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<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field style="Heading 3" italic="false" layout="Heading 3"><Font italic="false">Example 2.2.7 Differential Algebraic Equations</Font></Text-field>
</Input>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">There are two dependent variables L and T.  Here x<Font subscript="true">2</Font> is the independent variable as x<Font subscript="true">1</Font> can be replaced using the relation x<Font subscript="true">1</Font> + x<Font subscript="true">2</Font> = 1.  the algebraic equation k<Font subscript="true">1</Font>x<Font subscript="true">1</Font> + k<Font subscript="true">2</Font>x<Font subscript="true">2</Font> = 1 governs the temperature.  The differential equation is obtained using the differentiating equation k<Font subscript="true">1</Font>x<Font subscript="true">1</Font> + k<Font subscript="true">2</Font>x<Font subscript="true">2</Font> = 1 .  The initial condition is found by substituting values for constants and x<Font subscript="true">2</Font> into equation k<Font subscript="true">1</Font>x<Font subscript="true">1</Font> + k<Font subscript="true">2</Font>x<Font subscript="true">2</Font> = 1.</Text-field>
</Input>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:</Text-field>
</Input>
</Group>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(plots):</Text-field>
</Input>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The differential equation is entered here:</Text-field>
</Input>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[1]:=diff(L(x2),x2)=L(x2)/x2/(k[2]-1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JIkxHRiU2I0kjeDJHRiVGMCooRi1GJ0YwISIiLCYmSSJrR0YlNiMiIiNGJ0YnRjJGMg==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJMRzYiNiNJI3gyR0YpRisqKEYnIiIiRishIiIsJiZJImtHRik2IyIiI0YtRi5GLUYu</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The algebraic equation is entered here:</Text-field>
</Input>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[2]:=k[1]*x1+k[2]*x2-1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiMsKComJkkia0dGJTYjIiIiRi1JI3gxR0YlRi1GLSomJkYrRiZGLUkjeDJHRiVGLUYtRi0hIiI=">LCgqJiZJImtHNiI2IyIiIkYoSSN4MUdGJkYoRigqJiZGJTYjIiIjRihJI3gyR0YmRihGKCEiIkYo</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Relations for the equilibrium rations and the mole fraction are entered:</Text-field>
</Input>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">k[1]:=P1/P;k[2]:=P2/P;x1:=1-x2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJImtHNiI2IyIiIiomSSNQMUdGJUYnSSJQR0YlISIi">KiZJI1AxRzYiIiIiSSJQR0YkISIi</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJImtHNiI2IyIiIyomSSNQMkdGJSIiIkkiUEdGJSEiIg==">KiZJI1AyRzYiIiIiSSJQR0YkISIi</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjeDFHNiIsJiIiIkYmSSN4MkdGJCEiIg==">LCYiIiJGI0kjeDJHNiIhIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The Antoine equation is entered here.</Text-field>
</Input>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">P1:=10^(A[1]+B[1]/(T(x2)+C[1]));P2:=10^(A[2]+B[2]/(T(x2)+C[2]));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjUDFHNiIpIiM1LCYmSSJBR0YkNiMiIiJGKyomJkkiQkdGJEYqRissJi1JIlRHRiQ2I0kjeDJHRiRGKyZJIkNHRiRGKkYrISIiRis=">KSIjNSwmJkkiQUc2IjYjIiIiRikqJiZJIkJHRidGKEYpLCYtSSJUR0YnNiNJI3gyR0YnRikmSSJDR0YnRihGKSEiIkYp</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjUDJHNiIpIiM1LCYmSSJBR0YkNiMiIiMiIiIqJiZJIkJHRiRGKkYsLCYtSSJUR0YkNiNJI3gyR0YkRiwmSSJDR0YkRipGLCEiIkYs">KSIjNSwmJkkiQUc2IjYjIiIjIiIiKiYmSSJCR0YnRihGKiwmLUkiVEdGJzYjSSN4MkdGJ0YqJkkiQ0dGJ0YoRiohIiJGKg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Numerical values for the constants are entered:</Text-field>
</Input>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">P:=760*1.2;A[1]:=6.90565;B[1]:=-1211.033;C[1]:=220.79;A[2]:=6.95464;B[2]:=-1344.8;C[2]:=219.482;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiUEc2IiQiJT8iKiEiIg==">JCIlPyIqISIi</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJIkFHNiI2IyIiIiQiJ2wwcCEiJg==">JCInbDBwISIm</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJIkJHNiI2IyIiIiQhKEw1QCIhIiQ=">JCEoTDVAIiEiJA==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJIkNHNiI2IyIiIiQiJno/IyEiIw==">JCImej8jISIj</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJIkFHNiI2IyIiIyQiJ2thcCEiJg==">JCIna2FwISIm</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJIkJHNiI2IyIiIyQhJltNIiEiIg==">JCEmW00iISIi</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJIkNHNiI2IyIiIyQiJyNbPiMhIiQ=">JCInI1s+IyEiJA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The algebraic equation simplifies as:</Text-field>
</Input>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[2];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgqJikiIzUsJiQiJ2wwcCEiJiIiIiokLCYtSSJURzYiNiNJI3gyR0YvRiokIiZ6PyMhIiNGKiEiIiQhKEw1QCIhIiRGKiwmRipGKkYxRjVGKiQiK0c3XCc0IiEjNyomKUYlLCYkIidrYXBGKUYqKiQsJkYtRiokIicjWz4jRjhGKkY1JCEmW00iRjVGKkYxRipGOkY1Rio=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The initial condition for the temperature is found as:</Text-field>
</Input>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ti:=fsolve(subs(T(x2)=Ti,x2=0.4,eq[2]),Ti);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjVGlHNiIkIitDKDMmZSYqISIp">JCIrQygzJmUmKiEiKQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[1];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJMRzYiNiNJI3gyR0YpRisqKEYnIiIiRishIiIsJikiIzUsJiQiJ2thcCEiJkYtKiQsJi1JIlRHRilGKkYtJCInI1s+IyEiJEYtRi4kISZbTSJGLiQiK0c3XCc0IiEjN0YuRi1GLg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The differential equation for T is obtained by differentiating the algebraic equation:</Text-field>
</Input>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[3]:=diff(eq[2],x2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiQsKiouJCIraHEpeUsiISIqIiIiKSIjNSwmJCInbDBwISImRi0qJiQiKEw1QCIhIiRGLSwmLUkiVEdGJTYjSSN4MkdGJUYtJCImej8jISIjRi0hIiJGQEYtKUY4IiIjRkAtSSVkaWZmRyUqcHJvdGVjdGVkRzYkRjlGPEYtLUkjbG5HNiRGRUkoX3N5c2xpYkdGJTYjRi9GLSwmRi1GLUY8RkBGLUYtKiYkIitHN1wnNCIhIzdGLUYuRi1GQCouJCIrLjljdTlGLEYtKUYvLCYkIidrYXBGM0YtKiYkIiZbTSJGQEYtLCZGOUYtJCInI1s+I0Y3Ri1GQEZARi0pRmVuRkJGQEZDRi1GR0YtRjxGLUYtKiZGTkYtRlRGLUYt">LCoqLCkiIzUsJiQiJ2wwcCEiJiIiIiokLCYtSSJURzYiNiNJI3gyR0YvRiokIiZ6PyMhIiNGKiEiIiQhKEw1QCIhIiRGKkYsRjQtSSVkaWZmRyUqcHJvdGVjdGVkRzYkRi1GMUYqLUkjbG5HNiRGO0koX3N5c2xpYkdGLzYjRiVGKiwmRipGKkYxRjVGKiQiK2hxKXlLIiEiKkYkJCErRzdcJzQiISM3KiwpRiUsJiQiJ2thcEYpRioqJCwmRi1GKiQiJyNbPiNGOEYqRjUkISZbTSJGNUYqRk9GNEY5RipGPUYqRjFGKiQiKy45Y3U5RkVGSiQiK0c3XCc0IkZI</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The dependent variables are entered here:</Text-field>
</Input>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">vars:=(L(x2),T(x2));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkldmFyc0c2IjYkLUkiTEdGJDYjSSN4MkdGJC1JIlRHRiRGKA==">NiQtSSJMRzYiNiNJI3gyR0YlLUkiVEdGJUYm</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The governing equations are entered here:</Text-field>
</Input>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=(eq[1],eq[3]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXFzRzYiNiQvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JIkxHRiQ2I0kjeDJHRiRGLiooRisiIiJGLiEiIiwmKiYkIitHN1wnNCIhIzdGMCkiIzUsJiQiJ2thcCEiJkYwKiYkIiZbTSJGMUYwLCYtSSJUR0YkRi1GMCQiJyNbPiMhIiRGMEYxRjFGMEYwRjBGMUYxLCoqLiQiK2hxKXlLIiEiKkYwKUY4LCYkIidsMHBGPEYwKiYkIihMNUAiRkVGMCwmRkFGMCQiJno/IyEiI0YwRjFGMUYwKUZSIiIjRjEtRig2JEZBRi5GMC1JI2xuRzYkRilJKF9zeXNsaWJHRiQ2I0Y4RjAsJkYwRjBGLkYxRjBGMComRjRGMEZLRjBGMSouJCIrLjljdTlGSkYwRjdGMClGQEZXRjFGWEYwRlpGMEYuRjBGMEYzRjA=">NiQvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JIkxHNiI2I0kjeDJHRipGLCooRigiIiJGLCEiIiwmKSIjNSwmJCIna2FwISImRi4qJCwmLUkiVEdGKkYrRi4kIicjWz4jISIkRi5GLyQhJltNIkYvJCIrRzdcJzQiISM3Ri9GLkYvLCoqLClGMiwmJCInbDBwRjZGLiokLCZGOUYuJCImej8jISIjRi5GLyQhKEw1QCJGPUYuRkpGTS1GJTYkRjlGLEYuLUkjbG5HNiRGJkkoX3N5c2xpYkdGKjYjRjJGLiwmRi5GLkYsRi9GLiQiK2hxKXlLIiEiKkZFJCErRzdcJzQiRkIqLEYxRi5GOEZNRlBGLkZSRi5GLEYuJCIrLjljdTlGWkYxRkA=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The initial conditions are entered here.</Text-field>
</Input>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ICs:=(L(0.4)=100,T(0.4)=Ti);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkSUNzRzYiNiQvLUkiTEdGJDYjJCIiJSEiIiIkKyIvLUkiVEdGJEYpJCIrQygzJmUmKiEiKQ==">NiQvLUkiTEc2IjYjJCIiJSEiIiIkKyIvLUkiVEdGJkYnJCIrQygzJmUmKiEiKQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The numerical solution is obtained as:</Text-field>
</Input>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eqs,ICs},{vars},type=numeric);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The solution obtained is plotted here:</Text-field>
</Input>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">odeplot(sol,[x2,L(x2)],0.4..0.9,title=&quot;Figure Exp. 2.2.20&quot;,axes=boxed,thickness=4);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="300" type="two-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">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</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">odeplot(sol,[x2,T(x2)],0.4..0.9,title=&quot;Figure Exp. 2.2.21&quot;,color=green,axes=boxed,thickness=4);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="400" type="two-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">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</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The moles of liquid remaining as found as:</Text-field>
</Input>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol(0.9);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NyUvSSN4Mkc2IiQiIiohIiIvLUkiTEdGJTYjRiQkIjNrJj1sRWs9aSRvISM8Ly1JIlRHRiVGLCQiM2NvJT0uLndrNyIhIzo=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol(0.9)[2];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">Ly1JIkxHNiI2I0kjeDJHRiUkIjNrJj1sRWs9aSRvISM8</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">At the end of distillation, 6.83 moles of liquid remain.</Text-field>
</Input>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>