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[RETURN] to Chem 623 .
Solving problems with TK Solver Plus
TK Solver Plus is a tool for numerically solving sets of
equations, even when you can't (or don't want to) get an explicit
algebraic solution for the problem. All you do is list all the
equations that relate to the problem, then specify the values of any
variables that are known. The program then calculates the values of
any unknown variable that can be calculated according to the rules of
algebra, automatically solving the equations and making substitutions
as needed. (TK Solver Plus provides numerical answers only; it does
not provide symbolic solutions and does not "show its work",
that is, tell you what particular substitutions it took to arrive at
an answer.)
TK Solver Plus lets you explore the behavior of mathematically
inconvenient systems (such as a Van der Walls real gas) and crank out
the answers to numeric word problems much more simply than by using a
hand calculator, writing programs, or using a spreadsheet. The big
advantage over a spreadsheet is that you don't need to have
an explicit algebraic solution. Moreover, one set of equations
(called a model in TK-talk) can be used to solve many
variations on one type of problem, because any variable can be a known
or an unknown.
TK Solver can also handle unit conversions. Once you have defined a
set of unit conversion factors, you can enter known variables in any
of those units and ask for unknowns to be displayed in any of those
units.
For problems that can not be solved by direct substitution, the
program has an terative solver that can solve just about any
consistent set of equations (albeit more slowly than the direct
solver). You enter a first guess for one (or more) variables.
How to develop a TK Solver Plus model
In this section, we will develop a simple model to solve problems
relating to the ideal gas las, i.e. PV=nRT. This model will have
only one equation and 4 variables (R being a constant)
When you launch TK Solver Plus, you'll see a column of icons on the
left of the screen. Double-click on the Rules icon to bring up the
Rule sheet.
1. Type all the equations that relate to the problem on the Rule
Sheet in standard "computer algebra" notation
and press RETURN after each equation. In this case there is only
one equation, e.g. P*V=n*0.0821*T. Be sure to use unique variable
names for each variable. Also make sure that the equations are based
on a consistent set of physical units; that is, if one equation is
written for L in liters, the all the equations must be written for L in
liters.
As you enter the equations, a list of the variables is automatically
generated on the Variable Sheet. To see the Variable Sheet,
double-click on the Variables icon.
2. For each variable in the Variable Sheet, type in the units for
which the rules hold in the Unit column. In this case, since we used a value of 0.082 liter-atm/K-mole for R, L
must be in Liters, P in atmospheres, T in Kelvins, and n in number of
moles. You can make up your own set
of abbreviations for units, but you must be internally consistent.
3. (Optional) Double-click on the Units icon to bring up the Units
sheet. Type in any alternative units and the appropriate conversion
factors. Your abbreviations for units must be consistent with what
you typed in the units column of the Variable sheet.
4. (Optional) Briefly describe each variable in a note added to the
Comment column on the Variable Sheet, including a list of any
alternative units for which you have defined conversion factors in the
Unit Sheet.
How to use a TK Solver model
1. For each variable whose value is known, type in first its units in
the Unit column (if different than what is already there) and
then its value in the Input column. (You'll find that it's
best to enter the units first and then the value. The units must be
one of the ones defined on the Unit sheet). Leave the Input
column blank for unknown variables.
2. Type = to solve the model. Any unknown quantities that can be
calculated from the known quantities by the direct solver will be
computed and displayed in the Output column in the units
specified in the Unit column. You can change the units to
other alternatives if desired.
3. If that does not seem to work, try the iterative solver. Type a G
in the St column of one of the unknown variables in the
Variable sheet and enter a reasonable estimate of its value into the
Input column. This defines that variable as the guess
variable. Type = to start the iterative solver. The solution will
usually converge in a few iterations. In difficult cases you might
have to try different variables as the guess variable or different
values for the first guess value.
4. Save and Print the model in the usual way. Only the
active sheet is printed. You can elect to "print" the model "to
file", which is TK-talk for saving the model as an ASCII text file.
5. You can load a saved model from the disk with the Open
command in the File menu, as usual. The program then displays
a dialog box that asks you: Merge file with current model, or reset
the current model first? Ordinarily, you'll click on
Reset, which loads the new model in place the previous one.
6. There is actually much more to TK Solver Plus. It can plot
graphs, handle lists of input and output variables, user-defined
functions, etc. See the manual.
References:
There is an introductory tutorial in the manual. On-line help is
available from About TK Solver in the Apple menu. (The TK
Solver folder contains also some tutorials in the form of Hypercard
stacks; double-click on them to run then or open them with HyperDA.)
There are two books that describe chemistry applications of the
program:
Applications of TK Solver Plus in Chemical Equilibrium and Chemical
Analysis, of Drexel Univ (McGraw-Hill, 1990), and
General Chemistry with TK Solver, , U. of San
Diego.
[RETURN] to Chem 623 .
T. C. O'Haver, 1989
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