Nuclear entropy

The attainment of still lower temperatures, down to about 10" K, is achieved by making use of nuclear magnetic properties. The nuclear magnets are about 2000 times smaller than the magnet in a paramagnetic substance such as gadolinium sulfate, yet there is still a significant difference between the nuclear entropies even at temperatures as low as 10" K-... 

The values of S° represent the virtual or thermal entropy of the substance in the standard state at 298.15 K (25°C), omitting contributions from nuclear spins. Isotope mixing effects are also excluded except in the case of the H—system. 

In summary, the absolute entropies we calculate and tabulate are, in fact, not so absolute, since they do not include isotopic entropies of mixing nor nuclear spin alignment entropies. The entropies we tabulate are sometimes called practical absolute entropies. They can be used to correctly calculate AS for a chemical process, but they are not true" absolute entropies. 

Iversen, B.B., Larsen, F.K., Souhassou, M. and Takata, M. (1995) Experimental evidence forthe existence of non-nuclear maxima in the electron density distribution of metallic beryllium. A comparative study ofthe maximum entropy method and the multipole method, Acta Cryst., B51, 580-591. 

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].

Around 1 mK, the solid 3He, in zero magnetic field, undergoes a nuclear ordering its entropy falls by an order of magnitude (see Fig. 7.2) and the cooling power of the process... 

A well-known consequence of the permutational symmetry of the nuclear Hamiltonian is the low-temperature entropy of crystalline hydrogen, which is associated with the spin statistics of ortho- and para-112 - See, e.g., N. Davidson, Statistical Mechanics (New York, McGraw-Hill, 1962), Chapter 9. 

The meson fields op, too and po are found by solving a set of equations self-consistently as shown in [11], Also expressions for the energy density, pressure and the entropy density can be found there. The empirical values of the binding energy of nuclear matter and nuclear matter density are reproduced using the above mentioned parameterization. The nuclear matter EOS can be found expressing the chemical potentials as functions of temperature, baryon density... 

More insight into the reaction mechanism is given by the breakdowns in Table III. The negative entropy has important contributions from bimolecular work, non-adiabatic effects and nuclear tunnelling. Nuclear tunnelling (r = 3.5 (10, 11)) also... 

There is one further caveat. The above arguments have been developed in terms of a mononuclear catalyst. At the very least some entropy corrections will be needed for comparison with bi-nuclear catalysts. [Note These considerations were developed during postdoctoral work at Stanford University with Professor Henry Taube.]... 

A satisfactory explanation for this discrepancy was not available until the development of statistical thermodynamics with its methods of calculating entropies from spectroscopic data and the discovery of the existence of ortho- and parahydrogen. It then was found that the major portion of the deviation observed between Equations (11.24) and (11.25) is from the failure to obtain a tme equilibrium between these two forms of H2 molecules (which differ in their nuclear spins) during thermal measurements at very low temperatures (Fig. 11.4). If true equilibrium were established at all times, more parahydrogen would be formed as the temperature is lowered, and at 0 K, all the hydrogen molecules would be in the... 

Harold Clayton Urey, 1893-. Professor of chemistry at the Institute for Nuclear Studies at the University of Chicago and at the University of California. In 1931 Dr. Urey and his collaborators discovered deuterium, the heavy isotope of hydrogen. Pie has carried out notable researches on the entropy of gases and on the properties and separation of isotopes and has studied the chemical evidence of the earth s origin. 

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