.MCAD 304020000 1 79 298 0
.CMD PLOTFORMAT
0 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 21 15 0 0 3 
.CMD FORMAT  rd=d ct=10 im=i et=3 zt=15 pr=3 mass length time charge temperature tr=0 vm=0
.CMD SET ORIGIN 0
.CMD SET TOL 0.001000000000000
.CMD SET PRNCOLWIDTH 8
.CMD SET PRNPRECISION 4
.CMD PRINT_SETUP 1.000000 1.000000 1.200000 1.200000 0
.CMD HEADER_FOOTER 1 1 *empty* *empty* ^^^^^^^^^^^^^^^^^^^^^ 0 1 Created:^June^14,^1996|NModified:^|D |F Author:^George^Hardgrove|Npage^|P
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.CMD UNITS U=1
.CMD DIMENSIONS_ANALYSIS 0 0
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.TXT 4 1 298 0 0
Cg b78.000000,78.000000,167
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Times New Roman;}}\plain\cf1\fs24 \pard\qc {
\cf2\fs36\b IDEAL GAS LAW - INTRO TO MATHCAD\par }\pard {\cf2 
COMPUTATIONAL DOCUMENT}\par \pard\qc {\cf2 \par }\pard\qc {\cf2 by 
\par \par George Hardgrove\par Chemistry Department\par St. Olaf 
College\par Northfield, MN 55057\par \par }\pard\qc {\cf2 
hardgrov@lars.acc.stolaf.edu}}
.TXT 28 0 284 0 0
Cg b78.000000,78.000000,186
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;\red0\green0\blue0;}{
\fonttbl{\f0\fcharset0\fnil Times New Roman;}}\plain\cf1\fs24 \pard {
\cf2 © }{\cf2\fs20 Copyright}{\cf2  }{\cf2\fs20 George Hardgrove}{\cf2
\fs20  1996}{\cf2\fs16 .  }{\cf2\fs20 All rights reserved}{\cf2\fs16 .}{
\cf2\fs16   }{\cf2\fs20 You are welcome to use this document in your 
own classes but commercial use is not allowed without the permission 
of the author.}}
.TXT 8 0 109 0 0
Cg a73.000000,73.000000,39
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs24 \pard A.  Simple 
Calculations on the gas laws}
.EQN 4 0 99 0 0
{0:T}NAME:273.16
.EQN 0 14 111 0 0
{0:P}NAME:1.0000
.EQN 0 12 110 0 0
{0:V}NAME:22.414
.EQN 6 -26 102 0 0
{0:R}NAME:({0:P}NAME*{0:V}NAME)/({0:T}NAME)
.EQN 0 12 127 0 0
{0:R}NAME={18997}?_n_u_l_l_
.TXT 5 -11 132 0 0
Cg a72.000000,72.000000,45
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs24 \pard Now we 
calculate V for a series of P values. }
.EQN 4 -1 137 0 0
{0:R}NAME:0.08205
.EQN 0 16 138 0 0
{0:T}NAME:300
.TXT 0 10 142 0 0
Cg a45.000000,45.000000,25
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs24 \pard Set the values 
of R and T}
.EQN 4 -25 122 0 0
{0:i}NAME:0;30
.TXT 0 25 144 0 0
Cg a47.000000,47.000000,22
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs24 \pard Calculate at 
31 points}
.EQN 4 -25 126 0 0
({0:P}NAME)[({0:i}NAME):1+({0:i}NAME)/(10)
.TXT 0 25 146 0 0
Cg a47.000000,47.000000,25
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs24 \pard Calculate P at 
each point}
.EQN 7 -15 296 0 0
({0:V}NAME)[({0:i}NAME):({0:R}NAME*{0:T}NAME)/(({0:P}NAME)[({0:i}NAME))
.TXT 0 12 297 0 0
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs24 \pard Calculate V at 
each point and plot the graph}
.EQN 2 1 295 0 0
&&(_n_u_l_l_&_n_u_l_l_)&({0:V}NAME)[({0:i}NAME)@&&(_n_u_l_l_&_n_u_l_l_)&({0:P}NAME)[({0:i}NAME)
0 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
3 1 0 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 21 15 12 0 3 
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C x1,1,0,0
.TXT 5 1 153 0 0
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs24 \pard A 3-d graph - 
V as a function of P and T.}
.TXT 3 43 291 0 0
Cg a27.000000,27.000000,77
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs24 \pard Setting up the 
calculation\par \par \pard Choose number of points\par to plot in each 
direction}
.EQN 4 -42 22 0 0
{0:N}NAME:10
.EQN 3 0 21 0 0
{0:i}NAME:0;{0:N}NAME
.EQN 3 0 23 0 0
{0:j}NAME:0;{0:N}NAME
.TXT 2 50 292 0 0
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs24 \pard Limits of P 
and T}
.EQN 1 -50 26 0 0
{0:Pmax}NAME:5
.EQN 0 9 114 0 0
{0:Pmin}NAME:1
.EQN 0 9 113 0 0
{0:Tmin}NAME:100
.EQN 0 12 112 0 0
{0:Tmax}NAME:500
.TXT 3 21 293 0 0
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs24 \pard Steps in P and T}
.EQN 1 -51 30 0 0
{0:\DP}NAME:({0:Pmax}NAME-{0:Pmin}NAME)/({0:N}NAME)
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{0:\DT}NAME:({0:Tmax}NAME-{0:Tmin}NAME)/({0:N}NAME)
.EQN 5 -18 32 0 0
({0:P}NAME)[({0:i}NAME):{0:Pmin}NAME+{0:i}NAME*{0:\DP}NAME
.EQN 0 20 116 0 0
({0:T}NAME)[({0:j}NAME):{0:Tmax}NAME-{0:j}NAME*{0:\DT}NAME
.TXT 0 22 161 0 0
Cg a28.000000,28.000000,40
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs24 \pard P and T 
defined as single column arrays.}
.EQN 4 -42 34 0 0
{0:R}NAME:0.0821
.TXT 5 39 261 0 0
Cg a28.000000,28.000000,40
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs24 \pard 2-D array of V 
as a function of P and T.}
.EQN 1 -39 36 0 0
({0:Vol}NAME)[({0:j}NAME,{0:i}NAME):({0:R}NAME*({0:T}NAME)[({0:j}NAME))/(({0:P}NAME)[({0:i}NAME))
.TXT 6 36 294 0 0
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\fonttbl{\f0\fcharset0\fnil Times New Roman;}{\f1\fcharset0\fnil Arial;}}
\plain\cf1\fs24 \pard Mathcad displays the array indices as the x,y 
plane at the bottom of the figure to the left. There are 11 x 11 
elements in the Vol{\f1\dn j,i} array. You can see this as the axis 
label of the base of the figure, they range from 0 to 10. The value of Vol{
\f1\dn j,i} is shown as the vertical height above the x,y plane. Each 
curve extending from left to right is an isotherm. The temperature of 
each isotherm is T{\f1\dn j. }These are standard PV curves. \par \par 
The lines extending from the front to the back are isobars. Each one 
shows the variation of volume with temperature at a constant pressure. {
\cf2\b Are high temperatures to the front or back of the figure?}\par 
\par {\f1  }If you type, in a clean area of the worksheet, Vol 
followed by a plain = sign you will see the matrix. You can do this 
for T and P too. }
.EQN 1 -39 38 0 0
{0:Vol}NAME{1 4 3 10 35 0 35 30 0 1 0 1 4 -1 1 0 1 0 1 4 -1 1 0 1 1 1 4 -1 1 21 0 16777215 0 100 2 NO-TITLE}{57}
2 5 21 21 0 1 1.5 7
1 5 4 3 0 4 1 0
3 1 2 0.1
.TXT 48 0 165 0 0
C x1,1,0,0
.EQN 12 3 168 0 0
{0:P}NAME*{0:V}NAMEś{0:n}NAME*{0:R}NAME*{0:T}NAME
.TXT 0 25 174 0 0
Cg a45.000000,45.000000,21
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs24 \pard Expression for PV=nRT}
.EQN 6 -25 274 0 0
{0:V}NAMEś{0:n}NAME*{0:R}NAME*({0:T}NAME)/({0:P}NAME)
.TXT 10 24 200 0 0
Cg a44.000000,44.000000,97
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs24 \pard In these space 
to the left find the expression for V\par and its derivatives with 
respect to T and P.}
.TXT 31 -27 213 0 0
Cg a72.000000,72.000000,62
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs24 \pard Units      
Note how units are carried through on this example.}
.EQN 5 0 237 0 0
{0:T}NAME:300*{0:K}NAME
.EQN 0 12 243 0 0
{0:P}NAME:0.0023*{0:atm}NAME
.EQN 0 15 244 0 0
{0:n}NAME:0.225*{0:mole}NAME
.EQN 0 15 245 0 0
{0:R}NAME:(0.08206*{0:liter}NAME*{0:atm}NAME)/({0:K}NAME*{0:mole}NAME)
.EQN 7 -42 246 0 0
{0:V}NAME:({0:n}NAME*{0:R}NAME*{0:T}NAME)/({0:P}NAME)
.EQN 0 17 247 0 0
{0:V}NAME={0}?_n_u_l_l_
.TXT 7 -16 248 0 0
Cg a72.000000,72.000000,45
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs24 \pard Work out the 
exercise on gas velocities here.}