Absolute zero

Absolute zero (particle diagram)
At absolute zero (0 K or -273 ˚C), according to the kinetic theory of heat, particle movement should stop.
In physics, absolute zero refers to a zero indicator reading on an absolute temperature scale.

History
In 1703, Guillaume Amontons, a French physicist, mathematically derived the idea of an “absolute zero”. [1]

“It appears that the ‘extreme cold’ [absolute zero] of this thermometer is that which would reduce the air by its ‘spring’, to sustain no load at all.”
— Guillaume Amontons (1703), Publication [4]

In c.1780, William Irvine, based on the theories of Joseph Black, supposedly, calculated absolute zero; the following is a synopsis:

“Irvine’s particular theory was basically very simple in that the took the concept of ‘quantity of heat’ to its logical conclusion. Each and every body, according to Irving, contains a certain ‘absolute quantity of heat’, which is fixed by its heat capacity and its absolute temperature. If, for any reason, the heat capacity of a body should change then it must either emit or absorb heat; thus, the heats of combustion, of chemical reactions in general and the latent heats of fusion and vaporization are merely the consequences of abrupt changes in the heat capacities of the substances concerned. In fact, all productions or absorptions of heat indicate changes in heat capacity. Now this theorem enabled Irvine and his followers to calculate the absolute zero of temperature.”
Donald Cardwell (1971), From Watt to Clausius (pg. 55)

In 1848, Scottish physicist William Thomson publishes his “On an Absolute Thermometric Scale founded on Carnot’s Theory of the Motive Power of Heat, and Calculated from Regnault’s Observations”, in which he bases the concept of thermodynamics-based “absolute thermometric scale” on the 1824 formula for heat engine efficiency of French physicist Sadi Carnot. [2]

In 1925, Albert Einstein and Satyenda Bose predicted a new state of matter at ultra-low temperatures.

In 1995, Einstein and Bose's "new state of matter", called Bose-Einstein condensate, is created at 1.7E-7 K by Americans Eric Cornell and Carl Wieman at Colorado University, Boulder.

Entropy at absolute zero
In 1905, German physicist Walther Nernst introduced his heat theorem, later coming to be known as the third law of thermodynamics, which showed that absolute zero is unattainable. The essential problem Nernst tackled is that the state function formulation of heat Q called ‘equivalence-value’ (renamed 'entropy' in 1865), introduced formulaically by German physicist Rudolf Clausius in 1854 as:

\frac{Q}{T}
Division by zero (problem)
The division by zero problem: as x approaches 0 from the right, in the function y = 1/x, the value of y approaches infinity. As x approaches 0 from the left, y approaches minus infinity. On this logic, in the function S = Q/T, s approaches infinity as T approaches 0, for both positive or negative values of heat flow.

verbally defined as the "generation of the quantity of heat Q of the temperature T from work" becomes an infinite or undefined when the temperature becomes zero:

 \frac{Q}{0} \,

which thus leads to an unexplained inconsistency in the second law of thermodynamics at absolute zero. In other words, the possibility that there exists an actual state in nature of zero degrees temperature introduces the "division by zero" issue of mathematical functions. [3] In an alternative sense, both heat flow and temperature could simultaneously reach zero at absolute zero, giving the function S = 0/0, another non-computable result.

References
1. Shachtman, Tom. (1999). Absolute Zero and the Conquest of Cold (absolute zero: historical timeline, pgs. ix-x). Mariner Books.
2. Thomson, William. (1848). “On an Absolute Thermometric Scale Founded on Carnot’s Theory of the Motive Power of Heat” (pgs. 100-06), Cambridge Philosophical Society Proceedings for June 5; and Phil. Mag., Oct. 1848.
3. Division by zero – Wikipedia.
4. James, W.S. (1929). “The Discovery of the Gas Laws. II. Gay-Lussac’s Law” (abs), Science Progress in the Twentieth Century (1919-1933), 24(93):57-71.

External links
Absolute zero – Wikipedia.
Timeline of low temperature technology – Wikipedia.

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