Mathcad Professional 14.0 <description/> <author>Gustavus</author> <company>Parametric Technology Corporation</company> <keywords/> <revisedBy>User Name</revisedBy> </userData> <identityInfo> <revision>1</revision> <documentID>61101A97-1578-4EEE-AFBA-9305BDD8C0ED</documentID> <versionID>4CF7D70C-ADC9-4656-9A8F-E19A5BD3FCB6</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" 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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" 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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="false" optimize-expressions="false" exact-boolean="true" strings-use-origin="false" zero-over-zero="error"> <compatibility multiple-assignment="MC12" local-assignment="MC11"/> </calculationBehavior> <units> <currentUnitSystem name="mks" 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="true" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="232" 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="5" left="36" top="2.25" width="144.75" height="12" align-x="43.5" align-y="12" 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">Key for Mathcad Lab Assignment</p> </text> </region> <region region-id="7" left="24" top="32.25" width="213" height="12" align-x="27" align-y="42" 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">1. Simplify the following expressions numerically:</p> </text> </region> <region region-id="10" left="60" top="56.25" width="11.25" height="12" align-x="63" align-y="66" 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">a. </p> </text> </region> <region region-id="13" left="90" top="48.75" width="99.75" height="29.25" align-x="152.25" align-y="66" 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:plus/> <ml:apply> <ml:plus/> <ml:real>-5</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:sqrt/> <ml:real>6</ml:real> </ml:apply> <ml:real>9</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:real>9</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>76.272165526975911</ml:real> </result> </ml:eval> </math> <rendering item-idref="2"/> </region> <region region-id="15" left="60" top="86.25" width="11.25" height="12" align-x="63" align-y="96" 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">b. </p> </text> </region> <region region-id="17" left="90" top="87" width="21.75" height="12.75" align-x="99.75" align-y="96" 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">x</ml:id> <ml:real>2</ml:real> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="19" left="84" top="99" width="42.75" height="18.75" align-x="95.25" align-y="114" 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">y</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:real>5</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="37" left="168" top="111" width="27" height="12.75" align-x="177.75" align-y="120" 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="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">x</ml:id> <ml:real>-1</ml:real> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="21" left="84" top="123" width="43.5" height="12.75" align-x="94.5" align-y="132" 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">y</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>2.3890560989306495</ml:real> </result> </ml:eval> </math> <rendering item-idref="6"/> </region> <region region-id="38" left="162" top="123" width="42.75" height="18.75" align-x="173.25" align-y="138" 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="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">y</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:real>5</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="39" left="162" top="147" width="48.75" height="12.75" align-x="172.5" align-y="156" 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">y</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-4.6321205588285572</ml:real> </result> </ml:eval> </math> <rendering item-idref="8"/> </region> <region region-id="25" left="90" top="153" width="28.5" height="12.75" align-x="99.75" align-y="162" 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="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">x</ml:id> <ml:real>4.3</ml:real> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="26" left="84" top="165" width="42.75" height="18.75" align-x="95.25" align-y="180" 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="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">y</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:real>5</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="27" left="84" top="189" width="39" height="12.75" align-x="94.5" align-y="198" 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">y</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>68.699793699595773</ml:real> </result> </ml:eval> </math> <rendering item-idref="11"/> </region> <region region-id="44" left="66" top="212.25" width="11.25" height="12" align-x="69" align-y="222" 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">c. </p> </text> </region> <region region-id="46" left="84" top="213" width="125.25" height="12.75" align-x="166.5" align-y="222" 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:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve">ln</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">tan</ml:id> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:factorial/> <ml:real>4</ml:real> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-22.901387711331889</ml:real> </result> </ml:eval> </math> <rendering item-idref="12"/> </region> <region region-id="49" left="36" top="248.25" width="11.25" height="12" align-x="39" align-y="258" 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">2. </p> </text> </region> <region region-id="52" left="60" top="242.25" width="75.75" height="27.75" align-x="69" align-y="258" 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">r</ml:id> <ml:apply> <ml:mult/> <ml:real>0.08314</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">bar</ml:id> </ml:apply> <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="13"/> </region> <region region-id="54" left="150" top="249" width="39.75" height="12.75" align-x="159" align-y="258" 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">t</ml:id> <ml:apply> <ml:mult/> <ml:real>300</ml:real> <ml:id xml:space="preserve">K</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="64" left="48" top="278.25" width="75.75" height="33.75" align-x="58.5" align-y="294" 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:mult/> <ml:apply> <ml:mult/> 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width="37.5" height="12.75" align-x="77.25" align-y="330" 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">n</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>1</ml:real> <ml:id xml:space="preserve">mol</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="74" left="156" top="321" width="31.5" height="12.75" align-x="167.25" align-y="330" 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">v</ml:id> <ml:apply> <ml:mult/> <ml:real>1</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="18"/> </region> <region 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</ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="102" left="66" top="356.25" width="65.25" height="27.75" align-x="101.25" align-y="372" 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_ideal</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">r</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">v</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="20"/> </region> <region region-id="78" left="66" top="387" width="103.5" height="18.75" align-x="100.5" align-y="402" 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">P_ideal</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>2494200</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="pascal"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="21"/> </region> <region region-id="94" left="216" top="387" width="97.5" height="18.75" align-x="249" align-y="402" 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">P_vdw</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>2159631.1526479749</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="pascal"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="22"/> </region> <region region-id="91" left="66" top="411" width="83.25" height="12.75" align-x="100.5" align-y="420" 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">P_ideal</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">atm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>24.615840118430793</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="atmosphere"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="23"/> </region> <region region-id="97" left="216" top="411" width="80.25" height="12.75" align-x="249" align-y="420" 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">P_vdw</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">bar</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>21.596311526479749</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="bar"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="24"/> </region> <region region-id="92" left="66" top="429" width="81.75" height="12.75" align-x="100.5" 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">P_ideal</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">bar</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>24.942</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="bar"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="25"/> </region> <region region-id="98" left="216" top="429" width="81.75" height="12.75" align-x="249" 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">P_vdw</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">atm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>21.313902320730076</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="atmosphere"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="26"/> </region> <region region-id="101" left="36" top="465" width="7.5" height="12.75" align-x="39" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:real xmlns:ml="http://schemas.mathsoft.com/math30">3.</ml:real> </math> <rendering item-idref="27"/> </region> <region region-id="203" left="60" top="464.25" width="251.25" height="12" align-x="69.75" align-y="474" 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">Note: I re-defined my variables to remove the use of units. </p> </text> </region> <region region-id="210" left="84" top="489" width="42.75" height="12.75" align-x="99" align-y="498" 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">a1</ml:id> <ml:real>4.304</ml:real> </ml:define> </math> <rendering item-idref="28"/> </region> <region region-id="211" left="156" top="489" width="43.5" height="12.75" align-x="171.75" align-y="498" 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">b1</ml:id> <ml:real>0.037</ml:real> </ml:define> </math> <rendering item-idref="29"/> </region> <region region-id="212" left="216" top="489" width="50.25" height="12.75" align-x="229.5" align-y="498" 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">r1</ml:id> <ml:real>0.08314</ml:real> </ml:define> </math> <rendering item-idref="30"/> </region> <region region-id="213" left="78" top="500.25" width="225" height="33.75" align-x="190.5" align-y="522" 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">P_vdw2</ml:id> <ml:boundVars> <ml:id xml:space="preserve">n1</ml:id> <ml:id xml:space="preserve">t1</ml:id> <ml:id xml:space="preserve">vol</ml:id> <ml:id xml:space="preserve">a1</ml:id> <ml:id xml:space="preserve">b1</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">n1</ml:id> <ml:id xml:space="preserve">r1</ml:id> </ml:apply> <ml:id xml:space="preserve">t1</ml:id> </ml:apply> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">vol</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">n1</ml:id> <ml:id xml:space="preserve">b1</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">a1</ml:id> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">n1</ml:id> <ml:id xml:space="preserve">vol</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="31"/> </region> <region region-id="214" left="102" top="536.25" width="123" height="27.75" align-x="183.75" align-y="552" 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="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">P_ideal</ml:id> <ml:boundVars> <ml:id xml:space="preserve">n1</ml:id> <ml:id xml:space="preserve">t1</ml:id> <ml:id xml:space="preserve">vol</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">n1</ml:id> <ml:id xml:space="preserve">r1</ml:id> </ml:apply> <ml:id xml:space="preserve">t1</ml:id> </ml:apply> <ml:id xml:space="preserve">vol</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="32"/> </region> <region region-id="216" left="132" top="573" width="65.25" height="12.75" align-x="150.75" align-y="582" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="00000000-0000-0000-0000-000000000000" version-id="00000000-0000-0000-0000-000000000000" branch-id="00000000-0000-0000-0000-000000000000" revision-num="206786484" is-modified="true" region-id="0" href="C:\DOCUME~1\admin\LOCALS~1\Temp\mathcadintro_2001.mcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="00000000-0000-0000-0000-000000000000" version-id="00000000-0000-0000-0000-000000000000" branch-id="00000000-0000-0000-0000-000000000000" revision-num="205639284" is-modified="true" region-id="0" href="C:\DOCUME~1\admin\LOCALS~1\Temp\mathcadintro_2001.mcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">0f266f3e138dad056ee28d384c7ef22d</contentHash> <ml:define> <ml:id xml:space="preserve">vol</ml:id> <ml:range> <ml:sequence> <ml:real>0.5</ml:real> <ml:real>0.6</ml:real> </ml:sequence> <ml:real>2</ml:real> </ml:range> </ml:define> </ml:provenance> </math> <rendering item-idref="33"> <element-image-map> <box left="1.5" top="0.75" width="63.75" height="11.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="223" left="84" top="638.25" width="180" height="15" align-x="87" align-y="648" 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">A plot of V vs. P_ideal and P_vdw for NH<sub>3</sub> </p> </text> </region> <region region-id="217" left="36" top="654" width="241.5" height="129.75" align-x="36" align-y="654" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="34"/> <rendering item-idref="35"/> </region> <region region-id="225" left="36" top="800.25" width="310.5" height="12" align-x="41.25" align-y="810" 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">To test my definition of vol as an array, I typed <i>vol = </i>to get the following:</p> </text> </region> <region region-id="227" left="90" top="819" width="43.5" height="277.5" align-x="96" align-y="828" 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">vol</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="16" cols="1"> <ml:real>0.5</ml:real> <ml:real>0.6</ml:real> <ml:real>0.7</ml:real> <ml:real>0.79999999999999993</ml:real> <ml:real>0.89999999999999991</ml:real> <ml:real>0.99999999999999989</ml:real> <ml:real>1.0999999999999999</ml:real> <ml:real>1.1999999999999997</ml:real> <ml:real>1.2999999999999998</ml:real> <ml:real>1.4</ml:real> <ml:real>1.4999999999999998</ml:real> <ml:real>1.5999999999999996</ml:real> <ml:real>1.6999999999999997</ml:real> <ml:real>1.7999999999999998</ml:real> <ml:real>1.8999999999999997</ml:real> <ml:real>1.9999999999999996</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="36"/> </resultFormat> </math> <rendering item-idref="37"/> </region> <region region-id="229" left="18" top="1106.25" width="11.25" height="12" align-x="21" align-y="1116" 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">4. </p> </text> </region> <region region-id="231" left="42" top="1110" width="358.5" height="40.5" align-x="140.25" align-y="1134" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:integral/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">θ</ml:id> </ml:boundVars> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">θ</ml:id> </ml:apply> <ml:real>6</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">θ</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:lambda> </ml:apply> <ml:symResult> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:real>5</ml:real> <ml:id xml:space="preserve">θ</ml:id> </ml:apply> <ml:real>128</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">θ</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">θ</ml:id> </ml:apply> <ml:real>7</ml:real> </ml:apply> </ml:apply> <ml:real>8</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> 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