Why Is Alaska So Cool?
Activity 1 Answer Key
Activity 1: TI-83 + DATA + MODEL
Introduction to Computational Science and Mathematics Modeling
Using the TI-83 Plus Graphing Calculator
Answer Key
1. What is the volume when the temperature is 175 C? Which method did you use?
When the temperature is 175oC, the volume is approximately 448 cm3. If your
response is within cm3 of this, you are on the right track. If you use the trace
method, and your answer is within 20 cm3, then you're doing fair. In order to use the
trace method with greater precision, you need to zoom in and continue the trace at
smaller and smaller resolutions.
2. What is the temperature when the volume is 800 cm3? Which method did you use?
When the volume is 800 cm3, the temperature will be 525oC. If you are within one
degree of this value, you demonstrate that you understand the techniques.
3. Consider: If the temperature continually gets lower and lower, the volume continues to
shrink until (in theory) the volume has decreased to 0 cm3. Determine the temperature at
which the volume theoretically is reduced to zero. Which method did you use?
The temperature at which a gas theoretically has no volume (0 cm3), is -273oC. If your
calculations are within 2 degrees of this, you are close enough.
By very many and very precise investigations in laboratories around the world this
temperature is thought to be actually
-273.15oC. This is defined as absolute zero: -273.15oC = 0K, zero Kelvins.
4. Thought challenge: Give two reasons it is illogical to think that gases at lowest temperatures
in reality have no volume (feel free to research the question).
It is unreasonable to think that gases truly have no volume at absolute zero (or at
any temperature for that matter) for the following four considerations. In increasing
order of importance the considerations, respectively, have to do with (a) definition,
(b) simplifying assumptions, (c) experimental integrity, and (d) threshold or
limitations of human experience.

(a) Definition: Gas is a form of matter, and by definition matter takes up space
(that is, it has volume) however small that space may be.
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Why Is Alaska So Cool?

Activity 1 Answer Key
(b) Simplifying assumptions: The measured volume of a gas is almost entirely
the sum of spaces between its constituent atoms or molecules. In other words,
gas volumes measure the spaces between one molecule and its next neighbor
molecule. The volume due to the molecules or atoms themselves is assumed to
be so relatively small as not to be counted.
Thus, the measured volume changes of a gas are related directly to the distance
between gas molecules or atoms. But if that distance becomes zero, that is, if
there is no distance left between gas molecules or atoms so that the molecules or
atoms are "stacked" on one another, there yet will always remain a small volume
of matter (but a volume nonetheless) that is the volume of the gas molecules or
atoms themselves.

(c) Experimental integrity: The observation of a linear decrease in volume with
decrease in temperature applies to a gas. A gas is what the experiment was
about, right? However, as a gas cools it changes phase to liquid or to a solid. At
the moment of phase change, as the substance no longer is a gas, the behavior of
the original linear decrease in volume no longer properly applies. Thus, because
a fundamental aspect of the investigation has changed, any "results" after the
change are invalid. After all, we were originally studying gases and suddenly
we're dealing with liquids so extrapolation of the line to imply actual zero
volume therefore is not valid from an experimental viewpoint.
The way scientists like to speak of the matter (!) is to use the phrase "ideal gas."
That is, if we may pretend that a gas behaves exactly like our model predicts
(which no gas does for even more reasons than we have discussed here), then
this is an ideal gas. The ideal gas shrinks to no volume at 0K, and always
expands in a perfectly linear fashion with increasing temperature. But remember,
an ideal gas is a model, it is not real life.

(d) Threshold/limitations of human experience: This consideration does not
truly speak to the unreasonable aspect of the question, but deals with the limits of
what human beings may experience and measure. A fundamental tenet of the
scientific endeavor is that an event must have the capacity to be measured
according to objective standards. If an event cannot actually be measured, then it
is beyond the scope of science, and at most ignorance remains the last scientific
plea.
In a few laboratories on earth this coldest theoretical temperature is approached
within millionths of degrees, but absolute zero never actually has been reached
to the present moment. Indeed, some investigators report temperatures of 27pK,
or so. (One picokelvin is 0.000000000001K !) Consequently, no one really knows
what happens to gas or to any matter whatever at actual 0K. Indeed, at very low
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Why Is Alaska So Cool?
Activity 1 Answer Key
temperatures matter starts to behave in ways quite unlike the usual (including
events of superconductivity), and the causes for these unexpected and unusual
behaviors remain somewhat a mystery. As for the behavior of matter at absolute
zero itself, scientists have made their best guesses at it, but so far it remains an
even greater mystery in real life.
Some further questions for your consideration: Is absolute zero a temperature to be
found somewhere in the entire cosmos? If it did, by what means would you measure it?
Closer to home, is it possible to reach absolute zero in a laboratory on earth? You might
want to research the question. If you do, you will be introduced to the Carnot engine.
The results of your research may surprise you.
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