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.
  • (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 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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