Thermodynamics, definition

Thermodynamic Properties The variation in solvent strength of a supercritical fluid From gaslike to hquidlike values may oe described qualitatively in terms of the density, p, or the solubihty parameter, 6 (square root of the cohesive energy density). It is shown For gaseous, hquid, and SCF CO9 as a function of pressure in Fig. 22-17 according to the rigorous thermodynamic definition ... 

So far in this chapter our discussion has focused on thermochemistry, the study of the heat effects in chemical reactions. Thermochemistry is a branch of thermodynamics, which deals with all kinds of energy effects in all kinds of processes. Thermodynamics distinguishes between two types of energy. One of these is heat (q) the other is work, represented by the symbol w. The thermodynamic definition of work is quite different from its colloquial meaning. Quite simply, work includes all forms of energy except heat. 

Because dASt/dT = AC /T, from the thermodynamic definition, we have upon integration... 

To calculate the entropy of a substance, we use Boltzmann s formula, but the calculations are sometimes very difficult and require a lot of manipulation of Eq. 6. To measure the entropy of a substance, we use the thermodynamic definition, Eq. 1, in combination with the third law of thermodynamics. Because the third law tells us that S(0) = 0 and Eq. 2 can be used to calculate the change in entropy as a substance is heated to the temperature of interest, we can write... 

However, it can be proved simply that this equation cannot hold. By substituting the thermodynamic definitions of AH and AS into eq. (82), we get... 

The technical terms homogeneity and inhomogeneity defined in analytical chemistry must be distinguished from the physicochemical concept of homogeneity and heterogeneity (Danzer and Ehrlich [1984]). Whereas the thermodynamical definition refers to morphology and takes one-phase-or multi-phase states of matter as the criterion, the analytical-chemical definition is based on the concentration function... 

Equilibrium constants do not have units because in the strict thermodynamic definition of the equilibrium constant, the activity of a component is used, not its concentration. The activity of a species in an ideal mixture is the ratio of its concentration or partial pressure to a standard concentration (1 M) or pressure (1 atm). Because activity is a ratio, it is unitless and the equilibrium constant involving activities is also unitless. 

These activities can be verified if It can he shown that the solubility data of (8) are at stoichiometric saturation, but as mentioned above, this requires independent thermodynamic definition of K(x). 

The use of (T/100) as a variable has the advantage of making the parameters A, A2, A3, and A4 of similar magnitude. The application of standard thermodynamic definitions to the equation allows the equation parameters to be used to calculate the thermodynamic characteristics of the dissolution process summarized in Table I. When all four parameters of the equation... 

It is useful to keep in mind that the equilibrium constant is defined in terms of the difference in standard state free energies between products and reactants. Thus, for the reaction written in Equation 4.36 we obtained Equation 4.50, essentially by thermodynamic definition,... 

GENERAL EQUATIONS FOR THE ENTROPY OF GASES 143 conclude from Equation (6.111) that a natural thermodynamic definition of T is... 

The second law of thermodynamics can be expressed in terms of another state function, the entropy (S). The thermodynamics definition considers the change in entropy dS that occurs as a result of a physical or chemical change, and is based on the expression... 

Thermodynamic definitions relevant to catalysis and the role of electron microscopy... 

Thermodynamic definitions show that the first term of Eq. (1) is the enthalpy of mixing, AHu, while the second term is the negative of the excess entropy of mixing, ASm, multiplied by T. When all four parameters are zero, the liquid is ideal with a zero enthalpy and excess entropy of mixing. What has been called the quasiregular model, a = b = 0, has been used by Panish and Ilegems (1972) to fit the liquidus lines of a number of III—V binary compounds. The particular extension of this special case of Eq. (1) to a ternary liquid given by... 

Within the canonical ensemble, and using established thermodynamic definitions, all of the following are true... 

In practice, then, it is fairly straightforward to convert the potential energy determined from an electronic structure calculation into a wealth of thennodynamic data - all that is required is an optimized structure with its associated vibrational frequencies. Given the many levels of electronic structure theory for which analytic second derivatives are available, it is usually worth the effort required to compute the frequencies and then the thermodynamic variables, especially since experimental data are typically measured in this form. For one such quantity, the absolute entropy 5°, which is computed as the sum of Eqs. (10.13), (10.18), (10.24) (for non-linear molecules), and (10.30), theory and experiment are directly comparable. Hout, Levi, and Hehre (1982) computed absolute entropies at 300 K for a large number of small molecules at the MP2/6-31G(d) level and obtained agreement with experiment within 0.1 e.u. for many cases. Absolute heat capacities at constant volume can also be computed using the thermodynamic definition... 

The requirements for the thermodynamic definition of solubility are 1) well defined initial solid and final solution states, and 2) establishment of equilibrium between these two states. Under these conditions, the solubility at a given temperature and pressure is the concentration of the sample in solution. At a given temperature and pressure, the solid state is the stable crystalline state and the solution state is... 

The building of additive models begins with the portrayal of a system in an equilibrium state. This is true whether we are using a kinematic or a thermodynamic definition of equilibrium states. Each system is assumed to wind down to its lowest level of variable behaviour, a general statement that embraces a number of phenomena depending upon the level of complexity considered. This leads to a static model in which there is a sharp delineation between an event and its absence. There is a clear illumination of discrete events modelled to be cause and effect. 

Reaction Rates and Equilibria Have Precise Thermodynamic Definitions... 

The material covered in this chapter is self-contained, and is derived from well-known relationships such as Newton s second law and the ideal gas law. Some quantum mechanical results and the statistical thermodynamics definition of entropy are given without rigorous derivation. The end result will be a number of practical formulas that can be used to calculate thermodynamic properties of interest. 

The next important thermodynamic function that we must obtain is the entropy S. The statistical thermodynamic definition of entropy is... 

The thermodynamic definition of entropy says that the change in entropy dS in a process carried out reversibly is the heat absorbed in the process d Qrev divided by the temperature... 

Comparison of the combined first/second law (4.28) with (4.30) leads to the more general and rigorous thermodynamic definitions for the intensive properties T, —P respectively conjugate to the extensive properties S, V ... 

What is the physical nature of the Gibbs free energy, and what is free about it We can consider this question first from the viewpoint of fundamental thermodynamic definitions, with no microscopic molecular connotations. For a reversible change of state carried out under conditions of constant T and P, we can write... 

The Buckingham statement fares no better in this regard, for the concept of a true equilibrium state is no less tautological than that of a perfect crystal. Moreover, the implied restriction to true equilibrium states (presumably, those for which no kinetic conversion is possible on any timescale) is even more strongly at odds with fundamental thermodynamic definitions, as outlined in Sections 2.10 and 2.11. Indeed, such a restriction, if enforced zealously, would preclude application of thermodynamics to any chemical system—past, present, or future—except for the final universal Warmetod state.]... 

Finally, let us note some interesting identities for other thermodynamic potentials that follow from Equation (6.31). From the energy identity U = TS — PV + ix tj and basic thermodynamic definitions, we can readily infer that... 

Starting from A = — kT In Q and basic thermodynamic definitions, we obtain... 

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