Entropy third-law

Extrapolations are always subject to error, but fortunately the contribution to the entropy resulting from the extrapolation is a small part of the total. In glucose, for example, S g = 219.2 0.4 J-K -moF1, but the entropy contribution at 10 K obtained from the Debye extrapolation is only 0.28 J-K 1-mol 1. Well-designed cryogenic calorimeters are able to produce Cp measurements of high accuracy hence, the Third Law entropy obtained from the Cp measurements can also be of high accuracy. 

Giauque, whose name has already been mentioned in connection with the discovery of the oxygen isotopes, calculated Third Law entropies with the use of the low temperature heat capacities that he measured he also applied statistical mechanics to calculate entropies for comparison with Third Law entropies. Very soon after the discovery of deuterium Urey made statistical mechanical calculations of isotope effects on equilibrium constants, in principle quite similar to the calculations described in Chapter IV. J. Kirkwood s development showing that quantum mechanical statistical mechanics goes over into classical statistical mechanics in the limit of high temperature dates to the 1930s. Kirkwood also developed the quantum corrections to the classical mechanical approximation. 

Ulbrich and Waldbaum [14] pointed out that calorimetrically determined third law entropies for many geologically important minerals may be in error because site mixing among cations, magnetic spin disorder, and disorder among water molecules in the crystals is frozen in the samples used for calorimetric measurements. They have calculated corrections based on known crystallographic data for several minerals. 

Absolute zero, Calculation of third law entropies Equilibrium 10-12 lectures... 

Equation (5.79) provides the basis for thermochemical measurements of third-law entropies S3rd(T), as described in Sidebar 5.19. More rigorous values of S(T) are obtainable by T-dependent electrochemical studies, as described in Section 8.7. 

In conclusion, we may say that the third law in the form (5.79) is an idealized limit that is made plausible by statistical mechanics, and that underlies thermochemical measurements of third-law entropies for comparison with more accurate electrochemical values. However, it seems to play an essentially disposable role in the formal structure of equilibrium thermodynamics, somewhat analogous to the ideal gas concept in this respect. Equation (5.79) should not be considered a law in the sense that is used elsewhere in thermodynamic theory. 

From the third law, entropies are always positive, requiring that the chemical potential of all phases decrease with temperature. However, because entropy is a measure of randomness, 5m gas > liq >, S , sol, and the chemical potential falls most rapidly with temperature for the gas phase and least rapidly for the solid phase. In Fig. la (drawn for a particular value of pressure), as the temperature is increased, pliq(7 ) crosses psol(T) at the melting point, and the liquid remains the most stable phase until pgas(T) crosses pliq(r) at the boiling point. In Fig. lb (drawn for a different substance or at a different pressure), pgas(7 ) falls so rapidly with temperature that it crosses psol( T) before pliq(7 ) does. As a result, liquid is never the most stable phase and, at the given pressure, the solid sublimates directly to gas. 

These Third Law Entropies 1 can, in any case, be checkedandtestedusing alternative measurements of entropy. Examples are ... 

Here, Sr(Mg) and Sr(Zn) are the third law entropies of pure magnesium and pure zinc, respectively. The values of Sj(Mg) and S7(Zn) were taken from the NIST data [16,17]. In the present study, thermodynamic values are expressed as the formulation for 1 mole atom. 

A calorimetric entropy of 60.17 cal K mol" at 226.48 K was obtained by Koehler and Giauque ( ) for the ideal gas. If the lattice doesn t discriminate between F and 0 atoms then at 0 K a residual entropy of 2.75 cal k" mol exists and the third law entropy would be 62.92 cal k" raol". This value may be compared with 62.64 obtained statistically. The difference 0.3 cal K" mol" is within the range found for other molecules and explained on the basis of some discrimination in the lattice, see Koehler and Giauque, (9) for references. 

Claassen et al. ( ) calculate thermodynamic functions virtually identical with the JANAF values. These authors also correct the third law entropy reported by Grisard et al. (6) from measurements of heat capacity (14-285 K) and vapor pressure (226-303 K). The entropy at the normal boiling point becomes S (284.91 K) - 67.04 kcal mol when a non-ideality correction consistent with the... 

S (298.15 K) is selected as 53.5+1.0 cal K" mol" which minimizes differences between the second and third law entropies of vaporization determined from two Independent sets (7, 8 ) of vapor pressure data. Further details on the results of these analyses... 

The third law entropy based on measurements from 12 to 320° K. by Craig and coworkers 76) is 7.81 e. u. at 298° K. Using their heat capacities we calculate an enthalpy at 8° K. of 1195 cal./gram atom. In addition to the heat capacity data reviewed by Kelley 186), we have considered the values given by Kubaschewski 206, 206) and the measurements of McDonald and Stull 228). The heat of melting is 2140 cal./ gram atom from McDonald and Stull. Rossini and coworkers 274) have selected a melting point of 923° K. 

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