如何在热力学图下绘制区域？

Question

我的 MWE：

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{decorations.markings, arrows, arrows.meta,patterns.meta}

\tikzset{
    midar/.style 2 args={
        very thick,
        decoration={name=markings,
            mark=at position .55 with {\arrow{latex}},
            mark=at position 0 with {\fill circle (2pt);},
            mark=at position 1 with {\fill circle (2pt);}}
        ,postaction=decorate,
    },
}

\begin{document}
    
    \begin{tikzpicture}[thick]
        \draw[-{Latex}] (0,0) -- (0,5) node[above] {$P$};
        \draw[-{Latex}] (0,0) -- (5,0) node[right] {$V$};
        
        \draw[dashed] (0,4) node[left] {$P_{1}$} -| (1,0) node[below] {$V_{1}$};
        \draw[dashed] (0,1) node[left] {$P_{2}$} -| (4,0) node[below] {$V_{2}$};
        
        \draw (1,4) node[above left]{1};   
        \draw (4,1) node[above right]{2};  
        \draw[midar] (1,4) arc (180:270:3 and 3);
    \end{tikzpicture}
    
\end{document}

这是我从代码中得到的图片：

这是我正在尝试做的事情的一个想法：

Answer 1

tikzpicture在环境末尾附加以下代码

\fill[pattern=north east lines, pattern color=red] (4,0) -- (1,0) -- (1,4) arc (180:270:3 and 3) -- cycle;

当然，你需要添加\usetikzlibrary{patterns}你的序言。

Answer 2

如果您知道情节的功能，则可以使用另一种可能性fillbetween：

\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{arrows.meta,patterns}


\begin{document}

\begin{tikzpicture}
  \begin{axis}[
    xlabel={V},
    ylabel={P},
    yticklabels={,,},
    ytick style={draw=none},
    xticklabels={,,},
    xtick style={draw=none},
    samples=200,
    axis lines=center,
    ymin=0,xmin=0,
    ymax=10,xmax=10,
    no marks,
    every axis x label/.style={
        at={(ticklabel* cs:1.05)},
        anchor=west,
    },
    every axis y label/.style={
        at={(ticklabel* cs:1.05)},
        anchor=south,
    },
    ]
    \addplot[blue,domain=2:4,name path=A] {15*e^(-0.4*x)+2}; %plot
    \addplot[blue,domain=2:3,-Stealth] {15*e^(-0.4*x)+2}; %arrow plot
    \addplot+[black,domain=2:4,name path=B] {0};     % dummy plot
    \addplot+[pattern=north east lines,pattern color=red!60!white] fill between[of=A and B,soft clip={domain=2:4}]; % fillingbetween A and B
    
    \addplot+[dashed,black,domain=0:2] {8.74};
    \addplot+[dashed,black,domain=0:4] {5.03};
    \addplot+[black,ycomb] coordinates {(2, 8.74)};
    \addplot+[black,ycomb] coordinates {(4, 5.03)};
    
    \coordinate (m1) at (axis cs:2,8.74); %mark1
    \coordinate (m2) at (axis cs:4,5.03); %mark2

       
  \end{axis}

    \filldraw[fill=blue,draw=blue] (m1) circle(0.05) node[above] {\small 1};
    \filldraw[fill=blue,draw=blue] (m2) circle(0.05) node[right] {\small 2};


\end{tikzpicture}
\end{document}

Answer 3

编辑： 修正函数域，添加声明函数f(x)并添加了图表中缺失的元素。

变体 @Roland 回答使用patterns.meta库和稍微短一点的代码：

\documentclass[border=3.141592]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{arrows.meta,
                decorations.markings,
                patterns.meta}

\begin{document}
    \begin{tikzpicture}[
->-/.style = {decoration={%
    name=markings,
         mark=at position 0.5 with {\arrow{Stealth}}},
    postaction=decorate},
dot/.style = {circle, fill=blue, inner sep=0pt, minimum size=4pt,
              node contents={}},
                        ]
\begin{axis}[
declare function = {f(\x)=(12*e^(-1.4*\x)+1);},    
    axis lines=middle,
    xlabel=$V$, x label style={anchor=west},
    ylabel=$P$, y label style={anchor=south},
    xtick=\empty,
    ytick=\empty,
    xmin=0, xmax=5,
    ymin=0, ymax=5,
    clip=false,
    domain=1:4,
    every axis plot post/.append style={very thick, blue}
    ]
\addplot [name path=A] {f(x)}; %plot
\addplot [draw=none, name path=B] {0}; % x-domain
\addplot +[pattern={Lines[angle=45,distance={3pt}, line width=0.2pt]},
           pattern color=red] 
        fill between[of=A and B]; % patterns
\addplot [->-] {f(x)}; % for arrow on the middle of curve
%
\draw[densely dashed] (0,{f(1)}) node[left] {$P_1$} 
        -| (1,0) node[below] {$V_1$}    node[pos=0.5,dot,dot,label=1];
\draw[densely dashed] (0,{f(4)}) node[left] {$P_2$} 
        -| (4,0) node[below] {$V_2$}    node[pos=0.5,dot,dot,label=2];
\end{axis}
    \end{tikzpicture}
\end{document}