Intensive thermodynamic property

Fugacity is a thermodynamic property intensively used in chemical engineering, the most important being chemical equilibrium of gases at high pressures, and vapour-liquid equilibrium. The first subject is not covered here, but second topic will be discussed in detail in Chapter 6. Therefore, the problem is how to calculate fugacities... 

Two simulation methods—Monte Carlo and molecular dynamics—allow calculation of the density profile and pressure difference of Eq. III-44 across the vapor-liquid interface [64, 65]. In the former method, the initial system consists of N molecules in assumed positions. An intermolecule potential function is chosen, such as the Lennard-Jones potential, and the positions are randomly varied until the energy of the system is at a minimum. The resulting configuration is taken to be the equilibrium one. In the molecular dynamics approach, the N molecules are given initial positions and velocities and the equations of motion are solved to follow the ensuing collisions until the set shows constant time-average thermodynamic properties. Both methods are computer intensive yet widely used. 

The phase rule specifies the number of intensive properties of a system that must be set to estabUsh all other intensive properties at fixed values (3), without providing information about how to calculate values for these properties. The field of appHed engineering thermodynamics has grown out of the need to assign numerical values to thermodynamic properties within the constraints of the phase rule and fundamental laws. In the engineering disciplines there is a particular demand for physical properties, both for pure fluids and mixtures, and for phase equiUbrium data (4,5). 

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. 

The mechanism of radiative transfer in flares was found to depend on compn, flare diameter and pressure (Ref 69). The flare efficiency calcn is complicated by the drop-off in intensity at increasing altitudes and at very large diameters owing to the lower reaction temps (Ref 11, p 13) and the narrowing of the spectral emittance band (Ref 35). The prediction of the light output in terms of compn and pressure (ie, altitude) is now possible using a computer program which computes the equilibrium thermodynamic properties and the luminance (Ref 104) Flare Formulations... 

An alternative is to consider the value of the thermodynamic property per unit mass. Such quantities are called specific properties. Thus the specific volume is the volume per unit mass. It is the reciprocal of the density and is an intensive property. 

The reason that the PDT is an effective tool for the generation of physical models is that it treats an intensive thermodynamic property, and the distribution functions involved are simpler in the thermodynamic limit than if this were not the case [10]. An extended family of modeling tools then applies directly. The quasichemical approach is a general example. It amounts to stratification of the statistical problem... 

The term parametric pumping was coined by Wilhelm et al. [Wilhelm, Rice, and Bendelius, Ind. Eng. Chem. Fundam., 5,141-144 (1966)] to describe a liquid-phase adsorption process in which separation is achieved by periodically reversing not only flow but also an intensive thermodynamic property such as temperature, which influences adsorptivity. Moreover, they considered the concurrent cycling of pressure, pH, and electrical and magnetic fields. A lot of research and development has been conducted on thermal, pressure, and pH driven cycles, but to date only gas-phase pressure-swing parametric pumping has found much commercial acceptance. 

An alternative to the common device of determining relative intensities is a study of the fine structure of the scattered beam. This entails resolving the spectrum of scattered light into its three peaks, viz. a central peak and two side ones. The need is thus obviated to refer to I0 or, according to the apparatus, the scattering power of a standard calibration material. The method is used mainly for determining diffusion constants and thermodynamic properties of liquids. 

The units of q are calories per square centimeter per second and those of the thermal conductivity A are calories per centimeter per second per degree Kelvin. It is not the temperature, an intensive thermodynamic property, that is exchanged, but energy content, an extensive property. In this case, the energy density and the exchange reaction, which show similarity, are written as... 

This equation implies a double dependence of scattering intensities on concentration and observation angle [9]. By extrapolating the scattering data for each concentration to zero angle, the second virial coefficient, which is related to thermodynamic properties, may be measured [9,10,15-18],... 

The thermodynamic state is therefore considered equivalent to specification of the complete set of independent intensive properties 7 1 R2, Rn. The fact that state can be specified without reference to extensive properties is a direct consequence of the macroscopic character of the thermodynamic system, for once this character is established, we can safely assume that system size does not matter except as a trivial overall scale factor. For example, it is of no thermodynamic consequence whether we choose a cup-full or a bucket-full as sample size for a thermodynamic investigation of the normal boiling-point state of water, because thermodynamic properties of the two systems are trivially related. 

Eq.(2.2-4) is the phase rule of Gibbs. According to this rule a state with II phases in a system with N components is frilly determined (all intensive thermodynamic properties can be calculated) if a number of F of the variables is chosen, provided that g of all phases as function of pressure, temperature and composition is known. 

The properties of a substance can be classified as either intensive or extensive. Intensive properties, which include density, pressure, temperature, and concentration, do not depend on the amount of the material. Extensive properties, such as volume and weight, do depend on the amount. Most thermodynamic properties are extensive including energy (E), enthalpy (H), entropy (5), and free energy (G). 

Finally, the thermodynamic properties of a system considered as variables may be classified as either intensive or extensive variables. The distinction between these two types of variables is best understood in terms of an operation. We consider a system in some fixed state and divide this system into two or more parts without changing any other properties of the system. Those variables whose value remains the same in this operation are called intensive variables. Such variables are the temperature, pressure, concentration variables, and specific and molar quantities. Those variables whose values are changed because of the operation are known as extensive variables. Such variables are the volume and the amount of substance (number of moles) of the components forming the system. 

A thermodynamic property is said to be extensive if the magnitude of the property is doubled when the size of the system is doubled. Examples of extensive properties are volume V and amount of substance n. A thermodynamic property is said to be intensive if the magnitude of the property does not change when the size of the system is changed. Examples of intensive properties are temperature, pressure, and the mole fractions of species. The ratio of two extensive properties is an intensive property. For example, the ratio of the volume of a one-component system to its amount is the molar volume Vm = V/n. 

The inequalities of the previous paragraph are extremely important, but they are of little direct use to experimenters because there is no convenient way to hold U and S constant except in isolated systems and adiabatic processes. In both of these inequalities, the independent variables (the properties that are held constant) are all extensive variables. There is just one way to define thermodynamic properties that provide criteria of spontaneous change and equilibrium when intensive variables are held constant, and that is by the use of Legendre transforms. That can be illustrated here with equation 2.2-1, but a more complete discussion of Legendre transforms is given in Section 2.5. Since laboratory experiments are usually carried out at constant pressure, rather than constant volume, a new thermodynamic potential, the enthalpy H, can be defined by... 

The internal energy is homogeneous of degree 1 in terms of extensive thermodynamic properties, and so equation 2.2-8 leads to equation 2.2-14. All extensive variables are homogeneous functions of the first degree of other extensive properties. All intensive properties are homogeneous functions of the zeroth degree of the extensive properties. 

Equations 2.2-10 to 2.2-12 and equations 2.3-3 to 2.3-6 show that the thermodynamic properties of a system are interrelated in complicated, and sometimes unexpected, ways. The next section shows that the intensive variables for a thermodynamic system are not independent of each other. 

Pressure, volume, temperature, and number of moles are thermodynamic properties or thermodynamic variables of a system—in this case, a gas sample. Their values are measured by experimenters using thermometers, pressure gauges, and other instruments located outside the system. The properties are of two types those that increase proportionally with the size of the system, such as n and K called extensive properties, and those defined for each small region in the system, such as P and T, called intensive properties. Terms that are added together or are on opposite sides of an equal sign must contain the same number of... 

We have defined solutions as homogeneous phases, with uniform concentrations throughout. Clearly, the surface of a solution provides a different environment than its bulk, and we should expect intensive properties (concentrations as well as intensive thermodynamic properties) to vary in this region. The mechanical and thermal variables, P and T, however, can be taken as uniform throughout the solution. It should be emphasized that the surface region of the solution is very thin, just a few molecular diameters thick. Bulk properties of the solution will, thus, only be affected by the surface if the solution is composed of very small droplets. 

The most important chemical thermodynamic property is the chemical potential of a substance, denoted /x.18 The chemical potential is the intensive property that is the criterion for equilibrium with respect to the transfer or transformation of matter. Each component in a soil has a chemical potential that determines the relative propensity of the component to be transferred from one phase to another, or to be transformed into an entirely different chemical compound in the soil. Just as thermal energy is transferred from regions of high temperature to regions of low temperature, so matter is transferred from phases or substances of high chemical potential to phases or substances of low chemical potential. Chemical potential is measured in units of joules per mole (J mol 1) or joules per kilogram (J kg 1). 

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