Absolute zero, approach

This remarkable result has been verified by experimental measurements of specific heats at very low temperatures, viz., in liquid air and liquid hydrogen (cf. references in Chap. I.). It was formerly believed that the specific heats of solids approached small positive limiting values at the absolute zero, but the form of the curve at very low temperatures alters appreciably, and it may be inferred that the specific heat is vanishingly small at... 

It may reasonably be assumed that the terms in the expression for the entropy which depend on the temperature diminish, like the entropy of a chemically homogeneous condensed phase, to zero when T approaches zero, and the entropy of a condensed solution phase at absolute zero is equal to that part of the expression for the entropy which is independent of temperature, and depends on the composition (Planck, Thennodynamik, 3 Aufi., 279). 

The entropies of all perfect crystals approach zero as the absolute temperature approaches zero. 

Thus, even at temperatures well above absolute zero, the electrons are essentially all in the lowest possible energy states. As a result, the electronic heat capacity at constant volume, which equals d tot/dr, is small at ordinary temperatures and approaches zero at low temperatures. 

This is an expression of Nernst s postulate which may be stated as the entropy change in a reaction at absolute zero is zero. The above relationships were established on the basis of measurements on reactions involving completely ordered crystalline substances only. Extending Nernst s result, Planck stated that the entropy, S0, of any perfectly ordered crystalline substance at absolute zero should be zero. This is the statement of the third law of thermodynamics. The third law, therefore, provides a means of calculating the absolute value of the entropy of a substance at any temperature. The statement of the third law is confined to pure crystalline solids simply because it has been observed that entropies of solutions and supercooled liquids do not approach a value of zero on being cooled. 

The third law of thermodynamics, one version of which is as a system approaches absolute zero of temperature, all processes cease and the entropy of the system approaches a minimum value , is of little importance for biogenesis. It means that it is impossible to cool a system down to absolute zero (even via an infinite number of steps). 

Lewis and Gibson [3] also emphasized the positive entropy of solutions at 0 K and pointed out that supercooled liquids, such as glasses, even when composed of a single element (such as sulfur), probably retain a positive entropy as the temperamre approaches absolute zero. For these reasons Lewis and Randall [4] proposed the following statement of the third law of thermodynamics ... 

Many investigators have shown that ACp does approach zero as T approaches absolute zero. Nevertheless, these results in themselves do not constimte experimental evidence for the third law, which is a sufficient, but not a necessary, condition for Equation (11.12). If (0AG/07 )p is a nonzero, finite number, it can be shown by a series of equations corresponding to Equations (11.10) and (11.11) that Equation (11.12) is still valid. 

In other words, the temperature gradients of the pressure and volume vanish as absolute zero is approached. 

For Solid or Liquid. For either of these final states, it is necessary to have heat capacity data for the solid down to ternperamres approaching absolute zero. 

Entropy of Gaseous Cyclopropane at its Boiling Point. Heat capacities for cyclopropane have been measured down to temperatures approaching absolute zero by Ruehrwein and Powell [12]. Their calculation of the entropy of the gas at the boiling point, 240.30 K, is summarized as follows ... 

At low f thermal energy is not enough to ensure statistical occupancy of all energy levels accessible to each atom, and the heat capacity (either Cy or Cp) approaches zero as absolute zero is approached. 

It is more problematical to define the third law of thermodynamics compared to the first and second laws. Experimental work by Richards (1902) and Nemst (1906) led Nemst to postulate that, as the temperature approached absolute zero, the entropy of the system would also approach zero. This led to a definition for the third law of thermodynamics that at a temperature of absolute zero the entropy of a condensed system would also be zero. This was further refined by Planck (1911) who suggested this be reworded as the entropy of a pure element or substance in a perfect crystalline form is zero at absolute zero. 

Allusion has already been made to the Ebtvds constants of liquids at low temperatures which are rather less in the cases quoted than the normal value for ordinary temperatures although there is very little probability of association, more especially in the case of argon. At still lower temperatures K. Onnes has found K for hydrogen to be 1 4, so that this coefficient diminishes as the absolute zero is approached. For helium we may expect that a very abnormally low K will be found. 

Debye s investigations on the energy content of substances at low temperatures be expressible in the form u — Uq aT , where a is determinable from the heat capacity of the surface film, and the temperature coefficient of the heat of wetting should decrease rapidly as we approach the absolute zero. Furthermore it is evident that at this temperature the free and total surface energies should be identical in value, the total surface energy sinking first slowly and then rapidly as the critical temperature is reached. Confirmation likewise of the assumption Lt = 0 or that the temperature... 

Helium has a small (a and small force between atoms. This results in a very large Ax. This implies that it is extremely difficult for He atoms to "vibrate" with small displacement as a solid even as absolute zero is approached. 

Superconduction. You may have noticed in Figure 6.3 that the resistivity of pure copper approaches zero at absolute zero temperature that is, the residual resistivity is zero. An expanded scale shows that this is not really the case. Figure 6.6 shows that the residual resistivity in pure copper is about 10 ° m. This is the... 

The discovery of superconductivity was not very dramatic. When Dutch physicist Heike Kamerlingh Onnes succeeded in liquefying helium in 1908 he looked around for something worth measuring at that temperature range. His choice feU upon the resistivity of metals. He tried platinum first and found that its resistivity continued to decline at lower temperatures, tending to some small but finite value as the temperature approached absolute zero. He could have tried a large number of other metals with similar prosaic results. But he was in luck. His second metal, mercury, showed quite unorthodox behavior, and in 1911 he showed that its resistivity suddenly... 

Cryogenic Pertaining to liquified gases stored at temperatures approaching absolute zero. Normally, they have a boiling point of about -100°C. 

As defined by (4.19) or (4.21), it is easy to recognize that TK is an absolute (strictly non-negative) quantity. Furthermore, one can see from (4.19) that the highest possible efficiency ( —> 1) is achievable only at the absolute zero of the Kelvin scale (7"cK —> 0). In addition, the lowest efficiency of converting heat to work ( —> 0) occurs when the two reservoirs approach the same temperature (7j —> 7"cK), consistent with the statement of Kelvin s principle in Section 4.4. Such limits on engine efficiency can be used to paraphrase the three laws of thermodynamics in somewhat whimsical form as follows (the ultimate formulation of the no free lunch principle) ... 

NERNST HEAT THEOREM. For a homogeneous system, the rate of change of the free energy with temperature, as well as the rate of change of heat content with tempeiature, approaches zero as the temperature approaches absolute zero. 

Frequently, the context of a particular problem requires us to consider the limiting behaviour of a function as the value of the independent variable approaches zero. For example, consider the physical measurement of heat capacity at absolute zero. Since it is impossible to achieve absolute zero in the laboratory, a natural way to approach the problem would be to obtain measurements of the property at increasingly lower temperatures. If, as the temperature is reduced, the corresponding measurements approach some value m, then it may be assumed that the measurement of the property (in this case, heat capacity) at absolute zero is also m, so long as the specific heat function is continuous in the region of study. We say in this case that the limiting value of the heat capacity,... 

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