiabatic{\xA}{\Cc}});
\coordinate (E) at (C-|A);
% WORK
\fill[mylightblue,domain={\xA:\xB},samples=\N]
plot (\x,\adiabatic{\x}{\Ch}) --
plot[domain={\xB:\xA}](\x,\adiabatic{\x}{\Cc}) -- cycle;
\node[below=-5,blue,scale=.9] at ($(D)!.4!(B)$) {$W$};
% ADIABATIC TRANSFORMATION
\draw[myred,thick,midarr=.18,midarr=.75,domain={\xA:\xB},samples=\N]
(D) -- (A)
plot (\x,\adiabatic{\x}{\Ch});
\draw[blue,thick,midarr=.1,midarr=.62,domain={\xB:\xA},samples=\N]
(B) -- plot(\x,\adiabatic{\x}{\Cc});
\draw[blue!80!white,thick,midarr=.65]
(C)++(0,.02) -- ($(E)+(0,.02)$);
\draw[blue!80!black,thick,midarr=.55]
(E)++(0,-.03) -- ($(C)+(0,-.03)$);
\node[blue,above=2,right,scale=0.75] at (B) {exhaust};
\node[blue!80!black,right=12,below=-1,scale=0.75] at (E) {intake};
\node[myred,above left,scale=0.75] at (D) {spark};
% HEAT
\draw[>={LaTeX[width=5,length=4]},->,line width=2,mydarkred]
($(D)!.28!(A)$)++(-.2,0) --++ (.5,0) node[near end,left=10,scale=.8] {$Q_\text{h}$};
\draw[>={LaTeX[width=5,length=4]},->,line width=2,mydarkblue]
($(B)!.72!(C)$)++(-.2,0) --++ (.5,0) node[right=-2,scale=.8] {$Q_\text{c}$};
% POINTS
\fill[mydarkblue]
(A) circle(0.05)
(B) circle(0.05)
(C) circle(0.05)
(D) circle(0.05)
(E) circle(0.05);
% AXIS
\draw[->,thick] (0,-0.1*\ymax) -- (0,\ymax+0.1)
node[anchor=north east,inner sep=4,scale=1] {$P$};
\draw[->,thick] (-0.1*\xmax,0) -- (\xmax+0.1,0)
node[anchor=north east,inner sep=4,scale=1] {$V$};
\end{tikzpicture}
% PV diagram - Carnot cycle
\begin{tikzpicture}
\def\Th{1.20}
\def\Tc{0.45}
\def\Ch{0.4}
\def\Cc{1.9}
\def\N{40}
\def\gam{2.2}
\def\isotherm#1#2{{ #2/(#1) }}
\def\adiabatic#1#2{{ #2/(#1)^(\gam) }}
\def\xA{ (\Th/\Ch)^(1/(1-\gam)) }
\def\xB{ (\Th/\Cc)^(1/(1-\gam)) }
\def\xC{ (\Tc/\Cc)^(1/(1-\gam)) }
\def\xD{ (\Tc/\Ch)^(1/(1-\gam)) }
\coordinate (A) at ({\xA},{\isotherm{\xA}{\Th}});
\coordinate (B) at ({\xB},{\isotherm{\xB}{\Th}});
\coordinate (C) at ({\xC},{\isotherm{\xC}{\Tc}});
\coordinate (D) at ({\xD},{\isotherm{\xD}{\Tc}});
%\clip (-0.1*\xmax,-0.12*\ymax) rectangle (1.05*\xmax,1.1*\ymax);
% WORK
\fill[mylightblue,samples=\N]
plot[domain={\xA:\xB}] (\x,\isotherm{\x}{\Th}) --
plot[domain={\xB:\xC}] (\x,\adiabatic{\x}{\Cc}) --
plot[domain={\xC:\xD}] (\x,\isotherm{\x}{\Tc}) --
plot[domain={\xD:\xA}] (\x,\adiabatic{\x}{\Ch});
\node[blue,scale=.9] at ($(B)!.5!(D)$) {$W$};
% ADIABATIC & ISOTHERMIC TRANSFORMATIONS
\draw[myred,thick,midarr=.60,domain={\xA:\xB},samples=\N]
plot (\x,\isotherm{\x}{\Th}); % hot
\draw[blue,thick,midarr=.45,domain={\xB:\xC},samples=\N]
plot (\x,\adiabatic{\x}{\Cc}); % cold
\draw[blue,thick,midarr=.65,domain={\xC:\xD},samples=\N]
plot (\x,\isotherm{\x}{\Tc}); % cold
\draw[myred,thick,midarr=.40,domain={\xD:\xA},samples=\N]
plot(\x,\adiabatic{\x}{\Ch}); % hot
% POINTS
\fill[mydarkblue]
(A) circle(0.05) node[above=1,scale=.8] {1}
(B) circle(0.05) node[above right,scale=.8] {2}
(C) circle(0.05) node[above=1,scale=.8] {3}
(D) circle(0.05) node[below left,scale=.8] {4};
% HEAT
\draw[>={LaTeX[width=6,length=4]},->,line width=2,mydarkred]
(.28*\xmax,.488*\ymax) --++ (-89:.56)
node[pos=0,inner sep=0,anchor=-130,scale=.9] {$Q_\text{in}$};
\draw[>={LaTeX[width=6,length=4]},->,line width=2,mydarkblue]
(.47*\xmax,.12*\ymax) --++ (-89:.56)
node[inner sep=-2,anchor=60,scale=.9] {$Q_\text{out}$};
% AXIS
\draw[->,thick] (0,-0.1*\ymax) -- (0,\ymax+0.1)
node[anchor=north east,inner sep=4,scale=1] {$P$};
\draw[->,thick] (-0.1*\xmax,0) -- (\xmax+0.1,0)
node[anchor=north east,inner sep=4,scale=1] {$V$};
\end{tikzpicture}
\end{document}
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I think there is an error in the Carnot cycle. Q_{in} and Q_{out} arrows should go in the isothermal transformations, not in the adiabatic ones. They can’t change heat by definition.
Yes, I think you are right! I’ll try to fix it later! Thank you for the correction.