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Two Poorly understood Phenomena: Maxwell's Lever Rule & Expansion of Freezing Water

Matti Pitkänen


The view about condensed matter as a network with nodes identifiable as molecules and bonds as flux tubes is one of the basic predictions of TGD and obviously means a radical modification of the existing picture. In this essay, two old anomalies of standard physics are explained in this conceptual framework. Analytic equations of state quite generally fail in critical region for gas liquid-phase transition. Empirically the pressure in critical region depends only on temperature and is independent on molecular volume whereas equations of state predict this dependence. Maxwell's area rule and lever rule is the proposed modification equation of state in critical region. There are two phases corresponding to liquid and gas in the same pressure and the proportions of the phases vary so that the volume varies. The lever rule used for metal allows allows to explain the mixture but requires that there are two "elements" involved. What the second "element" is in the case of liquid-gas system is poorly understood. TGD suggests the identification of the second "element" as magnetic flux tubes connecting the molecules. Their number per molecule varies and above critical number a phase transition to liquid phase would take place. Second old problem relates to the numerous anomalies of water . The most well-known anomalies relate to the behavior near freezing point. Below 4 0C water expands rather than contracts as temperature is lowered. Also in the freezing an expansion takes place. A general TGD based explanation for the anomalies of water would be the presence of flux tubes with both ordinary and non-standard value of Planck constant heff/h=n. Flux tubes associated with hydrogen bonds could have also non-standard value of Planck constant in which case the flux tube length scales like n. The reduction of n would shorten long flexible flux tubes to short and rigid ones. This would force the molecules nearer to each other but also reduce their motility of molecules. This would create empty volume leading to an increase of volume per molecule as temperature is reduced. The energy for particles with non-standard value of Planck constant is higher than for ordinary ones. In freezing all dark flux tubes would transform to ordinary ones and the surplus energy would be liberated so that the latent heat should be anomalously high for all molecules forming hydrogen bonds.

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