Pressure-volume-temperature relation

The quantities B, B, / , and ft are called second virial coefficients C, C, y, and / third virial coefficients and D, D, 3, and 3 fourth virial coefficients. These coefficients are functions of the temperature and are characteristic of the individual gas. These equations reproduce the pressure-volume-temperature relations of gases accurately only for low pressures or small densities. 

The virial coefficients can be determined from studies of the pressure-volume-temperature relations of gases. A graphical method for determining the fugacity may be illustrated by the use of the equation of state... 

Pressure, Volume, Temperature Relations for a Liquid. In Chapter 2 it was shown that the behavior of gases could be expressed by a few simple laws which are, to a large extent, independent of the natm e of the gas. This is not true of liquids, and no simple law, analogous to the general gas law for gases, can be written governing the behavior of liquids. To be sure, expressions for the volume of a liquid as a function of temperature and pressure can be written. At constant pressure the volume of a liquid at any temperature T is given by... 

Douslin, D. R. Harrison, R. H. Pressure, Volume, Temperature Relations... 

Bridgman, P. W. (1912). Water in the liquid and five solid forms, under pressure. Proc. Am. Acad. Arts Sci. 47, 441-558. [50, 61] Bridgman, P. W. (1935). The pressure-volume-temperature relations of the liquid and the phase diagram of heavy water. J. Chem. Phys. 

Utracki, L. A., Simha, R., and Garcia-Rejon, A., Pressure-volume-temperature relations in nanocomposite. Macromolecules, 36, 2114—2121 (2003). 

Berg, J. I Simha, R Pressure-volume-temperature relations in liquid and glassy selenium. Journal of Non-Crystalline Solids, 22(1), pp. 1-22 (1976). 

Effect of Crystallization on Pressure-Volume-Temperature Relations... 

R. E. Gibson and O. H. Loeffler, Pressure-Volume-Temperature Relations in Solutions, n. The Energy-Volume Coefficients of Aniline, Nitrobenzene, Bromobenzene and Chlorobenzene. J. Am. Chem. Soc., 61,2515-2522 (1939). 

Dreisbach presents tables on the pressure, volume, temperature relations of organic compounds, using Cox charts for families of compounds. In the last chapter of Gaydon s book, dissociation energies for 275 molecules are listed. 

Sage, B. H., J. G. Schaafsma, and W. M. Lacey. Phase equilibria in hydrocarbon systems, V pressure volume-temperature relations and thermal properties of propane. lEC 26 1218-1224 (1934). 

Pressure-Volume-Temperature Relations of Vapors. Petroleum vapors do not obey the perfect gas laws. In general, low-molecular-... 

The volume of gaseous mixtures may be computed for any condition that is not close to the envelope in the diagram, from the pressure-volume-temperature relations of the hypothetical material C using the pseudo critical point designated as c (Example 5-5). Lines of constant volume are indicated on the diagram. 

Shima R, Utracki L A, Garcia-Rejon A (2001), Pressure-volume-temperature relations of a poly-e-caprolactam and its nanocomposite . Composite Interfaces, 8, 345-53. 

Eijliations of State. An equation of state can be an exceptional tool for property prediction and phase equihbrium modeling. The term equation of state refers to the equihbrium relation among pressure, volume, temperature, and composition of a substance (2). This substance can be a pure chemical or a uniform mixture of chemicals in gaseous or Hquid form. 

Ideal gas law A relation between pressure, volume, temperature, and amount for any gas at moderate pressures ... 

Temperature Tgo in the range between 3.0 and 24.5561 K is defined in terms of 3He or 4He constant volume gas thermometers (CVGT), calibrated at the triple points of Ne and H2, and at a temperature between 3.0 and 5.0 K that has been obtained from vapor pressure versus temperature relations for He. 

The ideal gas law, PV = nRT, is an equation of state that summarizes the relations describing the response of an ideal gas to changes in pressure, volume, temperature, and amount of molecules it is an example of a limiting law. 

Dodson, C.R. and Standing, M.B. Pressure, Volume, Temperature and Solubility Relations for Natural Gas-Water Mixtures, Drill, and Prod. Prac., API (1944) 173-179. 

Just as the gas laws apply to all pure gases, regardless of chemical identity, they also apply to mixtures of gases, such as air. The pressure, volume, temperature, and amount of a gas mixture are all related by the ideal gas law. 

The methods used in predicting these thermodynamic properties employ (a) an equation of state, relating the pressure-volume-temperature characteristics of the fluids (b) ideal gas state heat capacities of the individual components and (c) binary interaction coefficients between the components. The development of these basic relationships is not within the scope of this paper. Technical literature sources of the thermodynamic equations and data are given in the references. 

The next term that is used or implied throughout this chapter is state function. A state function is a property of a system that is only related to its current conditions—it is not concerned with how it got to be at those conditions. An example would be a beaker of water at 50 °C. The beaker of water possesses a certain temperature, volume, and energy under these conditions. It does not matter if it was once filled with ice and reached 50°C by being warmed or if it was once boiling and reached 50°C by being cooled. The state functions, among which are pressure, volume, temperature, energy, and enthalpy, simply describe the substance as it is at a particular moment. 

Thermodynamic properties, such as internal energy and enthalpy, from which one calculates the heat and work requirements of industrial processes, are not directly measurable. They can, however, be calculated from volumetric data. To provide part of the background for such calculations, we describe in this chapter the pressure-volume-temperature (PVT) behavior of pure fluids. Moreover, these PVT relations are important in themselves for such purposes as the metering of fluids and the sizing of vessels and pipelines. 

IDEAL GAS LAW-RELATING PRESSURE, VOLUME, TEMPERATURE, AND MOLES... 

Quach, A. Wilson, P. S. Simha, R., "The Effects of Stereoregularity on the Pressure-Volume-Temperature and Related Properties of Poly(methyl methacrylate)," J. Macromol. Sci., Phys., B9, 533 (1974). 

Zoller, P., "A Study of the Pressure-Volume-Temperature Relationships of Four Related Amorphous Polymers Polycarbonate, Polyarylate, Phenoxy, and Polysulfone," J. Polym. Sci., Polym. Phys. Ed., 20, 1453 (1982). 

Estimate pressure—volume—temperature (PVT) relations, cohesive energy densities, pair correlation functions, X-ray scattering curves, elastic constants, and other properties. 

Dodson, C. R., and M. B. Standing, Pressure-Volume-Temperature and Solubility Relations for Natural-Gas-Water Mixtures, API Drilling and Production Practice, p. 173, 1944. 

Equations of state are relations between pressure, volume, temperature and the amount(s) of substance in the system. In the two-dimensional case the corresponding equation relates x to A, T and all n° s, or to the fractions 6 of the surface covered. Such equations are important for several reasons. 

Because pressure, volume, temperature, and the number of moles present are all interrelated, it would be helpful if one equation could describe their relationship. Remember that the combined gas law relates volume, temperature, and pressure of a sample of gas. 

The van der Waals equation applies strictly to pure real gases, not to mixtures. For a mixture like the one resulting from the reaction of part (a), it may still be possible to define effective a and b parameters to relate total pressure, volume, temperature, and total number of moles. Suppose the gas mixture has a = 4.00 atm moU and b = 0.0330 L moU. Recalculate the pressure of the gas... 

Use the ideal gas law to relate pressure, volume, temperature, and nnmber of moles of an ideal gas and to do stoichiometric calculations involving gases (Section 9.3, Problems 19-32). 

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