Entropy of a mixture

The critical size of the stable nucleus at any degree of under cooling can be calculated widr an equation derived similarly to that obtained earlier for the concentration of defects in a solid. The configurational entropy of a mixture of nuclei containing n atoms widr o atoms of the liquid per unit volume, is given by the Boltzmann equation... 

Having found tlie entropy of a mixture of gases in Eq. (2.8), it is a simple thing to find the Gibbs free energy, from the relation... 

Next, let us consider the entropy of the homogeneous phase and compare it with the entropy of a mixture of two pure components. The entropy of the pure components will be just the part determined from the CTCp... 

The entropy of a mixture of real gases is readily determined by making use of Eq. (7-167) and the relation... 

If there are two or more physically distinguishable isomeric forms, the entropy of a mixture must include a term for the entropy of mixing. For i different species, the mole fraction of each of which is the entropy of mixing (per mole of final mixture) is given by... 

As a result of the increased number of configurational possibilities, the entropy of a mixture is higher than the sum of the entropies of the components in the demixed state, under otherwise identical conditions. 

From Eqs. 11.1.24 and 11.1.25, and the fact that the entropy of a mixture is given by the additivity rule S = Y ,i ntSi, we conclude that the entropy of an ideal gas mixture equals the sum of the entropies of the unmixed pure ideal gases, each pure gas having the same temperature and occupying the same volume as in the mixture. 

Most of the assumptions are based on idealized models, indicating the limitations of the mathematical methods employed and the quantity and type of experimental data available. For example, the details of the combinatorial entropy of a binary mixture may be well understood, but modeling requires, in large measure, uniformity so the statistical relationships can be determined. This uniformity is manifested in mixing rules and a minimum number of adjustable parameters so as to avoid problems related to the mathematics, eg, local minima and multiple solutions. 

The partial molar entropy of a component may be measured from the temperature dependence of the activity at constant composition the partial molar enthalpy is then determined as a difference between the partial molar Gibbs free energy and the product of temperature and partial molar entropy. As a consequence, entropy and enthalpy data derived from equilibrium measurements generally have much larger errors than do the data for the free energy. Calorimetric techniques should be used whenever possible to measure the enthalpy of solution. Such techniques are relatively easy for liquid metallic solutions, but decidedly difficult for solid solutions. The most accurate data on solid metallic solutions have been obtained by the indirect method of measuring the heats of dissolution of both the alloy and the mechanical mixture of the components into a liquid metal solvent.05... 

A closed vessel of volume 2.5 L contains a mixture of neon and fluorine. The total pressure is 3.32 atm at 0.0°C. When the mixture is heated to 15°C, the entropy of the mixture increases by 0.345 J-K. What amount (in moles) of each substance (Ne and F2) is present in the mixture ... 

The structure of a simple mixture is dominated by the repulsive forces between the molecules [15]. Any model of a liquid mixture and, a fortiori of a polymer solution, should therefore take proper account of the configurational entropy of the mixture [16-18]. In the standard lattice model of a polymer solution, it is assumed that polymers live on a regular lattice of n sites with coordination number q. If there are n2 polymer chains, each occupying r consecutive sites, then the remaining m single sites are occupied by the solvent. The total volume of the incompressible solution is n = m + m2. In the case r = 1, the combinatorial contribution of two kinds of molecules to the partition function is... 

State properties, of mixtures, 24 671-672 State right to know (RTK) laws, ink regulation under, 14 332 State safety acts/regulations, 21 830-831 States, change in entropy between, 24 649 State variables, to fix the properties of a mixture, 24 681—682 STATGRAPHICS plus 5 (quality and design)... 

In equilibrium, impurities or vacancies wiU be distributed uniformly. Similarly, in the case of two gases, as above, once a thorough mixture has been formed on both sides of the partition, the diffusion process is complete. Also at that stage, the entropy of the system has reached its maximum value because the information regarding the whereabouts of the two gases has been minimized. In general, it should be remembered that entropy of a system is a measure of the information available about that system. Thus, the constant increase of entropy in the universe, it is argued, should lead eventually to an absolutely chaotic state in which absolutely no information is available. 

Substituting Equation (53) into Equation (45) gives a statistical expression for the solute contribution to the configurational entropy of the mixture ... 

Flory-Huggins Theory. The simplest quantitative model for AGmx that includes the most essential elements needed for polymer blends is the Flory-Huggins theory, originally developed for polymer solutions (3,4). It assumes the only contribution to the entropy of mixing is combinatorial in origin and is given by equation 3, for a unit volume of a mixture of polymers A. and B. Here, pt and... 

In Section 7.1 we discussed the thermodynamic condition for a stable mixture given in the Flory-Huggins equation (Eq. 7.1-6), where AS denotes the increase of entropy due to mixing. This equation is based on Boltzmann s principle stating that the entropy of a... 

If we have a mixture of AT molecules of one gas, N2 of another, and so on, the general phase space will first contain a group of coordinates and momenta for the molecules of the first gas, then a group for the second, and so on. The partition function will then be a product of terms like Eq. (3.5), one for each type of gas. The entropy will be a sum of terms like Eq. (1.14), with n in place of n, and Pt, the partial pressure, in place of P. But this is just the same expression for entropy in a mixture of gases which we have assumed thermodynamically in Eq. (2.7). Thus the results of Sec. 2 regarding the thermodynamic functions of a mixture of gases follow also from statistical mechanics. 

---