Pressure-volume-temperature

Hydrogen bonded materials show much greater deviations from the perfect gas laws than do nonassociated substances. Convenient measures of the extent of deviation are the virial coefficients B, C, D, etc., in the generalized gas law equation 

TABLE 2-VII Comparison of Second Viri2d Coefficient (.6) for Some Simple Gases 

By a combination of this and the Berthelot equation, values of the equilibrium constant were found at several temperatures, and the dimerization enthalpy found from the usual log K vs. /T plot. 

FIGURE 2-9 Second virial coefficient of chloroform-diethyl ether mixtures at several temperatures. [From Lambert, Disc. Faraday Soc. 15, 226 (1953).] 

This technique does not diagnose H bonds. When it is applied to such compounds is GO2, esters, and acetaldehyde, dimerization constants are found of the same order of magnitude as for water, alcohols, and amines. However, when H bonds are known to be present, it can give reasonable values. The thermodynamic properties of H bonds are discussed fully in Chapter 7. 

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The pressure—volume—temperature (PVT) behavior of many natural gas mixtures can be represented over wide ranges of temperatures and pressures by the relationship... 

Other pressure—volume—temperature (PVT) relationships may be found in the Hterature ie, Benedict, Webb, Rubin equations of state (4—7) the Benedict, Webb, Rubin, Starling equation of state (8) the Redlich equation of state (9) and the Redlich-Kwong equation of state (10). 

In the broadest sense, thermodynamics is concerned with mathematical relationships that describe equiUbrium conditions as well as transformations of energy from one form to another. Many chemical properties and parameters of engineering significance have origins in the mathematical expressions of the first and second laws and accompanying definitions. Particularly important are those fundamental equations which connect thermodynamic state functions to real-world, measurable properties such as pressure, volume, temperature, and heat capacity (1 3) (see also Thermodynamic properties). 

Equations of State. Equations of state having adjustable parameters are often used to model the pressure—volume—temperature (PVT) behavior of pure fluids and mixtures (1,2). Equations that are cubic in specific volume, such as a van der Waals equation having two adjustable parameters, are the mathematically simplest forms capable of representing the two real volume roots associated with phase equiUbrium, or the three roots (vapor, Hquid, sohd) characteristic of the triple point. 

Cluusius-Clupeyron Eijliation. Derived from equation 1, the Clapeyron equation is a fundamental relationship between the latent heat accompanying a phase change and pressure—volume—temperature (PVT data for the system (1) ... 

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. 

Vugacity Coefficients. An exact equation that is widely used for the calculation of fugacity coefficients and fugacities from experimental pressure—volume—temperature (PVT) data is... 

The idea of using reduced variables to correlate the pressure—volume—temperature properties of gases, was suggested by van der Waals in 1873. The... 

R. R. Dreisbach, Pressure—Volume—Temperature Telationships of Organic Compounds, Handbook Publishers, Sandusky, Ohio, 1952, pp. 294. 

Computed from pressure-volume-temperature tables in the Vasserman monographs referenced under Table 2-165. 

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

Shay, R. M., Estimating Linear Shrinkage of Semicrystalline Resins from Pressure-Volume Temperature (pvT) Data, SPE-IMD Newsletter 49, Fall 1998. 

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. 

The terms p, T, and v are characteristic reducing parameters which may be obtained by fitting pressure-volume-temperature data (density, thermal expansion coefficient, and thermal pressure coefficient) for each pure component in the mixture (3,12). Values of p, v, and T are given in Tables I and II. 

The fugacity coefficients in Equation (7.29) can be calculated from pressure-volume-temperature data for the mixture or from generahzed correlations. It is frequently possible to assume ideal gas behavior so that = 1 for each component. Then Equation (7.29) becomes... 

Volumetric equations of state (EoS) are employed for the calculation offluid phase equilibrium and thermo-physical properties required in the design of processes involving non-ideal fluid mixtures in the oil, gas and chemical industries. Mathematically, a volumetric EoS expresses the relationship among pressure, volume, temperature, and composition for a fluid mixture. The next equation gives the Peng-Robinson equation of state, which is perhaps the most widely used EoS in industrial practice (Peng and Robinson, 1976). 

Water exists in three basic forms vapor, liquid, and solid. The relationship among the three forms of water is described by the pressure-volume-temperature phase diagram (Figure 1.1). 

DREISBACH, R. R. (1952) Pressure-volume-temperature Relationships of Organic Compounds, 3rd edn (Handbook Publishers). 

The reactor volume is taken as the volume of the reactor physically occupied by the reacting fluids. It does not include the volume occupied by agitation devices, heat exchange equipment, or head-room above liquids. One may arbitrarily select the temperature, pressure, and even the state of aggregation (gas or liquid) at which the volumetric flow rate to the reactor will be measured. For design calculations it is usually convenient to choose the reference conditions as those that prevail at the the inlet to the reactor. However, it is easy to convert to any other basis if the pressure-volume-temperature behavior of the system is known. Since the reference volumetric flow rate is arbitrary, care must be taken to specify precisely the reference conditions in order to allow for proper interpretation of the resultant space time. Unless an explicit statement is made to the contrary, we will choose our reference state as that prevailing at the reactor inlet and emphasize this choice by the use of the subscript zero. Henceforth,... 

Reaction of K3Co(CN) with PMMA. A 1.0 g sample of PMMA and 1.0g of the cobalt compound were combined in a standard vessel and pyrolyzed for 2 hrs at 375°C. The tube was removed from the oven and the contents of the tube were observed to be solid (PMMA is liquid at this temperature). The tube was reattached to the vacuum line via the break-seal and opened. Gases were determined by pressure-volume-temperature measurements on the vacuum line and identified by infrared spectroscopy. Recovered were 0.22g of methyl methacrylate and 0.11 g of CO and C02. The tube was then removed from the vacuum line and acetone was added. Filtration gave two fractions, 1.27g of acetone insoluble material and 0.30g of acetone soluble (some soluble material is always lost in the recovery process). The acetone insoluble fraction was then slurried with water, 0.11 g of material was insoluble in water. Infrared analysis of this insoluble material show both C-H and C-0 vibrations and are classified as char based upon infrared spectroscopy. Reactions were also performed at lower temperature, even at 260°C some char is evident in the insoluble fraction. 

Natural gas mixtures, pressure-volume-temperature (PVT) behavior of, 12 370 Natural gas production, 12 372-378 13 592 nitrogen in, 17 287 Natural gas reserves, 12 366-369 estimate of undiscovered, 12 368 Natural gas reservoirs, 12 372 Natural graphite, 12 771-799 analytical and test methods for, 12 786-790... 

It is possible to combine Avogadro s law and the combined gas law to produce the ideal gas equation, which incorporates the pressure, volume, temperature, and amount relationships of a gas. The ideal gas equation has the form of... 

Gas law problems, like all problems, begin with isolating the variables and the unknown from the question. The usual suspects in gas law problems are pressure, volume, temperature, and moles. You will need to deal with at least two of these properties in every problem. 

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