Temperature Thermodynamic functions

Because of its use in pyrotechnics and propellants, thermal decomposition of this salt has been studied for a long time. Simchen77 has given references back to 1816. High-temperature thermodynamic functions are listed in the JANAF tables. We have given those listed by HSC. 

High Temperature Thermodynamic Functions for the Lanthanide Metals ... 

Johnson, G. K., Papatheodorou, G. N., and Johnson, C. E., 1980, The enthalpies of formation and high temperature thermodynamic functions of the arsenic sulfides AS4S4) and (AS2S3) Journal of Chemical Thermodynamics, v. 12, p. 545-57. 

MEZ/TIL] Mezaki, R., Tilleux, E. W., Jambois, T. F., Margrave, J. L., High-temperature thermodynamic functions for refractory compounds, Advances in thermophysical properties at extreme temperatures and pressures, pp. 138-145, Ameriean society of mechanical engineers, (1960). Cited on page 209. 

The heat of combustion of a compound is the heat of rection for the complete oxidation process. For any alkane, the products of combustion are CO2 and H2O, the latter generally assumed to be in the liquid state (However, at high temperatures thermodynamic functions for water are generally tabulated in the gaseous state.) We start by writing the balanced equation for the reaction. 

In Chapter 2 we discuss briefly the thermodynamic functions whereby the abstract fugacities are related to the measurable, real quantities temperature, pressure, and composition. This formulation is then given more completely in Chapters 3 and 4, which present detailed material on vapor-phase and liquid-phase fugacities, respectively. 

A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

A thermodynamic function for systems at constant temperature and pressure that indicates whether or not a reaction is favorable (AG < 0), unfavorable (AG > 0), or at equilibrium (AG = 0). 

Propylene oxide is a colorless, low hoiling (34.2°C) liquid. Table 1 lists general physical properties Table 2 provides equations for temperature variation on some thermodynamic functions. Vapor—liquid equilibrium data for binary mixtures of propylene oxide and other chemicals of commercial importance ate available. References for binary mixtures include 1,2-propanediol (14), water (7,8,15), 1,2-dichloropropane [78-87-5] (16), 2-propanol [67-63-0] (17), 2-methyl-2-pentene [625-27-4] (18), methyl formate [107-31-3] (19), acetaldehyde [75-07-0] (17), methanol [67-56-1] (20), ptopanal [123-38-6] (16), 1-phenylethanol [60-12-8] (21), and / /f-butanol [75-65-0] (22,23). 

Although equation 35 is a simple expression, it tends to be confusing. In this equation the enthalpy difference appears as driving force in a mass-transfer expression. Enthalpy is not a potential, but rather an extensive thermodynamic function. In equation 35, it is used as enthalpy pet mole and is a kind of shorthand for a combination of temperature and mass concentration terms. 

Most thermometry using the KTTS direcdy requites a thermodynamic instmment for interpolation. The vapor pressure of an ideal gas is a thermodynamic function, and a common device for reali2ing the KTTS is the helium gas thermometer. The transfer function of this thermometer may be chosen as the change in pressure with change in temperature at constant volume, or the change in volume with change in temperature at constant pressure. It is easier to measure pressure accurately than volume thus, constant volume gas thermometry is the usual choice (see Pressure measurement). 

Above 962°C, the freezing point of silver, temperatures on the ITS-90 ate defined by a thermodynamic function and an interpolation instmment is not specified. The interpolation instmment universally used is an optical pyrometer, manual or automatic, which is itself a thermodynamic device. 

Once the values of thermodynamic functions, Aff, ASp. ate known at a given temperature the value for the function can be calculated at any other temperature by ... 

Boron Monoxide and Dioxide. High temperature vapor phases of BO, B2O3, and BO2 have been the subject of a number of spectroscopic and mass spectrometric studies aimed at developiag theories of bonding, electronic stmctures, and thermochemical data (1,34). Values for the principal thermodynamic functions have been calculated and compiled for these gases (35). 

Whereas this two-parameter equation states the same conclusion as the van der Waals equation, this derivation extends the theory beyond just PVT behavior. Because the partition function, can also be used to derive aH the thermodynamic functions, the functional form, E, can be changed to describe this data as weH. Corresponding states equations are typicaHy written with respect to temperature and pressure because of the ambiguities of measuring volume at the critical point. 

The protonation equilibria for nine hydroxamic acids in solutions have been studied pH-potentiometrically via a modified Irving and Rossotti technique. The dissociation constants (p/fa values) of hydroxamic acids and the thermodynamic functions (AG°, AH°, AS°, and 5) for the successive and overall protonation processes of hydroxamic acids have been derived at different temperatures in water and in three different mixtures of water and dioxane (the mole fractions of dioxane were 0.083, 0.174, and 0.33). Titrations were also carried out in water ionic strengths of (0.15, 0.20, and 0.25) mol dm NaNOg, and the resulting dissociation constants are reported. A detailed thermodynamic analysis of the effects of organic solvent (dioxane), temperature, and ionic strength on the protonation processes of hydroxamic acids is presented and discussed to determine the factors which control these processes. 

It follows that although the thermodynamic functions can be measured for a given distribution system, they can not be predicted before the fact. Nevertheless, the thermodynamic properties of the distribution system can help explain the characteristics of the distribution and to predict, quite accurately, the effect of temperature on the separation. 

The calculations that have been carried out [56] indicate that the approximations discussed above lead to very good thermodynamic functions overall and a remarkably accurate critical point and coexistence curve. The critical density and temperature predicted by the theory agree with the simulation results to about 0.6%. Of course, dealing with the Yukawa potential allows certain analytical simplifications in implementing this approach. However, a similar approach can be applied to other similar potentials that consist of a hard core with an attractive tail. It should also be pointed out that the idea of using the requirement of self-consistency to yield a closed theory is pertinent not only to the realm of simple fluids, but also has proved to be a powerful tool in the study of a system of spins with continuous symmetry [57,58] and of a site-diluted or random-field Ising model [59,60]. 

Lack of termination in a polymerization process has another important consequence. Propagation is represented by the reaction Pn+M -> Pn+1 and the principle of microscopic reversibility demands that the reverse reaction should also proceed, i.e., Pn+1 -> Pn+M. Since there is no termination, the system must eventually attain an equilibrium state in which the equilibrium concentration of the monomer is given by the equation Pn- -M Pn+1 Hence the equilibrium constant, and all other thermodynamic functions characterizing the system monomer-polymer, are determined by simple measurements of the equilibrium concentration of monomer at various temperatures. 

Values for the thermodynamic functions as a function of temperature for condensed phases are usually obtained from Third Law measurements. Values for ideal gases are usually calculated from the molecular parameters using the statistical mechanics procedures to be described in Chapter 10. In either... 

J. Boerio-Goates, "Heat-Capacity Measurements and Thermodynamic Functions of Crystalline a-D-Glucose at Temperatures from 0 K to 350 K.". J. Chem. Thermodyn.. 23, 403-409 (1991). 

Example 9.3 Calculate the pressure of atomic chlorine in Cl2(g) at a total pressure of 1.00 bar and a temperature of 2000 K. Do the calculation (a) using the thermodynamic functions in Table 4.3, and (b) using equation (9.58), which requires Cp m expressed as a function of T, obtained from Table 2.1, and compare the results. 

Table A4.1 Thermodynamic functions of an ideal gas. (Use R = 8.314510 J-K l mol 1 and SI units for pressure, temperature, and all molecular data.)...

Vapor pressures and vapor compositions in equilibrium with a hypostoichiometric plutonium dioxide condensed phase have been calculated for the temperature range 1500 I H 4000 K. Thermodynamic functions for the condensed phase and for each of the gaseous species were combined with an oxygen-potential model, which we extended from the solid into the liquid region to obtain the partial pressures of O2, 0, Pu, PuO and Pu02 as functions of temperature and of condensed phase composition. The calculated oxygen pressures increase rapidly as stoichiometry is approached. At least part of this increase is a consequence of the exclusion of Pu +... 

The process we have followed Is Identical with the one we used previously for the uranium/oxygen (U/0) system (1-2) and Is summarized by the procedure that Is shown In Figure 1. Thermodynamic functions for the gas-phase molecules were obtained previously (3) from experimental spectroscopic data and estimates of molecular parameters. The functions for the condensed phase have been calculated from an assessment of the available data, Including the heat capacity as a function of temperature (4). The oxygen potential Is found from extension Into the liquid phase of a model that was derived for the solid phase. Thus, we have all the Information needed to apply the procedure outlined In Figure 1. 

In this paper we describe (1) the gas-phase thermodynamic functions (2) the condensed-phase thermodynamic functions (3) the oxygen potential (and the phase boundaries that are consistent with It) and (4) the resulting vapor pressure and composition as functions of temperature and composition of the condensed phase. 

Thermodynamic Functions of the Gases. To apply Eqs. (1-10), the free energies of formation, Ag , for all gaseous species as a function of temperature are required. Tabulated data were fit by a least-squares procedure to derive an analytical equation for AG° of each vapor species. For the plutonium oxide vapor species, the data calculated from spectroscopic data (3 ) were used for 0(g) and 02(g), the JANAF data (.5) were used and for Pu(g), data from the compilation of Oetting et al. (6) were used. The coefficients of the equations for AG° of the gaseous species are included in Table I. 

The uncertainties in the condensed-phase thermodynamic functions arise from (1) the possible existence of a solid-solid phase transition in the temperature range 2160 to 2370 K and (2) the uncertainty in the estimated value of the liquid heat capacity which is on the order of 40%. While these uncertainties affect the partial pressures of plutonium oxides by a factor of 10 at 4000 K, they are not limiting because, at that temperature, the total pressure is due essentially entirely to O2 and 0. 

A number of other thermodynamic properties of adamantane and diamantane in different phases are reported by Kabo et al. [5]. They include (1) standard molar thermodynamic functions for adamantane in the ideal gas state as calculated by statistical thermodynamics methods and (2) temperature dependence of the heat capacities of adamantane in the condensed state between 340 and 600 K as measured by a scanning calorimeter and reported here in Fig. 8. According to this figure, liquid adamantane converts to a solid plastic with simple cubic crystal structure upon freezing. After further cooling it moves into another solid state, an fee crystalline phase. 

Reaction enthalpies may also vary with temperature. Most tabulations of thermodynamic functions are for T = 298 K, so we assume that is the temperature unless otherwise specified. 

C06-0116. For the constant-temperature process that follows, give the sign (+, -, or 0) for each of the specified thermodynamic functions. In each case give a brief account of your reasoning (a) A (b)... 

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