| Pseudo-variables |
| Deciding
what to plot |
| You need to have available the relevant equations for the
experiment you will carry out or which has already been carried out. You need to
know which variables have been altered and which variables are, for this particular data
set, constant. The constants might be universal constants (e.g.
G, e, h, c),
local constants (density of fluid being used, focal length of lens, resistivity
of wire) or pure numbers. Here is a diagram of the
standard straight-line equation Y = M X + C
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A function containing
variables or pseudo-variables and numbers only |
= |
A combination of constants
and numbers only |
´ |
A function containing
variables or pseudo-variables and numbers only |
+ |
A combination of constants
and numbers only |
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| Your primary task is to manipulate the given equations
into such a form that you can fit it into these boxes. Suppose, for example,
that you start with a modified version of Van der Waals' equation |
|
 |
| where
a depends on what gas you use,
T is the temperature
and R the universal gas constant. For the purposes of this exercise,
a, T and
R
are constants, while p and
V are the raw variables. Multiplying out and
re-arranging gives |
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 |
| so our box equation becomes |
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| and if we plot
pV
on the vertical axis against
1/V
on the horizontal axis, we will obtain a straight line whose gradient is
-a
and whose vertical intercept is
RT. |
| There is no limit to the number of ways in which
you can generate functions of the raw variables to produce new
'plotting' variables to go into the purple boxes. What is crucial is
that neither of the raw variables variable can be allowed to spill over into the green
'constant' boxes. |
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