Spin entropy

In crystals for which n0 is large, such as iodine, the lowest symmetric and the lowest antisymmetric state have practically the same energy and properties, and each corresponds to one eigenfunction only. As a result a mixture of symmetric and antisymmetric molecules at low temperatures will behave as a perfect solid solution, each molecule having just its spin quantum weight, and the entropy of the solid will be the translational entropy plus the same entropy of mixing and spin entropy as that of the gas. This has been verified for I2 by Giauque.17 Only at extremely low temperatures will these entropy quantities be lost. 

Fig. 7.2. Entropies (divided by the gas constant R) of liquid and solid3 He along the melting curve. The disorder of nuclear spin entropy, corresponding to S /R = ln(2/ +1) = In 2 is marked. The two curves cross at the minimum of die melting curve at 315 mK and 29 bar [[12] p. 214].

S °( N2H4) = 57.1 while S XCdh) = 52.5. If we add on It In 4 for spin we obtain the difference of about 7 Gibbs/mole. Actually the spin entropy is not needed to account for the transition state entropy of 4 Gibbs/mole if we assume the loose complex. 

It is clear from eqs (7) and (8) that Fs[M] monotonously increases with M, so that — as expected — the minimum of Fs[Af] corresponds to M = 0, for which the spin entropy attains the highest value. It is convenient to introduce the spin susceptibility xs related to... 

Continuous phase transitions show anomalies in the specific heat and magnetic susceptibility (or magnetization) at or very near Tg. There is, however, no latent heat as in so-called first-order transitions but of course there is a decrease in spin entropy. 

New heat capacity data on oxides over the cryogenic region from 51 °K. to 300°K. have been reported by Weller and King (190) on scandium (III) oxide and on a composition (Ce203.33) assumed to be cerium (III) oxide with Ce02 as a contaminant. The entropies at 298.15°K. are 17.88 and 6.00 cal./(mole °K.), respectively. Extrapolation below 51 °K. on SC2O3 amounts to 0.48 cal./(mole °K.), that on the cerium compound to 5.67 since the total spin entropy (2R In 2) was included in addition to the sizeable lattice contribution. 

White, Friedman, and Johnston (343) have measured the critical constants for normal hydrogen and have found 33.244 K. and 12.797 atmospheres. Woolley, Scott, and Brickwedde have presented data on the dissociation energy and the thermodynamic properties for the ideal diatomic gas, including contributions from nuclear spin. We have omitted the spin entropy in compiling our tables. Thermodynamic properties for the ideal monatomic gas have been computed at the National Bureau of Standards (395). Note that the reference state represents 2 gram atomic weights for this element. 

Since atoms retain their nuclear spins unaltered in all processes except those involving ortho-para conversions, there is no change in the nuclear spin entropy. It is consequently the common practice to omit the nuclear spin contribution, leaving what is called the practical entropy or virtual entropy. ... 

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