The Zero of Entropy

There is no theoretical relation between the entropies of different chemical elements. We can arbitrarily choose the entropy of every pure crystalline element to be zero at zero kelvins. Then the experimental observation expressed by Eq. 6.0.1 requires that the entropy of every pure crystalline compound also be zero at zero kelvins, in order that the entropy change for the formation of a compound from its elements will be zero at this temperature. 

A classic statement of the third law principle appears in the 1923 book Thermodynamics and the Free Energy of Chemical Substances by G. N. Eewis and M. Randall  

Walther Nemst was a German physical chemist best known for his heat theorem, also known as the third law of thermodynamics. 

Nemst was bom in Briesen, West Prussia (now Poland). His father was a disnict judge. 

At Leipzig University, in 1888, he published the Nemst equation, and in 1890 the Nemst dishibution law. 

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This is a usefiil equation because the third law sets the zero of entropy for every pure substance and thus permits calculations of absolute entropies at temperature T by Eq. (5) of Chapter 4. 

The argument is not quite complete, because we have not shown that when each subsystem has an entropy of zero, so does the entire system. The zero of entropy will be discussed in Sec. 6.1. 

As explained in Sec. 6.1, by convention the zero of entropy of any substance refers to the pure, perfectly-ordered crystal at zero kelvins. In practice, experimental entropy values depart from this convention in two respects. First, an element is usually a mixture of two or more isotopes, so that the substance is not isotopically pure. Second, if any of the nuclei have spins, weak interactions between the nuclear spins in the crystal would cause the spin orientations to become ordered at a very low temperature. 

Statistical mechanical theory applied to spectroscopic measurements provides an accurate means of evaluating the molar entropy of a pure ideal gas from experimental molecular properties. This is often the preferred method of evaluating Sm for a gas. The zero of entropy is the same as the practical entropy scale—that is, isotope mixing and nuclear spin interactions are ignored. Intermolecular interactions are also ignored, which is why the results apply only to an ideal gas. 

Since the number density p is uniquely defined it follows from (2.41) that there is no arbitrariness about the adsorptions with respect to the equimolar surface, that is r ,p) = ir and F (p) = <. However the values of At) and A depend on the zeros of entropy and energy, so it follows from (2.42) and (2.43) that Fp( , and Fp( > are not uniquely defined. It is convenient to consider only the configurational part of entropy and energy. 

For those who are familiar with the statistical mechanical interpretation of entropy, which asserts that at 0 K substances are nonnally restricted to a single quantum state, and hence have zero entropy, it should be pointed out that the conventional thennodynamic zero of entropy is not quite that, since most elements and compounds are mixtures of isotopic species that in principle should separate at 0 K, but of course do not. The thennodynamic entropies reported in tables ignore the entropy of isotopic mixing, and m some cases ignore other complications as well, e.g. ortho- and para-hydrogen. 

When a process is completely reversible, the equahty holds, and the lost work is zero. For irreversible processes the inequality holds, and the lost work, that is, the energy that becomes unavailable for work, is positive. The engineering significance of this result is clear The greater the irreversibility of a process, the greater the rate of entropy production and the greater the amount of energy that becomes unavailable for work. Thus, every irreversibility carries with it a price. 

Deals with the concept of entropy, which serves as a means of determining whether or not a process is possible. Defines the zero entropy state for any substance in a single, pure quantum state as the absolute zero of temperature. 

Conventional Partial Molal Entropy of (H30)+ and (OH)-. Let us now consider the partial molal entropy for the (1I30)+ ion and the (OH)- ion. If we wish to add an (HsO)+ ion to water, this may be done in two steps we first add an H2O molecule to the liquid, and then add a proton to this molecule. The entropy of liquid water at 25°C is 16.75 cal/deg/mole. This value may be obtained (1) from the low temperature calorimetric data of Giauque and Stout,1 combined with the zero point entropy predicted by Pauling, or (2) from the spectroscopic entropy of steam loss the entropy of vaporization. 2 Values obtained by the two methods agree within 0.01 cal/deg. 

The entropy per molecule of liquid water will therefore be 16.75 e.u., divided by Avogadro s constant. We have next to consider the change of entropy when a proton is added to a water molecule to give an (II30)+ ion. It is this quantity that is arbitrarily put equal to zero in Latimer s scale. We see at once that the value that must be allotted to the (HaO)+ ion in Latimer s list is 16.75 e.u. 

There are three different approaches to a thermodynamic theory of continuum that can be distinguished. These approaches differ from each other by the fundamental postulates on which the theory is based. All of them are characterized by the same fundamental requirement that the results should be obtained without having recourse to statistical or kinetic theories. None of these approaches is concerned with the atomic structure of the material. Therefore, they represent a pure phenomenological approach. The principal postulates of the first approach, usually called the classical thermodynamics of irreversible processes, are documented. The principle of local state is assumed to be valid. The equation of entropy balance is assumed to involve a term expressing the entropy production which can be represented as a sum of products of fluxes and forces. This term is zero for a state of equilibrium and positive for an irreversible process. The fluxes are function of forces, not necessarily linear. However, the reciprocity relations concern only coefficients of the linear terms of the series expansions. Using methods of this approach, a thermodynamic description of elastic, rheologic and plastic materials was obtained. 

Just as the intrinsic energy of a body is defined only up to an arbitrary constant, so also the entropy of the body cannot, from the considerations of pure thermodynamics, be specified in absolute amount. We therefore select any convenient arbitrary standard state a, in which the entropy is taken as zero, and estimate the entropy in another state /3 as follows The change of entropy being the same along all reversible paths linking the states a and /3, and equal to the difference of the entropies of the two states, we may imagine the process conducted in the following two steps ... 

With motion along the connodal curve towards the plait point the magnitudes Ui and U2, Si and S2, and ri and r2, approach limits which may be called the energy, entropy, and volume in the critical state. The temperature and pressure similarly tend to limits which may be called the critical temperature and the critical pressure. Hence, in evaporation, the change of volume, the change of. entropy, the external work, and the heat of evaporation per unit mass, all tend to zero as the system approaches the critical state ... 

The entropy of a condensed chemically homogeneous substance vanishes at the zero of absolute temperature ... 

A significant question is whether the asymmetric contribution to the transport matrix is zero or nonzero. That is, is there any coupling between the transport of variables of opposite parity The question will recur in the discussion of the rate of entropy production later. The earlier analysis cannot decide the issue, since can be zero or nonzero in the earlier results. But some insight can be gained into the possible behavior of the system from the following analysis. 

As stressed at the end of the preceding section, there is no proof that the asymmetric part of the transport matrix vanishes. Casimir [24], no doubt motivated by his observation about the rate of entropy production, on p. 348 asserted that the antisymmetric component of the transport matrix had no observable physical consequence and could be set to zero. However, the present results show that the function makes an important and generally nonnegligible contribution to the dynamics of the steady state even if it does not contribute to the rate of first entropy production. 

Response to the driving force is defined as the rate of change of the extensive parameter Xk, i.e. the flux Jk = (dXk/dt). The flux therefore stops when the affinity vanishes and non-zero affinity produces flux. The product of affinity and associated flux corresponds to a rate of entropy change and the sum over all k represents the rate of entropy production,... 

The third law of thermodynamics states that, for a perfect crystal at absolute zero temperature, the value of entropy is zero. The entropy of a molecule at other temperatures can be computed from the heat capacities and heats of phase changes using... 

What I emphasize is that you can have no care at all about the decrease of entropy in chemical reactions as long as they proceed near absolute zero. 

At times t < f0 w [where f0 ° is an infinitesimal amount less than f0 ], the density is zero. Only after the pair is formed can there be any probability of its existence [499]. This is cause and effect, but strictly only applicable at a macroscopic level. On a microscopic scale, time reversal symmetry would allow us to investigate the behaviour of the pair at time and so it reflects the inappropriateness of the diffusion equation to truly microscopic phenomena. The irreversible nature of diffusion on a macroscopic scale results from the increase of entropy, and should be related to microscopic events described by the Sturm—Liouville equation (for instance) and appropriately averaged. 

The total entropy of a substance in a state defined as standard. Thus, the standard states of a solid or a liquid are regarded as those of the pure solid or Ihe pure liquid, respectively, and at a stated temperature. The standard state of a gas is at 1 atmosphere pressure and specified temperature, and its standard entropy is the change of entropy accompanying its expansion to zero pressure, or its compression from zero pressure to 1 atmosphere. The standard entropy of an ion is defined in a solution of unit activity, by assuming that the standard entropy of the hydrogen ion is zero. 

So far, we have been able to calculate only changes in the entropy of a substance. Can we determine the absolute value of the entropy of a substance We have seen that it is not possible to determine absolute values of the enthalpy. However, entropy is a measure of disorder, and it is possible to imagine a perfectly orderly state of matter with no disorder at all, corresponding to zero entropy an absolute zero of entropy. This idea is summarized by the third law of thermodynamics ... 

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