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.CMD FORMAT rd=d ct=10 im=i et=3 zt=15 pr=3 mass length time charge temperature tr=0 vm=0
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.CMD HEADER_FOOTER 1 1 *empty* *empty* ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 0 1 Creation^Date:^June^14,^1996|NModified:^September^1996|N |F|N Author:^George^Hardgrove|Npage^|P
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.TXT 7 1 36 0 0
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Times New Roman;}}\plain\cf1\fs24 \pard\qc {\fs36\b IDEAL GAS
LAW - INTRO TO MATHCAD}©\par \pard\qc by \par \par George Hardgrove
\par Chemistry Department \par St. Olaf College\par Northfield, MN
55057\par \par \pard\qc hardgrov@lars.acc.stolaf.edu}
.TXT 24 0 37 0 0
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Times New Roman;}}\plain\cf1\fs24 \pard © {\fs20 Copyright} {\fs20
George Hardgrove}{\fs20 1996}{\fs16 . }{\fs20 All rights reserved}{
\fs16 .}{\fs16 }{\fs20 You are welcome to use this document in your
own classes but commercial use is not allowed without the permission
of the author.}}
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Times New Roman;}}\plain\cf1\fs24 \pard {\b STUDENT INSTRUCTIONS}}
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Times New Roman;}}\plain\cf1\fs24 \pard \tab Welcome to MATHCAD!
This program is a combination text editor and calculator. It could be
used to write lab reports, lecture notes, etc. as any text editor can
do, but it can also do calculations and even derive formulas which
most text editors cannot do.\par \par \tab MATHCAD documents in this
course come in sections (Some of the comments in this document are
specific instructions for the St. Olaf students. Students at other
campuses should follow the instructions of their own instructor.). The
sections are::\par \par 1. A written set of instructions for a
calculation (such as this one) with a filename ending in ...ins.mcd
These instruction files are stored on the disk in case you need to
print one out. It is a good idea to print this document so that you
can use it while you are working with the executable worksheet for
this assignment.\par \par 2. The actual calculations are done in a
...run file. The instructions in the gasins.mcd file are to help you
perform the tasks in the file named gasrun.mcd.\par \par 3. If
your calculations require tabulated data, these are often stored in
......PRN files. \par }
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Times New Roman;}}\plain\cf1\fs24 \pard So now let's get
started. Find a computer with MATHCAD 6.0 available. On the program
screen you should find an icon for Mathsoft app. With the mouse
move the cursor to this icon and click on it. A new screen should
appear and you then click on the MATHCAD PLUS 6.0 icon to start the
program. A screen labeled Mathcad PLUS should appear with buttons at
the top and an empty workspace. In Windows 95 the MATHCAD icon should
take you directly to the work screen; follow the instructions of your
instructor on how to start Mathcad on the computers in your
laboratory. In the upper right corner click on the button to increase
the screen size (the square in Windows 95). \tab }
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Times New Roman;}}\plain\cf1\fs24 \pard At this point press the
open file button (second from the left in the long row). Next select
the disk drive ({\b c} for hard disk, {\b a} for floppy) where the
MATHCAD programs documents are stored. Then locate and click on the
icon for gasrun.mcd. You can double-click on this icon, or click once
on it and then click on the 'open' button and the document should
appear. At this point click on the 'Edit' menu and on 'Regions' and
then on 'View Regions.' You will note that each mathematical
expression is in its own region, and that the sections of text are in
their own regions.\par \par {\b EXERCISE 1} (very easy)\par \tab You
should note values of T, P, and V are given for a gas at what used to
be called standard pressure and temperature. What units should be
supplied to each of these quantities? Note the symbol := which
appears in these expressions. This is the 'assign value' type of
symbol - the values of the expressions on the right are assigned to
the variables on the left. Press the F9 function key. This should
cause the document to calculate values. Record the value for R. What
are its units?\par \par {\b EXERCISE 2}\par \tab Now we wish to
calculate R in different units. Change the pressure to 101325 (in
pascals) and the volume should correspond to m{\up 3}. 1 m{\up 3} = 10{
\up 3} liters. To change a number place the cursor on the number.
You may see a vertical line (called the insertion point) in among the
numbers. You can eliminate characters to the left and right of the
insertion point by pressing 'Backspace' or 'Delete.' Another way to
eliminate a number is to get the insertion point into the number and
then press the 'up-arrow' key. This should enclose the number inside
a blue box. Press 'Delete' and the number should go away to be
replaced by a rectangle with one corner chopped off called the
placeholder. Now type the new number. Press F9 to recalculate. What
are the units of T, P, and V? What are the value and units for R? }
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Times New Roman;}}\plain\cf1\fs24 \pard {\b Subscripts}\par \par
\tab In the computational document we note the equation V{\dn i}=RT/P{
\dn i}. For a given temperature T=300 K we wish to calculate values
of V corresponding to a range of values for P. By typing i:=0..30
(Type a colon ':' to get the := symbol and type a semicolon ';' to get
the ...) we choose to calculate values of P at 31 points. This is done
on the next line where to get a subscript we typed '[ ' then the
subscript immediately after the P, we then pressed the up arrow key to
select the whole quantity rather than just the subscript. This means
that we will have P values from 1 to 4 at intervals of 0.1. Next we
calculate V{\dn i} for each value of P{\dn i} using the same technique
for the subscript. Type P= and V= to see the arrays. Now we
plot a graph of V vs. P. Do one or two calculations by hand with your
calculator to check your work.\par \par {\b EXERCISE 3}\par \tab Here
you can test your understanding. Modify the computational document to
calculate V for 21 temperatures from 200 to 400 K at a pressure of
1.00 atmosphere. Adjust the quantities on the graph to get the
desired plot. You do the adjusting by clicking on the graph and then
clicking on the axis label. Now you can change the label.\par \par
\tab In the next part of the document you will see a 3-D plot where V
is shown as a surface that is a function of P and T. Information about
the 3D plot is included in the run document. \par \par Next let's
learn how to do simple symbolic operations with Mathcad. Go to page 3
of the {\b run} document.\par \par {\b Symbolic Operations}\par \tab
Solve for variable: Note the expression in the computational document
\par 'PV=nRT'. (The type of equal sign in this expression, in bold,
is the logical equal and to get it you type 'cntr ='.) To solve for V
click on V and then press the up-arrow key and hopefully you will
enclose V in a little blue box. It is now "selected." Then click on
'Symbolic', then 'solve for variable'. The answer will appear below
the original equation. \par \tab \par \tab To make this into an
equation you need to select it and put it on the clipboard. Holding
the left mouse button down move the cursor toward the expression.
When you get close enough a dotted line will surround the expression.
Click on cut (scissors) and the expression will disappear to the
clipboard. Then type 'Vcntr=' and then click on the paste button (8th
from the left) and the expression will reappear.}
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Times New Roman;}}\plain\cf1\fs24 \pard {\b Differentiate on Variable}
\par \par \tab Move the cursor down the page to an empty space and
press either the 'paste' button or type 'cntr v'. The expression for
V will then appear. Click on T and use up-arrow to select it. Then
on the 'Symbolic' menu select 'Differentiate on Variable' and the
derivative will appear below. \par \par {\b EXERCISE 4}\par \tab Go
back to the expression for V and find the derivative with respect to
P. \par \par {\b EXERCISE 5}\par \tab Enter into the worksheet the
equation PV=wRT/MP where w is the weight of the gas in grams and M is
the molecular weight in grams/mole. Use the symbolic facility to
solve for the molecular weight M. Find the derivative with respect to
T. If the temperature of a gas sample should be 5 K too high
calculate how far off the molecular weight will be.\par \par {\b Units}
\par \tab Note the illustration for units in the computational
document. Units are considered quantities multiplied by the number.
To enter 10 Kg you type '10' then * then press 'cntr u'. Usually you
can find the units you are looking for in the right-hand column.
Select the unit kg and then click on 'insert'.\par \par {\b EXERCISE 6}
\par \tab The root mean square velocity of a molecule is given by}
.EQN 69 24 42 0 0
{0:vel}NAME:\((3*{0:R}NAME*{0:T}NAME)/({0:M}NAME))
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Times New Roman;}}\plain\cf1\fs24 \pard Set up the constants
with their units and calculate the root mean square velocity for O{\dn 2}
. Hint: the square root sign is on the arithmetic pallet (the button
that looks like a calculator). The values of constants with their
units are: R=8.314 joule/(K*mole), T=300 K, and M=0.032 kg/mole.}