Exercise 1.1.22

Question

You place a frozen pie in an oven and bake it for an hour. Then you take it out and let it cool. Describe how the temperature of the pie  changes as time passes. Then sketch a rough graph of the temperature of the pie as a function of time.

Khagan Gulusoy · Accepted Answer

After placing the frozen pie of the initial temperature $T_{0}$ in the oven at time point $t_{0}$ , its temperature starts rising. As soon as its temperature converges against the temperature of the oven $T_{oven}$ , it becomes constant. When we take the pie out of the oven at time point $t_{1}$ , the temperature of the pie starts decreasing until it is equal to the room temperature $T_{room}$ . After that, the temperature of the pie will again stay constant.

\begin{figure}[H] \centering
\begin{tikzpicture}[scale=0.9]

\begin{axis}[
            width=6cm,height=6cm,
             scale only axis,
             axis lines=middle,
             xmin=0,xmax=25,
             ymin=-5,ymax=22,
             ytick={-5, 20, 14},
             yticklabels={$T_0$, $T_{	ext{oven}}$, $T_{	ext{room}}$},
             xtick={0, 4.5*pi},
             xticklabels={$t_0$, $t_1$},
             axis line style = thick,
             xlabel={$	au,$ time},
             %ylabel={$t$, temperature},
             axis on top,
             samples=50
            ]

\addplot [domain=0:8, samples=50, color=violet, ultra thick] {-25/64*(x-8)^2+20};
\addplot [domain=8:4.5*pi, samples=2, color=violet, ultra thick] {20};
\addplot [domain=4.5*pi:5.5*pi, samples=50, color=violet, ultra thick] {3*sin(deg(x))+17};
\addplot [domain=5.5*pi:24, samples=2, color=violet, ultra thick] {14};
\addplot +[dashed,gray] coordinates {(4.5*pi,0) (4.5*pi,20)};
\addplot +[dashed,gray] coordinates {(0,20) (4.5*pi,20)};
\addplot +[dashed,gray] coordinates {(0,14) (5.5*pi,14)};
  
\end{axis}

\end{tikzpicture}
\end{figure}

Exercise 1.1.22

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Exercise 1.1.22

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