Thermodynamic probability INDEX

Although the Langelier index is probably the most frequently quoted measure of a water s corrosivity, it is at best a not very reliable guide. All that the index can do, and all that its author claimed for it is to provide an indication of a water s thermodynamic tendency to precipitate calcium carbonate. It cannot indicate if sufficient material will be deposited to completely cover all exposed metal surfaces consequently a very soft water can have a strongly positive index but still be corrosive. Similarly the index cannot take into account if the precipitate will be in the appropriate physical form, i.e. a semi-amorphous egg-shell like deposit that spreads uniformly over all the exposed surfaces rather than forming isolated crystals at a limited number of nucleation sites. The egg-shell type of deposit has been shown to be associated with the presence of organic material which affects the growth mechanism of the calcium carbonate crystals . Where a substantial and stable deposit is produced on a metal surface, this is an effective anticorrosion barrier and forms the basis of a chemical treatment to protect water pipes . However, the conditions required for such a process are not likely to arise with any natural waters. 

To establish [5] the thermodynamic meaning of the index of probability r/ = (ip — H)/9, it is assumed that the distribution g = ev changes as the condition of the system changes, but always subject to the normalization condition f evdfl = 1. It follows that the derivative d f evdQ, = 0. It is assumed that both 9 and tp, as well as extensive parameters may be altered, such that... 

MC simulations are performed with N = 10 molecules, each with four n.n. molecules on a 2d square lattice, at constant P and T, and with the same model parameters as for the MF analysis. To each molecules we associate a cell on a square lattice. The Wolffs algorithm is based on the definition of a cluster of variables chosen in such a way to be thermodynamically correlated." To define the Wolffs cluster, a bond index (arm) of a molecule is randomly selected this is the initial element of a stack. The cluster is grown by first checking the remaining arms of the same initial molecule if they are in the same Potts state, then they are added to the stack with probability Psame = ttiin... 

From a product standpoint, the major benefit of the melt transesterification approach is that it produces resin with a most probable (thermodynamic) molecular weight distribution. Hence, under normal processing conditions, the anhydrous resin exhibits no tendency to change molecular weight or the melt flow index (MFI) (via redistribution). 

This lack of unification can be illustrated by the following example. Margenau and Murphy state that the most satisfactory formulation of the laws of thermodynamics is probably that of Caratheodory, based on the properties of PfaflBan differential equations, yet the Caratheodory formulation is dealt with in such a cursory manner (p. 98) in the revision of Lewis and Randall s Thermodynamics , by Pitzer and Brewer, that it is not listed in either the name or the subject index. Nevertheless, many practical workers in this country and in America will undoubtedly study and use this modern version of Lewis and Randall s book. 

For some types of events the order of the outcomes i = l,2,3,...,f has meaning. For others it does not. For statistical thermodynamics the order usually has meaning and i represents the value of some physical quantity. On the other hand, the index i may be just a label. The index i = 1,2,3 can represent the colors of socks, [red, green, blue], or [green, red, blue], where the order is irrelevant. Probability distributions can describe either case. 

The LSI is probably the most widely used indicator of cooling-water scale potential. It is purely an equilibrium index and deals only with the thermodynamic driving force for calcium carbonate scale formation and growth. It provides no indication of how much scale (CaCOs)... 

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