Mathcad Professional 14.0 <description/> <author>John N. Harb</author> <company/> <keywords/> <revisedBy>student</revisedBy> </userData> <identityInfo> <revision>1</revision> <documentID>C72CA63F-8A50-420C-960C-6CAB5FCD4D95</documentID> <versionID>4681C292-8460-4114-B639-78B88381E1AF</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 1"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" 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font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="List"> <blockAttr margin-left="14.4" margin-right="0" text-indent="-14.4" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Indent"> <blockAttr margin-left="108" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Title"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="24" font-weight="bold" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Subtitle" base-style="Title"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="18" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> </textStyles> </textRendering> <mathRendering equation-color="#000"> <operators multiplication="narrow-dot" derivative="derivative" literal-subscript="large" definition="colon-equal" global-definition="triple-equal" local-definition="left-arrow" equality="bold-equal" symbolic-evaluation="right-arrow"/> <mathStyles> <mathStyle name="Variables" font-family="Times New Roman" font-charset="0" font-size="14" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Constants" font-family="Times New Roman" font-charset="0" font-size="14" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 1" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 2" font-family="Courier New" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 3" font-family="Arial" font-charset="0" font-size="10" font-weight="bold" font-style="normal" underline="false"/> <mathStyle name="User 4" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="italic" underline="false"/> <mathStyle name="User 5" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 6" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 7" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Math Text Font" font-family="Times New Roman" font-charset="0" font-size="14" font-weight="normal" font-style="normal" underline="false"/> </mathStyles> <dimensionNames mass="mass" length="length" time="time" current="current" thermodynamic-temperature="temperature" luminous-intensity="luminosity" amount-of-substance="substance" display="false"/> <symbolics derivation-steps-style="vertical-insert" show-comments="false" evaluate-in-place="false"/> <results numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="false" show-footer-frame="false" header-footer-start-page="1" paper-code="1" orientation="portrait" print-single-page-width="false" page-width="612" page-height="792"> <margins left="86.4" right="86.4" top="86.4" bottom="86.4"/> <header use-full-page-width="false"/> <footer use-full-page-width="false"/> </pageModel> <colorModel background-color="#fff" default-highlight-color="#ffff80"/> <language math="en" UI="en"/> </presentation> <calculation> <builtInVariables array-origin="0" convergence-tolerance="0.001" constraint-tolerance="0.001" random-seed="1" prn-precision="4" prn-col-width="8"/> <calculationBehavior automatic-recalculation="true" matrix-strict-singularity-check="true" optimize-expressions="false" exact-boolean="true" strings-use-origin="false" zero-over-zero="0"> <compatibility multiple-assignment="MC12" local-assignment="MC12"/> </calculationBehavior> <units> <currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="in"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="false" save-text-images="false" screen-dpi="120"/> <miscellaneous> <handbook handbook-region-tag-ub="65" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="3" left="18" top="9" width="338.4" height="22.8" align-x="40.8" align-y="24" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="16">Example<sp count="3"/>van der Waals Equation of State (CO</f> <f size="16"> <sub>2</sub> </f> <f size="16">)</f> </p> </text> </region> <region region-id="5" left="54" top="48" width="75" height="21.6" align-x="78" align-y="60" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="c">T</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>304.2</ml:real> <ml:id xml:space="preserve">K</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="10" left="204" top="38.4" width="102" height="36.6" align-x="223.2" align-y="60" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">R</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>8.314</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">mol</ml:id> <ml:id xml:space="preserve">K</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="21" left="342" top="48" width="62.4" height="16.8" align-x="359.4" align-y="60" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">P</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>50</ml:real> <ml:id xml:space="preserve">atm</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="22" left="342" top="72" width="58.8" height="16.8" align-x="360" align-y="84" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>400</ml:real> <ml:id xml:space="preserve">K</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="7" left="54" top="78" width="78.6" height="21.6" align-x="77.4" align-y="90" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="c">P</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>72.9</ml:real> <ml:id xml:space="preserve">atm</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="12" left="24" top="113.4" width="182.4" height="15.6" align-x="41.4" align-y="126" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="14">Define Interaction Parameters</f> </p> </text> </region> <region region-id="13" left="48" top="142.2" width="91.2" height="51.6" align-x="64.2" align-y="174" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>27</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="c">T</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>64</ml:real> <ml:id xml:space="preserve" subscript="c">P</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="17" left="186" top="147" width="112.8" height="47.4" align-x="201" align-y="174" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">a</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.36532392012509246</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilogram"/> <unitReference unit="meter" power-numerator="5"/> <unitReference unit="mole" power-numerator="-2"/> <unitReference unit="second" power-numerator="-2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="8"/> </region> <region region-id="18" left="42" top="213.6" width="60.6" height="46.2" align-x="58.8" align-y="240" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">b</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">R</ml:id> <ml:id xml:space="preserve" subscript="c">T</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>8</ml:real> <ml:id xml:space="preserve" subscript="c">P</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="19" left="180" top="213" width="126" height="42" align-x="195.6" align-y="240" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">b</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>4.2799145884925953E-05</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="meter" power-numerator="3"/> <unitReference unit="mole" power-numerator="-1"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="10"/> </region> <region region-id="31" left="30" top="281.4" width="272.4" height="15.6" align-x="47.4" align-y="294" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="14">Define Function- equation to solve for volume</f> </p> </text> </region> <region region-id="20" left="42" top="320.4" width="141" height="42" align-x="79.2" align-y="342" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">V</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">P</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">R</ml:id> <ml:id xml:space="preserve">T</ml:id> </ml:apply> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">V</ml:id> <ml:id xml:space="preserve">b</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">V</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="23" left="234" top="326.4" width="160.8" height="36.6" align-x="297.6" align-y="348" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>2</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">mol</ml:id> </ml:apply> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>3458419.6532784132</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="pascal"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="12"/> </region> <region region-id="34" left="18" top="389.4" width="406.8" height="15.6" align-x="35.4" align-y="402" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="14">Define initial guess using ideal gas law.<sp count="2"/>Use Root Function to Solve</f> </p> </text> </region> <region region-id="25" left="60" top="416.4" width="57" height="36.6" align-x="79.2" align-y="438" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">V</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">R</ml:id> <ml:id xml:space="preserve">T</ml:id> </ml:apply> <ml:id xml:space="preserve">P</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="29" left="156" top="416.4" width="84.6" height="36.6" align-x="174" align-y="438" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">V</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">mol</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.65642240315815448</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="liter"/> <unitReference unit="mole" power-numerator="-1"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="14"/> </region> <region region-id="24" left="48" top="468" width="134.4" height="21.6" align-x="91.8" align-y="480" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="vdw">V</ml:id> <ml:apply> <ml:id xml:space="preserve">root</ml:id> <ml:sequence> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">V</ml:id> </ml:apply> <ml:id xml:space="preserve">V</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="27" left="222" top="458.4" width="109.2" height="36.6" align-x="264.6" align-y="480" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ff0" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="vdw">V</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">mol</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.58497052138744166</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="liter"/> <unitReference unit="mole" power-numerator="-1"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="16"/> </region> <region region-id="48" left="24" top="509.4" width="207" height="15.6" align-x="48" align-y="522" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="14">Compare to Corresponding States</f> </p> </text> </region> <region region-id="65" left="276" top="516.6" width="90" height="27.6" align-x="291" align-y="528" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="12">From Table 5.4-2</f> </p> </text> </region> <region region-id="49" left="36" top="524.4" width="52.2" height="41.4" align-x="58.8" align-y="546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" 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