Symbols, thermodynamic

Fig. 50. Superconducting phase diagram of Ui jpThxBei3 for x <0.10 (Kromer et al., 2002). Full lines and symbols thermodynamic phase boundaries broken lines and open symbols lines of anomalies. and 7 denote line of anomalies from minimum in the thermal expansion coeffi-cient a (7), 7max is the line of anomalies from the maximum in C(7) and or(7). A, B and C denote distinct SC phases in the 7 -crossing model.

The relations which permit us to express equilibria utilize the Gibbs free energy, to which we will give the symbol G and which will be called simply free energy for the rest of this chapter. This thermodynamic quantity is expressed as a function of enthalpy and entropy. This is not to be confused with the Helmholtz free energy which we will note sF (L" j (j, > )... 

It is conventional to use molality—moles of solute per kilogram of solvent (symbol m)—as the concentration unit in electrolyte thermodynamics. Accordingly, we shall represent the concentrations of both the indifferent electrolyte and the polymer in these units in this section m3 and m2, respectively. In the same dilute (with respect to polymer) approximation that we have used elsewhere in this chapter, m2 is related to the mass volume system of units C2 by... 

Postiilate 5 affirms that the other molar or specific thermodynamic properties of PVT systems, such as internal energy U and entropy S, are also functions of temperature, pressure, and composition. Tnese molar or unit-mass properties, represented by the plain symbols U, and S, are independent of system size and are called intensive. Temperature, pressure, and the composition variables, such as mole fraction, are also intensive. Total-system properties (V U S ) do depend on system size, and are extensive. For a system containing n moles of fluid, M = nM, where M is a molar property. 

Partial Molar Properties Consider a homogeneous fluid solution comprised of any number of chemical species. For such a PVT system let the symbol M represent the molar (or unit-mass) value of any extensive thermodynamic property of the solution, where M may stand in turn for U, H, S, and so on. A total-system property is then nM, where n = Xi/i, and i is the index identifying chemical species. One might expect the solution propei fy M to be related solely to the properties M, of the pure chemical species which comprise the solution. However, no such generally vahd relation is known, and the connection must be establi ed experimentally for eveiy specific system. 

The numbers iVj and N- are only equal if there are no degeneracies. The sum in the denominator runs over all available molecular energy levels and it is called the molecular partition function. It is a quantity of immense importance in statistical thermodynamics, and it is given the special symbol q (sometimes z). We have... 

The combination of properties (U + PV) occurs so frequently in thermodynamics that it is given a special symbol, H, and termed the enthalpy or heat content" of the system. Thus Equation 2-107 can be written as... 

The combination of properties U - TS occurs so frequently in thermodynamic analysis that it is given a special name and symbol, namely A, the work fimction or maximum luork (because it represents the maximum work per unit mass, obtainable during any isothermal reversible change in any given system). Therefore, it is seen that... 

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. 

This notation by Kroger-Vink is very intuitive. However, the laws of thermodynamic equilibrium may not be applied to these symbols because the elements are not independent of each other as required by thermodynamics. For example the formation of the interstitial metal ion re-... 

Chemical Students (Methuen, 1911), references to the latter under the symbol H. M. have been made whenever it appeared desirable. In spite of (or perhaps on account of) recent attempts to prove the contrary, I am of the opinion that no satisfactory progress can be made even in the elementary parts of thermodynamics without a good working knowledge of the calculus. 

Students often ask, What is enthalpy The answer is simple. Enthalpy is a mathematical function defined in terms of fundamental thermodynamic properties as H = U+pV. This combination occurs frequently in thermodynamic equations and it is convenient to write it as a single symbol. We will show later that it does have the useful property that in a constant pressure process in which only pressure-volume work is involved, the change in enthalpy AH is equal to the heat q that flows in or out of a system during a thermodynamic process. This equality is convenient since it provides a way to calculate q. Heat flow is not a state function and is often not easy to calculate. In the next chapter, we will make calculations that demonstrate this path dependence. On the other hand, since H is a function of extensive state variables it must also be an extensive state variable, and dH = 0. As a result, AH is the same regardless of the path or series of steps followed in getting from the initial to final state and... 

The most common states of a pure substance are solid, liquid, or gas (vapor), state property See state function. state symbol A symbol (abbreviation) denoting the state of a species. Examples s (solid) I (liquid) g (gas) aq (aqueous solution), statistical entropy The entropy calculated from statistical thermodynamics S = k In W. statistical thermodynamics The interpretation of the laws of thermodynamics in terms of the behavior of large numbers of atoms and molecules, steady-state approximation The assumption that the net rate of formation of reaction intermediates is 0. Stefan-Boltzmann law The total intensity of radiation emitted by a heated black body is proportional to the fourth power of the absolute temperature, stereoisomers Isomers in which atoms have the same partners arranged differently in space, stereoregular polymer A polymer in which each unit or pair of repeating units has the same relative orientation, steric factor (P) An empirical factor that takes into account the steric requirement of a reaction, steric requirement A constraint on an elementary reaction in which the successful collision of two molecules depends on their relative orientation. 

Due to its modularity, the software comes in many parts (shown in Fig. 9). The Chemkin package is composed of four important pieces the Interpreter, the Thermodynamic Data Base, the Linking File, and the Gas-Phase Subroutine Library. The Interpreter is a program that first reads the user s symbolic description of the reaction mechanism. It then extracts thermodynamic information for the species involved from the Thermodynamic Data Base. The user may add to or modify the information in the data base by input to the Interpreter. In addition to printed output, the Interpreter writes a Linking File, which contains all the pertinent information on the elements, species, and reactions in the mechanism. 

Figure 4. Susceptibility of the energy moment at To — 2. The symbols are static Monte Carlo results [1] and the curve is obtained from a local thermodynamic approximation [1] using the bulk susceptibilities from a Lennard-Jones equation of state [90], (From Ref. 1.)...

The primary quantities M, L, T are sufficient to describe most problems in mechanics. In thermodynamics and other thermal applications it is customary to add an absolute temperature. In this case the dimension of the Boltzmann constant, for example, is given by [A] = ML2T 20 l, where the symbol 9 is used here for the dimension of the absolute or thermodynamic temperature. 

Here the coefficients Cn and Cv are of no interest the meanings of the remaining symbols are clear from Fig. 4, where FF is the Fermi level at a thermodynamic equilibrium (in the dark) FnF and FPFP are Fermi quasi levels (in the presence of illumination) for electrons and holes, respectively Fs in Fig. 4 denotes the bending of the bands near the surface ( Fb is taken to be greater than zero if the bands are bent upward). 

We can express the use of all the different units in evolution in the language of thermodynamics. While the genome is defined by a DNA sequence so that each base has a singular intensive property as in a computer code of symbols, by way of contrast, the protein content of a cell is an extensive property being concentration dependent and therefore varies under circumstances such as temperature and pressure although... 

The enthalpy change of a reaction, AH, is the heat energy change when the reaction is carried out at constant pressure. It is necessary to express these values under standard conditions. For enthalpy changes measured under standard conditions, the symbol AH is used. Thermodynamic standard conditions are ... 

C) eq is the symbol for the thermodynamic equilibrium constant in this expression gases are represented by pressures and solutes in aqueous solution by molarities. 

The ground state (0 kJ/mol) for the CL molecule is represented by the term symbol 3v . The first excited state (92 kJ/mol above the ground state) is a 1 singlet (electrons spin paired with both electrons in either the n x or the n y level). The 1 v state with paired spin electrons, one each in the 7i v and n y levels, is the next excited level 155 kJ/mol above the ground state. Reduction of 02 by one electron yields the superoxide ion (02), a radical anion. Reduction by two electrons yields the peroxide ion, (02 ). Bond lengths and bond orders for these are given in Table 4.2. As noted in equation 4.2, the reduction potential for 02 in the presence of protons is thermodynamically favorable. Therefore, reversible binding of O2 to a metal can only be achieved if competition with protons and further reduction to superoxide and peroxide are both controlled.8... 

In this expression, the square brackets refer to the activity of the component although it is more convenient to use its concentration. This approximation is generally satisfactory, except at very high concentrations, and is particularly suitable for analytical use. Where it is necessary to distinguish between the constant obtained using concentrations and the true thermodynamic equilibrium constant Ka the former may be termed the equilibrium quotient and assigned the symbol Q. The exact relation between Ke and Q has been the subject of much investigation and speculation. In this... 

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