It is not possible and yet in this impossible

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Unformatted text preview: ationship between the volume of a gas and the temperature of the gas at constant number of moles n and pressure p. Holding the pressure constant on the cylinder (as simple as not adding any weight to the cylinder, making its pressure equal to atmospheric pressure), he measured the volume of a gas as he heated and cooled the cylinder. Charles discovered on plotting volume and temperature that there was a direct proportionality, that is, as temperature increased, so increased volume. He wrote the corresponding proportionality as VαT |n,P The next step, as with Boyle, is to remove the proportionality by adding a constant; Dakota State University Page 127 of 232 Experiment 10: Gas Laws General Chemistry I and II Lab Manual V = rT where r is some constant, or V T =r Since r is constant for any two states 1 and 2, we can write V1 V2 T1 = T2 Unfortunately, there IS a problem with Charles. See, if you have one of the temperatures set at zero, then the equation becomes undefined. How does one circumvent this problem? Well, Charles’ did so by extrapolating his data all the way to V=0. Such a condition, where the volume occupied by the gas is zero, is only possible for an ideal gas, and since there are no ideal gases, this becomes a hypothetical limit. It is not possible, and yet, in this impossible situation, Charles’ noticed something wonderful; no matter what gas, or mixture of gases he used, no matter what pressure he kept the gas, no matter how many moles of gas he started with, these lines all extrapolated to e xactly the same temperature; -273.15o C. No matter what he did, he could NEVER reach a temperature in his extrapolations below this temperature; that means that this must be the theoretical limit of the temperature scale. Recall that temperature is directly related to kinetic energy, or motion. Doesn’t it make sense, then, that there must be a point where there is no more motion, where the temperature is so cold that all motion in a molecule actually stops? And once this state is reached, is it possible to have a lower temperature, since temperature is related to motion of molecules? No, of course not, because we can never have less motion than absolutely no motion at all. This temperature is called “absolute zero”; it is the coldest temperature theoretically possible, and it corresponds to a state where there is no molecular motion at all; no movement, no vibration, nothing. We can use this fact to get around the “undefined equation” problem. If we take the centigrade temperature scale, and add to it –273.15, then we get a new temperature scale where the temperature can never go below zero. In fact, since this was a theoretical limit only, we can never reach absolute zero either, so we will always have a positive number for temperature. We call this temperature “Kelvin” (the corresponding absolute temperature based on the Fahrenheit scale is called “Rankine”). Whenever working with temperature in the gas laws, you must always convert to Kelvin. In respiration, Boyle’s Law is the one that relates to the action of the lungs. As one expands his/her diaphragm, t...
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