Absolute zero, unattainability

In the Lewis and Gibson statement of the third law, the notion of a perfect crystalline substance , while understandable, strays far from the macroscopic logic of classical thennodynamics and some scientists have been reluctant to place this statement in the same category as the first and second laws of thennodynamics. Fowler and Guggenheim (1939), noting drat the first and second laws both state universal limitations on processes that are experunentally possible, have pointed out that the principle of the unattainability of absolute zero, first enunciated by Nemst (1912) expresses a similar universal limitation ... 

The principle of tire unattainability of absolute zero in no way limits one s ingenuity in trying to obtain lower and lower thennodynamic temperatures. The third law, in its statistical interpretation, essentially asserts that the ground quantum level of a system is ultimately non-degenerate, that some energy difference As must exist between states, so that at equilibrium at 0 K the system is certainly in that non-degenerate ground state with zero entropy. However, the As may be very small and temperatures of the order of As/Zr (where k is the Boltzmaim constant, the gas constant per molecule) may be obtainable. 

An alternate statement of the Third Law is the 1912 statement by W. Nernst Absolute zero is unattainable. To show the equivalence of the two statements of the Third Law consider the process... 

But absolute zero is unattainable, so all particles move. Furthermore, the particles never retain an invariant speed because inelastic collisions cause some particles to decelerate and others to accelerate. As a result, everything emits some electromagnetic waves, even if merely in the context of a dynamic thermal equilibrium with the object exchanging energy with its surroundings. 

R. H. Fowler and E. A. Guggenheim [Statistical Thermodynamics (Cambridge University Press, Cambridge, 1939)] criticized this statement as well as similar statements (to be quoted below) which imply that the entropy of perfect crystalline substances is zero. According to Fowler and Guggenheim, the only valid third-law inference is the unattainability of absolute zero, as expressed in the following statement ... 

In place of the familiar Fahrenheit and Celsius (centigrade) units of temperature, the study of gases uses the Kelvin temperature scale, which is based on the idea of absolute zero. The theory is that there is a temperature, called absolute zero (0 K), at which all movement stops. Scientific experimentation has come very close to achieving absolute zero (within thousandths of a degree), but some scientists believe that absolute zero itself is unattainable. 

With this, the development of Classical Thermodynamics was complete. Or was it In as late as the middle of twentieth century it was argued and agreed that the principle of unattainability of the absolute zero is synonymous with the third law statement of entropy i.e., entropy of a crystalline substance is zero at absolute zero temperature . 

In other words, since one cannot attain the limit T = 0 one must require that in every conceivable situation dS/3z)tT/ 0 as T — 0. Thus, (dS/dz)T not only approaches zero but with Q T does so faster than 1 /. This gives rise to the principle of unattainability of the absolute zero of temperature. The statement (dS/dz)T —> 0 as T 0 is incorporated in another Law ... 

Since the absolute zero is in fact unattainable this integral is really the... 

The third law of thermodynamics assigns by convention a zero entropy value to any pure substance (either an element or a compound) at absolute zero and in internal equilibrium. At absolute zero, atoms have very little motion. Absolute zero temperature is unattainable. 

The maximum work obtainable from a heat engine increases as the lower temperature is decreased, or the upper increased similarly, it can be seen from equation (18.12) that the minimum amount of work which must be done in a given refrigeration process increases as the refrigeration temperature T is lowered. Since T2 — T increases at the same time as Ti is decreased, the ratio (T2 — Ti)/ Ti, in equation (18.12), increases rapidly as the temperature Ti is diminished. If the latter temperature were to be the absolute zero, it is evident from equation (18.12) that an infinite amount of work would be necessary to transfer heat to an upper temperature even if this is only very slightly above 0° K. It follow s, therefore, that as the temperature of a system is lowered the amount of work required to lower the temperature further increases rapidly and approaches infinity as the absolute zero is attained. This fact has sometimes been expressed in the phrase the unattainability of the absolute zero of temperature. ... 

You cannot get out of the game (because absolute zero is unattainable). 

This law we shall call the Principle of the Unattainability of the Absolute Zero (65). 

The proof which I have given above has been discussed by H. A. Lorentz, Czukor, Pdlanyi, and Einstein. H. A. Lorentz limits himself to the communication of a deduction by which my Heat Theorem can be proved if the principle of the Unattainability of the Absolute Zero which I proposed is assumed to be correct. I myself was, and still am, of the opinion that this principle follows of necessity... 

As is not the case with energy and enthalpy, it is possible to determine the absolute value of entropy of a system. To measure the entropy of a substance at room temperature, it is necessary to add up entropy from the absolute zero up to 25°C (77°F). However, the absolute zero is unattainable in practice. This dilemma is resolved by applying the third law of thermodynamics, which states that the entropy of a pure, perfect crystalline substance is zero at the absolute zero of temperature. The increase in entropy from the lowest reachable temperature upward can then be determined Ifom heat capacity measurements and enthalpy changes due to phase transitions. 

This situation was rectified in 1954 when by international agreement the definition of the temperature scale was changed so that now the triple point of water is fixed by definition at 273.16 on the Kelvin scale. The Kelvin scale now has therefore one labeled fixed point instead of two unlabeled fixed points with 100 divisions in between. (Alternatively you could think of the new scale as having two fixed points, one at absolute zero and the other at the triple point of water, with 273.16 divisions in between, but since absolute zero is unattainable it is hardly a fixed point in the usual sense.)... 

National and regional authorities responsible for the protection of public health must consider the concentration of residues of veterinary drug residues, pesticides, and other chemicals that may be in food regardless of whether the substance is allowed for that use. In many regions, in the absence of an approval for the substance, the concentration of residues allowed in food is considered to be zero. In practical terms, this is frequently defined by the technical capability of the analytical method. Attempts to improve on zero include the ALARA (as low as reasonably achievable) approach, which recognizes that absolute zero is unattainable, and describes an approach that considers what is technically achievable, the resources needed to achieve that technical goal, and the benefit gained. 

It is also often stated that according to the third law of thermodynamics, absolute zero is unattainable by a suitable process through a finite number of steps. This statement is often presented as an alternative formulation of the third law of thermodynamics. 

However, other authors think that this theorem is due to the second and the third law simultaneously. This means that the theorem of the unattainability of absolute zero temperature is not a consequence of the third law exclusively. If this is valid, with the statement of the unattainability of absolute zero we cannot trace back the third law of thermodynamics. Nowadays, there are various formulations of the third law of thermodynamics. 

At this point, much of the theory and practice of chemical thermodynamics has been presented. It is worth pausing to reflect on just how it is that delicate measurements near absolute zero temperature, combined with a bunch of differential equations which refer to unattainable conditions, are essential in deciphering the origins of ore deposits, metamorphic rocks, and other geological phenomena. 

Before discussing this question it may be remarked, that imperfect crystals would not be expected to have zero entropy. Also it might be very difficult to determine whether or not a crystal is perfect, at very low temperature, except by the investigation of its entropy. Therefore there is some danger of circularity in the argument. Moreover there is no evidence that the absolute zero can ever be reached on the contrary it seems quite unattainable, as if there is really a kind of infinity of temperature between 0 K and, say, 1 K. What we have to discuss, therefore, is really an extrapolated entropy namely its apparent value at T s 0, as extrapolated from the lowest temperatures attainable in calorimetric measurements. This is normally a temperature of a few K upwards. 

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