Entropy curve

Figure 6 shows the entropy curve obtained during the lithiation process. Starting from a high and positive value of 60J/(mol.K) at x 0, AS(x)... 

The resulting plot shows three curves two mountain plots derived from the MFE structure and the pairing probabilities and a positional entropy curve. Well-defined regions are identified by low entropy. By superimposing several mountain plots, structures can easily be compared. 

Compression cycles are shown in Figs 8a and 8b. The former indicates the effect of various values of n in PVn = constant and it is seen that the work done is the area under the temperature-entropy curve. Figure 8b illustrates the three-stage compressor of this problem. The final temperature T2, found from T2/T1 = (P2lP ) y X)lr 1S 390 K. The dotted lines illustrate the effect of imperfect interstage cooling. 

If the mean field expressions were accurate, the mean field entropy curves in Fig. 7, the curves with symbols, would coincide with the entropy from simulations. All of the mean field theories overestimate the entropy of the high-temperature phase, and Nagle s expression also overestimates the entropy of the low-temperature phase. We can ask whether the mean field expressions are meaningful for our model, regardless of whether our model accurately corresponds to experiment. In actuality, our model is reasonably close to experiment. Two occupation probabilities for ice III and IX are traditionally called a and (3. Our value for a, 38%, at the transition is close to the experimental values, 33% and 35%." Our (3,... 

It is certainly clear from an examination of the experimental differential entropy curve for argon on rutile (9) that the entropy terms dropped from Eq. (35) are not negligible in this case, at least up to 6 = 4.5. In fact, in the notation of Eq. (35), dSs/dN — (SL/N) is about one-half of R In x at 6 = 2.4 and these two quantities are about equal at 6 = 4.5. One may hope that the refinements discussed above will make some contribution to understanding such entropy effects as well as deviations from the third power law (the two problems are of course related). 

AOSS-U entropy curves for H20, HDO, D20, H2S, and H2Se as a function of temperature. 

As the entropy plot shows us, the shape of the entropy curve and the dx/dT function (Fig. 20) share a similar shape. This points us to Eqs. 35 or 37. It seems that the left side of the entropy plot may just be the result of the presence of the mixed-phase states, while for the right side of the entropy plot, there is some true entropy change hidden along with the dx/dT contribution. By using Eqs. 35 or 37, we present a way to separate the two contributions, and so estimate more trustworthy entropy change values. We plot the entropy change values obtained directly from the Maxwell relation, as a function of dx/dT. This is shown in Fig. 22(a), for the data shown in Figs. 21(a) and 20. 

By eliminating the contribution of the temperature derivative of the mixed-phase fraction, the entropy peak effect is eliminated, in a justified way. The resulting entropy curve resembles the results obtained from specific heat measurements when compared to results from magnetic measurements, as seen in Refs. (Liu et al., 2007) and (Tocado et al, 2009), among others. 

Goedken, and Gritmon(J3) in 1977 to investigate the thermodynamic parameters of a variety of aminopolycarboxylate ligands across the lanthanide series. Variations in the enthalpy and entropy curves vs. Z were attributed to different degrees and patterns of dehydration as well as the increasing polydentate nature of the complexation. The linear relationship between log 6 and ZpKa of... 

The last physically meaningful trajectory considered in the present work is the adiabat. This trajectory is defined as constant entropy curve. The entropy is calculated as the following. We compute excess free energy by integrating the equation of states Fe /iNk T) = F - Fid)/NkBT = l/ kBT) P p ) - p kBl)lp dp. The excess entropy can be computed via Sgx = U — Fex)/NkBT. The total entropy is 5 = Sex + id, where the ideal gas entropy is Sid/NkB = 3/21n(r) — ln(/o) + The last term in this expression is constant and... 

J.D. Raistrick et al. [2, 6] were perhaps the first who studied the thermodynamics of electrochemical insertion of lithium into HASP. In these works, Gibbs energy and entropy of lithiation of mngsten and vanadium bronzes have been measured along with the determination of lithium diffiision coefficient The OCP and entropy curves of LixNao seWOs were smooth, confirming formation of the solid solution within the interval 0.0004 < x < 0.35. However, dA5/dx,... 

Figure 2.10 presents the thermodynamic and crystallographic properties of lithium nickel cobalt oxide LixNio 8Coo 202. The entropy curve is consistent with... 

It is of considerable interest to consider in greater detail plots of the enthalpy interaction parameters for the alkali chloride-magnesium chloride systems. These are shown in Fig. 8, taken from the work of Kleppa and McCarty. Note in particiilar the sharp dip in X near N qi2 0.33 for the systems containing KCl, RbCl, and CsCl. This correlates with the "anomalous partial entropy curves for these mixtures, and undoubtedly reflects the tendency of these systems to form the complex anion MgCl. Note also that the dip is completely absent in the silver chloride and lithium chloride system, and occurs only as a very broad minimum in sodium chloride-magnesium chloride. This is consistent with the nearly ideal entropy found in these systems. 

Now let us consider the non-electrolytes. Here we have two very distinct types of behaviour. There are the so-called hydro-phobic, and the hydrophilic effects. The hydrophobic effect can be shown schematically from a consideration of the thermodynamics of hydrocarbon solutions. Usually a non-ideal solution arises because the two components either strongly attract each other or strongly repel each other the effects are shown in the enthalpy. Figure 8 shows various types of behaviour, as reflected in the excess thermodynamic functions (Rowlinson, 1969). The drawn out lines are free energies, the broken lines are enthalpies and the dotted lines are the entropy curves. A positive free energy means a positive deviation from ideal behaviour. In normal systems AG follows the AH curve fairly benzene-MeOH. In... 

The difference of the microcanonical surface entropies in the transition regime defines the surface entropy. In the case of the aggregation transition, it is given by the maximum separation between the Gibbs hull and the entropy curve as shown in Fig. 11.5 HsiEsep) — S Esep), where HsiE)f HsiE) is the concave Gibbs hull... 

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