Understanding the third law

Over the years, many experiments have been carried out which confirm the third law. The experiments have generally been of two types. In one type the change of entropy for a change of phase of a pure substance or for a standard change of state for a chemical reaction has been determined from equilibrium measurements and compared with the value determined from the absolute entropies of the substances based on the third law. In the other type the absolute entropy of a substance in the state of an ideal gas at a given temperature and pressure has been calculated on the basis of statistical mechanics and compared with those based on the third law. Except for well-known, specific cases the agreement has been within the experimental error. The specific cases have been explained on the basis of statistical mechanics or further experiments. Such studies have led to a further understanding of the third law as it is applied to chemical systems. 

According to statistical mechanics, the value of zero for the entropy function of a system is obtained when all molecules comprising the system are in the same quantum state. This statement applies to any state of aggregation gas, liquid, or solid. Now all substances1 have an infinite number of possible quantum states, and consequently the state in which all the 

1 We do not consider here the case in which a nuclear magnetic subsystem or any other subsystem that has a limited number of quantum states may be considered as a thermodynamic system separate from the other parts of the total molecular system. 

The condition discussed in the previous paragraph demands certain care in the experimental determination of absolute entropies, particularly in the cooling of the sample to the lowest experimental temperature. In order to approach the condition that all molecules are in the same quantum state at 0 K, we must cool the sample under the condition that thermodynamic equilibrium is maintained within the sample at all times. Otherwise some state may be obtained at the lowest experimental temperature that is metastable with respect to another state and in which all the molecules may not be in the same quantum state at 0 K. 

We must also consider the conditions that are implied in the extrapolation from the lowest experimental temperature to 0 K. The Debye theory of the heat capacity of solids is concerned only with the linear vibrations of molecules about the crystal lattice sites. The integration from the lowest experimental temperature to 0 K then determines the decrease in the value of the entropy function resulting from the decrease in the distribution of the molecules among the quantum states associated solely with these vibrations. Therefore, if all of the molecules are not in the same quantum state at the lowest experimental temperature, excluding the lattice vibrations, the state of the system, figuratively obtained on extrapolating to 0 K, will not be one for which the value of the entropy function is zero. 

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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 ... 

Why Do We Need to Know This Material The second law of thermodynamics is the key to understanding why one chemical reaction has a natural tendency to occur bur another one does not. We apply the second law by using the very important concepts of entropy and Gibbs free energy. The third law of thermodynamics is the basis of the numerical values of these two quantities. The second and third laws jointly provide a way to predict the effects of changes in temperature and pressure on physical and chemical processes. They also lay the thermodynamic foundations for discussing chemical equilibrium, which the following chapters explore in detail. 

The third law of thermodynamics states that the entropy of a perfect crystal is zero at a temperature of absolute zero. Although this law appears to have limited use for polymer scientists, it is the basis for our understanding of temperature. At absolute zero (-273.14 °C = 0 K), there is no disorder or molecular movement in a perfect crystal. One caveat must be introduced for the purist - there is atomic movement at absolute zero due to vibrational motion across the bonds - a situation mandated by quantum mechanical laws. Any disorder creates a temperature higher than absolute zero in the system under consideration. This is why absolute zero is so hard to reach experimentally ... 

We see from this discussion that a third generalization is necessary. Up to this point in the text we have been concerned solely with the macroscopic properties. However, in order to obtain an understanding of the third law we must use some concepts concerning the entropy function, based on statistical mechanics. We do so in this chapter with the assumption that the basic concepts that are used are familiar to the reader. 

Liquid helium presents an interesting case leading to further understanding of the third law. When liquid 4He, the abundant isotope of helium, is cooled at pressures of < 25 bar, a second-order transition takes place at approximately 2 K to form liquid Hell. On further cooling Hell remains liquid to the lowest observed temperature at 10 5 K. Hell does become solid at pressures greater than about 25 bar. The slope of the equilibrium line between liquid and solid helium apparently becomes zero at temperatures below approximately 1 K. Thus, dP/dT becomes zero for these temperatures and therefore AS, the difference between the molar entropies of liquid Hell and solid helium, is zero because AV remains finite. We may assume that liquid Hell remains liquid as 0 K is approached at pressures below 25 bar. Then, if the value of the entropy function for sol 4 helium becomes zero at 0 K, so must the value for liquid Hell. Liquid 3He apparently does not have the second-order transition, but like 4He it appears to remain liquid as the temperature is lowered at pressures of less than approximately 30 bar. The slope of the equilibrium line between solid and liquid 3He appears to become zero as the temperature approaches 0 K. If, then, the slope is zero at 0 K, the value of the entropy function of liquid 3He is zero at 0 K if we assume that the entropy of solid 3He is zero at 0 K. Helium is the only known substance that apparently remains liquid as absolute zero is approached under appropriate pressures. Here we have evidence that the third law is applicable to liquid helium and is not restricted to crystalline phases. 

We thus can obtain a consistent set of absolute values of the entropy function for pure substances from thermal measurements alone on the practical basis of assigning the value of zero to the entropy function at 0 K with the exclusion of nuclear and isotopic effects, within the understanding of the third law as discussed in Section 15.4. The calculation of the entropy function of pure substances in the ideal gas state by the methods of statistical mechanics must be consistent with the practical basis. In addition to obtaining absolute values by the methods that have been discussed, values can also be obtained from equilibrium measurements from which ASe can be determined for some change of state. If all but one of the absolute values in the equivalent sum VjSP are known, then the value of that one can be calculated. 

Equation (16-2) allows the calculations of changes in the entropy of a substance, specifically by measuring the heat capacities at different temperatures and the enthalpies of phase changes. If the absolute value of the entropy were known at any one temperature, the measurements of changes in entropy in going from that temperature to another temperature would allow the determination of the absolute value of the entropy at the other temperature. The third law of thermodynamics provides the basis for establishing absolute entropies. The law states that the entropy of any perfect crystal is zero (0) at the temperature of absolute zero (OK or -273.15°C). This is understandable in terms of the molecular interpretation of entropy. In a perfect crystal, every atom is fixed in position, and, at absolute zero, every form of internal energy (such as atomic vibrations) has its lowest possible value. 

Professor Walter Hermann von Nernst (1864-1941) was one of the pioneers in the development of electrochemical theory and is generally given credit for first stating the third law of thermodynamics. He won the Nobel Prize in chemistry in 1920 for his contributions to our understanding of thermodynamics. 

Understand the meaning of entropy (5) in terms of the number of microstates over which a system s energy is dispersed describe how the second law provides the criterion for spontaneity, how the third law allows us to find absolute values of standard molar entropies (5°), and how conditions and properties of substances influence 5° ( 20.1) (SP 20.1) (EPs 20.4-20.7, 20.10-20.23)... 

We conclude this brief discussion of deviations from the third law by stating that, although the cases of nonconformity are frequent, we can usually understand their origin with the aid of molecular concepts and quantum statistics. The latter discipline permits calculation of thermodynamic quantities, thereby providing a useful check on experimental data indeed, it often supplies answers of greater accuracy. In this way, it is possible to use the third law to build up tables of absolute entropies of chemical substances. 

If you scan the values for 5° in Appendix E, you will see that several aqueous ions have values that are less than zero. The third law of thermodynamics states that for a pure substance the entropy goes to zero only at 0 K. Use your understanding of the solvation of ions in water to explain how a negative value of S° can arise for aqueous species. 

The physics of materials at low temperatures is now a large and important topic, and a complete understanding of the third law requires some knowledge of statistical mechanics and even some quantum mechanics. A fairly brief overview is Wilks (1961). However, for those whose interests lie at the other end of Earth s temperature spectrum and are mainly interested in having accurate thermochemical data, the only important aspect of the third law is that it provides an absolute reference point for entropy data. 

Of the three laws of thermodynamics, the third law is the least discussed, though it is the most profound in some sense. This is so because, unlike the first two laws, the third law has direct contact with quantum mechanics. Thus, it is not surprising that the development, along with complete understanding, of the third law, was concomitant with the establishment of quantum theory itself in the first quarter of the last century. 

For convenience (and in accordance with our understanding of entropy as a measure of disorder), we take this common value to be zero. Then, with this convention, according to the Third Law,... 

The contenet of the third law of thermodynamics is summarized in Fig. 2.4. The third law is particularly easy to understand if one combines the macroscopic entropy definition of entropy with its statistical, microscopic interpretation through the Boltzmann equation, Eq. (11). The symbol k is the Boltzmaim constant, the gas constant R divided by Avogadro s number and W is the thermodynamic probability, representing the number of ways a system can be arranged on a microscopic level. One can state the third law, as proposed by Nernst and formulated by Lewis and Randall, as follows "If... 

So, now maybe we can combine your understanding of the third law. It says that entropy, S, is basically statistical where W in Boltzmann s equation refers to the number of ways the system can exist. In the case of a perfectly crystalline system, W might evolve into a number more than 1 if the atoms swing and sway during vibration, but at 0°K, the vibrations will be minimized, although maybe not completely. There are more pitfalls as we consider this further, but first let us look at die simple interpretation of absolute entropy ... 

A I hesitate to get into that because there are three ways that are set forth in the German law to compensate the inventor. One is by using an analogy to licensing. If there were a license issued for an invention at a certain royalty rate, then a percentage of that royalty would be paid back to the inventor as his share. Another way is to try to determine the value of the invention in terms of profits back to the company and take a percentage of that. The third way is to simply come to some mutual understanding between the employer and inventor(s) on an arbitrary basis. 

Firefighters have to be able to read, understand, and act on complex written materials—not only fire law and fire procedures, but also scientific materials about fire, combustible materials, and chemicals. They have to be able to think clearly and independently because lives depend on decisions they make in a split second. They have to be able to do enough math to read and understand pressure gauges, or estimate the height of a building and the amount of hose needed to reach the third floor. They have to be able to read maps and floor plans so they can get to the emergency site quickly or find their way to an exit even in a smoke-filled building. 

Finally, what is a third important ingredient in the forensic science training format I see it as a need to guide the student in understanding the role of science in the total scheme of the administration of justice. For years we have heard many eminent forensic scientists make strong appeals for the scientist to remain aloof from the crime scene, from the investigator, from the legal counsel, from the accused, and from the philosophy of the law itself. The scientist is told that his objective interpretation of the evidence will be a sufficient end in itself. 

Stated differently, the third ingredient calls for an understanding of the evolution of Anglo-Saxon law and its subsequent adaptation and modification in America. Throughout this evolution runs a continuous thread of concern for just, fair and humane treatment of those fellow men who become subjects of litigation. 

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