Absolute temperature unattainability

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. 

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 ... 

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. ... 

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.)... 

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. 

The attainment of extreme conditions and the examination and understanding of how matter behaves under previously unattainable conditions is a constant stimulus to scientists. The concept of an absolute zero of temperature has been with us for many years and the challenge of reaching as close as possible to that limit is nothing new. However, dramatic advances have been made in recent years and this book provides articles describing some of these advances, written by leading experts in these fields. The title of the volume also stresses molecules that is, here we are concerned with the production and behaviour of molecules — as distinct from atoms — under cold and ultra-cold conditions. In particular, emphasis is placed on the chemical reactions of species at low temperatures — and on how the study of chemical reactions can be pushed to ever lower temperatures. 

If no adiabatic process can lead to zero temperature, one might ask if some other kind of process might lead to zero temperature. Unless a heat reservoir already exists at zero temperature, conduction of heat away from an object cannot do the job, since heat flows from a hotter to a cooler object. A refrigerator cannot do the job, since its coefficient of performance must be less than that of a Carnot refrigerator, which approaches zero as the lower temperature approaches zero. We therefore conclude that no process can cause a system to attain 0 K, which is therefore called absolute zero. The unattainability of absolute zero is a consequence of both the second and third laws. 

Nemst s theorem is applicable only to equilibrium systems. From the third law of thermodynamics, it follows that absolute zero is unattainable because, according to eq. (3.5.27), if near a temperature of absolute zero, a small amount of heat is taken off a system (AT -> 0), a large enough (in a limit infinite) entropy change will take place this contradicts Nemst s theorem. 

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