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How do we know the extrapolated graph to calculate 0 K is linear all theway? How close are researchers to achieving 0 K experimentally? Is itpossible to achieve it and sustain it? How do they do it if the sensing mechanisms would have to be higher than 0 K? (Like Heisenberguncertainty principle) Is light or the speed of light at all affected at those temperatures(below 4 K?)
Answer 1:

Well -- this is a tough one, all about 0 Kelvin and the models:

1. I presume that you refer to the ideal gas equation of state -- PV = nRkT, from which one can predict absolute zero with some accuracy, by extrapolating back from higher temperatures. Ok -- in fact, the equations only describe the behavior of monatomic gasses at temperatures sufficiently high that the probability of gas-gas collisions is minimal. If you were to plot the PV relation for any particular gas, you would definitely see non-linear behavior as the gas is cooled past its condensation point. However, condensation forces are very short range, and for the gas fraction, the energy of the atoms is hardly effected. So we get an estiamte of a temperature that is relatively unbiased at higher temperatures as long as the gas law is holding; i.e. atoms not sticking to the wall or diffusing into the container, etc. So -- curve is not linear -- but we measure in a temperature range in which there is little likelyhood of substantial non-linear effects, and extrapolate from there.

2. Achieving 0K over some macroscopic sample has not been accomplished, however, researchers have come very close-- i.e. temperatures in the nano-kelvin range, for brief periods. Recently, there
have been a number of people making samples of BEC (Bose-Einstein
Condensate) from a variety of
atoms (most being alkali-metals). In such samples, millions of atoms are
at a temperature that is
so cold that atoms pair to create Bose (even-spin) superparticles which
need not obey the Pauli
principle and may all fall to the same state. These samples then have
properties similar to superfluid
helium (also a condensate -- but much easier to make). The current theory for such superfluids is that they are heat superconductors (heat travels at the speed of sound and does not diffuse into the material) composed of a warm fraction (for He 2.17K) and a cold fraction (0K). The warm fraction behaves like a normal fluid, but the cold fraction, being a superconductor, causes the macroscopic
phnomena associated with He. (i.e. Helium in a vessel rapidly boils
until 2.17K is reached, then (despite the gas pressure increasing -- indicating faster boiling, the visable fluid appears to stop boiling at all... in fact, is is the heat superconduction -- reflecting heat pressure wave until they hit the surface, where they pick up some atoms and turn into gas.) So in a sense, we can see the properties of materials at 0K, even if the material is not at 0K.

3. Measuring such temperatures is tricky -- but is usually done spectroscopically, since we can often see transitions that are swamped at higher termperatures. Surprisingly the light itself may only add a very small amount of heat, we choose the frequency so that such interactions are minimized.
You are quite right in mentioning the Heisenberg uncertanty principle --
it isn't easy to measure a system without adding some small amount of disorder, so it is often the case that the measurement tells the state of the system before the measurement was made....

4. The speed of light in a vacuum is not affected by the temperature (although what is the temp of a vacuum?) However, the speed of light a material is often so affected.
Recent experiments with sodium BEC's have shown astonishingly low values for c at certain frequencies
-- as low as several centimeters per second... This surprising finding was reported in Physics Today some months ago, and I believe was reported in Nature, as well.

An early definition of 0K, (18th century) has oK when all motion has ceased, in a material. In more modern times, the definition has changed to -- all states above the zero point energy are empty (even spin)
and all states above the Pauli exclusion point are unfilled (odd spin).
This change was made to reflect the variety of phenomena seen at such cold temperatures, (He never freezes at 1 atm. regardless how cold it is...). As more knowledge is gained, this definition will no doubt change as well.

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