By Raymond E Kirk; Donald F Othmer; Martin Grayson; David Eckroth; et al
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Additional info for Kirk-Othmer Encyclopedia of Chemical Technology Vol 7
111) to − p (α) − p (β) δV (α) ≥ 0 (113) Equation (113) is fulfilled if the following conditions are met: P1: FYD Revised Pages Encyclopedia of Physical Science and Technology EN002-101 May 17, 2001 20:51 781 Chemical Thermodynamics 1. Both variations, δV (α) > 0 and δV (α) < 0, are possible and p (α) = p (β) (deformable phase boundary). 2. Variation δV (α) is impossible, δV (α) = 0, and p (α) > p (β) , p (α) = p (β) , or p (α) < p (β) (undeformable or rigid phase boundary). 3. Variation δV (α) is possible only in one direction, δV (α) ≥ 0 and p (α) ≤ p (β) (semideformable phase boundary).
I. HISTORY OF COMPUTATIONAL CHEMISTRY As early as 1929, only 3 years after Schr¨odinger’s formulation of the fundamental equation that bears his name, Dirac stated correctly, The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. Hence, the further development of quantum chemistry was aiming at approximate solutions of the Schr¨odinger equation by simplifying the required mathematical treatment.
3. Variation δV (α) is possible only in one direction, δV (α) ≥ 0 and p (α) ≤ p (β) (semideformable phase boundary). Similar considerations concerning sets B and C yield the conditions for heat-conducting (T (α) = T (β) ), nonconducting (T (α) > T (β) , T (α) = T (β) , or T (α) < T (β) ), and semi(β) conducting (T (α) ≥ T (β) ) and for permeable (µi(α) = µi ), (β) (β) (β) (α) (α) (α) impermeable (µi > µi , µi = µi , or µi < µi ), and (β) semipermeable (µi(α) ≥ µi ) phase boundaries. E. Phase Equilibria 1.