Thermodynamics absolute zero unattainability

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. 

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 ... 

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 . 

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. 

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. 

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 thermodynamics and some scientists have been reluctant to place this statement in the same category as the first and second laws of thermodynamics. Fowler and Guggenheim (1939), noting that the first and second laws both state universal limitations on processes that are experimentally 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 the unattainability of absolute zero in no way limits one s ingenuity in trying to obtain lower and lower thermodynamic 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/A (where k is the Boltzmann constant, the gas constant per molecule) may be obtainable. 

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. 

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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