State intensive properties

However, because both Rj and R2 are infinite in extent and have the same dead-state intensive properties, it... 

Because the macroscopic-intensive properties of homogeneous fluids in equilibrium states ate functions of T, P, and composition, it follows that the total property of a phase fiM can be expressed functionally as in equation 113 ... 

The state (or behaviour) of a system is described by variables or properties which may be classified as (a) extensive properties such as mass, volume, kinetic energy and (b) intensive properties which are independent of system size, e.g., pressure, temperature, concentration. An extensive property can be treated like an intensive property by specifying that it refers to a unit amount of the substance concerned. Thus, mass and volume are extensive properties, but density, which is mass per unit volume, and specific volume, which is volume per unit mass, are intensive properties. In a similar way, specific heat is an intensive property, whereas heat capacity is an extensive property. 

As described above, the combination of EPR and Mossbauer spectroscopies, when applied to carefully prepared parallel samples, enables a detailed characterization of all the redox states of the clusters present in the enzyme. Once the characteristic spectroscopic properties of each cluster are identified, the determination of their midpoint redox potentials is an easy task. Plots of relative amounts of each species (or some characteristic intensive property) as a function of the potential can be fitted to Nernst equations. In the case of the D. gigas hydrogenase it was determined that those midpoint redox potentials (at pFi 7.0) were —70 mV for the [3Fe-4S] [3Fe-4S]° and —290 and —340mV for each of the [4Fe-4S]> [4Fe-4S] transitions. 

The phase rule states that, when equilibrium conditions are sustained, a minimum number of intensive properties of the (subsurface) system can be used to calculate its remaining properties. An intensive property is a property that is independent of the amount of substance in the domain. Examples of intensive properties include temperature (7), pressure (P), density (p), and chemical potential (p), which is a relative measure of the potential energy of a chemical compound. The phase rule specifies the minimum number of intensive properties that must be determined to obtain a comprehensive thermodynamic depiction of a system. 

A phase is defined as a state of matter that is uniform throughout in terms of its chemical composition and physical state in other words, a phase may be considered a pure substance or a mixture of pure substances wherein intensive properties do not vary with position. Accordingly, a gaseous mixture is a single phase, and a mixture of completely miscible liquids yields a single hquid phase in contrast, a mixture of several solids remains as a system with multiple solid phases. A phase rule therefore states that, if a limited number of macroscopic properties is known, it is possible to predict additional properties. 

Any characteristic of a system is called a property. The essential feature of a property is that it has a unique value when a system is in a particular state. Properties are considered to be either intensive or extensive. Intensive properties are those that are independent of the size of a system, such as temperature T and pressure p. Extensive properties are those that are dependent on the size of a system, such as volume V, internal energy U, and entropy S. Extensive properties per unit mass are called specific properties such as specific volume v, specific internal energy u, and specific entropy. s. Properties can be either measurable such as temperature T, volume V, pressure p, specific heat at constant pressure process Cp, and specific heat at constant volume process c, or non-measurable such as internal energy U and entropy S. A relatively small number of independent properties suffice to fix all other properties and thus the state of the system. If the system is composed of a single phase, free from magnetic, electrical, chemical, and surface effects, the state is fixed when any two independent intensive properties are fixed. 

It should be emphasized that the criterion for macroscopic character is based on independent properties only. (The importance of properly enumerating the number of independent intensive properties will become apparent in the discussion of the Gibbs phase rule, Section 5.1). For example, from two independent extensive variables such as mass m and volume V, one can obviously form the ratio m/V (density p), which is neither extensive nor intensive, nor independent of m and V. (That density cannot fulfill the uniform value throughout criterion for intensive character will be apparent from consideration of any 2-phase system, where p certainly varies from one phase region to another.) Of course, for many thermodynamic purposes, we are free to choose a different set of independent properties (perhaps including, for example, p or other ratio-type properties), rather than the base set of intensive and extensive properties that are used to assess macroscopic character. But considerable conceptual and formal simplifications result from choosing properties of pure intensive (R() or extensive QQ character as independent arguments of thermodynamic state functions, and it is important to realize that this pure choice is always possible if (and only if) the system is macroscopic. 

Definition Two macroscopic systems having all the same numerical values of the independent intensive properties are said to be in the same state (regarded as identical for thermodynamic purposes). 

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. 

Equation (6.35b) shows that the new intensive variable, chemical potential pi, as introduced in this chapter, is actually superfluous for the case c = 1, because its variations can always be expressed in terms of the old variations dT dP. Thus, as stated in Inductive Law 1 (Table 2.1), only two degrees of freedom (independently variable intensive properties) suffice to describe the thermodynamic variability of a simple c = 1 system. This confirms (as expected) that chemical potential pu only becomes an informative thermodynamic variable when chemical change is possible, that is, for c > 2 chemical components. 

We have previously emphasized (Section 2.10) the importance of considering only intensive properties Rt (rather than size-dependent extensive properties Xt) as the proper state descriptors of a thermodynamic system. In the present discussion of heterogeneous systems, this issue reappears in terms of the size dependence (if any) of individual phases on the overall state description. As stated in the caveat regarding the definition (7.7c), the formal thermodynamic state of the heterogeneous system is wholly / dependent of the quantity or size of each phase (so long as at least some nonvanishing quantity of each phase is present), so that the formal state descriptors of the multiphase system again consist of intensive properties only. We wish to see why this is so. 

The second class of control variables comprises derivative strength-type ( intensive ) properties Rb such as temperature and pressure. Each Rt is related through the fundamental equation (8.72) to a conjugate extensity Xt by a derivative relationship ( equation of state ) of the form [cf. (3.32), (4.33)]... 

Various properties of crystals can be used to inspect c,( ,r), provided that appropriate detectors for the intensity of input and output signals are available. If the monitor response is sufficiently fast, one may determine the time dependence of solid state reactions. The monitoring of reactants and/or reaction products can serve this purpose, but the relation between signal intensity (property) and concentration Cj) must always be established first. Since functions of state are related to one another in a unique way, any equilibrium property can, in principle, be used to determine However, the necessary assumption of local equilibrium must still be... 

Some authors state that the reaction rate is d /dt where t stands for time. But dfydt is proportional to the size of the reactor and, hence, is an extensive property like , and not an intensive property, as should be the reaction rate, according to the definition of the term. The derivative dt /dt is to be called the reactor productivity, but not the reaction rate. 

A.5 State whether the following are extensive or intensive properties (a) the color of copper sulfate (b) the temperature of boiling liquid oxygen (LOX) (c) the cost of platinum metal (d) the energy content of a beaker of water. 

The term state refers to material with a specified set of properties at a given time. It is not a function of the system configuration but only of its intensive properties. 

Specific heat and molar heat / V I capacity are intensive properties that depend on the state of the substance. 

The term ionisation potential (IP) refers to an intensive property of a single atom or ion in the gas phase. Measured spectroscopically, it is equal to the energy difference between En+ and E(n+1)+ (n = 0,1,2,...), both species being in their respective ground states. Loosely, but perhaps more usefully, the ionisation potential of an atom or ion is equal to the energy required to remove its outermost electron. The ionisation potential is usually measured in electron volts (eV), although it is sometimes tabulated in the spectroscopic unit of reciprocal centimetres (cm-1) leV s 8066 cm-1. 

The electron affinity of an atom or ion is the counterpart of the ionisation potential. It is an intensive property, defined as the energy released when the atom in its ground state accepts an electron, i.e. the difference in energy between the ground state of E and that of E- with the sign convention that exothermic electron affinities are positive. Electron affinities, like ionisation potentials, are expressed in eV. 

The system of our choice will usually prevail in a certain macroscopic state, which is not under the influence of external forces. In equilibrium, the state can be characterized by state properties such as pressure (P) and temperature (T), which are called "intensive properties." Equally, the state can be characterized by extensive properties such as volume (V), internal energy (U), enthalpy (H), entropy (S), Gibbs energy (G), and Helmholtz energy (A). 

The state of a system is defined by its properties. Extensive properties are proportional to the size of the system. Examples include volume, mass, internal energy, Gibbs energy, enthalpy, and entropy. Intensive properties, on the other hand, are independent of the size of the system. Examples include density (mass/volume), concentration (mass/volume), specific volume (volume/mass), temperature, and pressure. 

Experience shows that for a system that is a homogeneous mixture of Ns substances, Ns + 2 properties have to be specified and at least one property must be extensive. For example, we can specify T, P, and amounts of each of the Ns substances or we can specify T, P, and mole fractions x, of all but one substance, plus the total amount in the system. Sometimes we are only interested in the intensive state of a system, and that can be described by specifying Ns + 1 intensive properties for a one-phase system. For example, the intensive state of a solution involving two substances can be described by specifying T, P, and the mole fraction of one of substances. 

The intensive variables T, P, and nt can be considered to be functions of S, V, and dj because U is a function of S, V, and ,. If U for a system can be determined experimentally as a function of S, V, and ,, then T, P, and /q can be calculated by taking the first partial derivatives of U. Equations 2.2-10 to 2.2-12 are referred to as equations of state because they give relations between state properties at equilibrium. In Section 2.4 we will see that these Ns + 2 equations of state are not independent of each other, but any Ns+ 1 of them provide a complete thermodynamic description of the system. In other words, if Ns + 1 equations of state are determined for a system, the remaining equation of state can be calculated from the Ns + 1 known equations of state. In the preceding section we concluded that the intensive state of a one-phase system can be described by specifying Ns + 1 intensive variables. Now we see that the determination of Ns + 1 equations of state can be used to calculate these Ns + 1 intensive properties. 

State functions which depend on the mass of material are called extensive properties (e.g., U, V). On the other hand some state functions are independent of the amount of materials. These are called intensive properties (e.g., P, T). 

Thermodynamic Model. In the equilibrium state, the intensive properties -temperature, pressure and chemical potentials of each component- are constant in the overall system. Since the fugacities are functions of temperature, pressure and compositions, the equilibrium condition... 

The Gibbs phase rule allows /, the number of degrees of freedom of a system, to be determined. / is the number of intensive variables that can and must be specified to define the intensive state of a system at equilibrium. By intensive state is meant the properties of all phases in the system, but not the amounts of these phases. Phase equilibria are determined by chemical potentials, and chemical potentials are intensive properties, which are independent of the amount of the phase that is present. The overall concentration of a system consisting of several phases, however, is not a degree of freedom, because it depends on the amounts of the phases, as well as their concentration. In addition to the intensive variables, we are, in general, allowed to specify one extensive variable for each phase in the system, corresponding to the amount of that phase present. 

The entropy generated in a steady-state system is the entropy added to the surroundings, if this entropy is transported in a reversible manner. This is a convenient operational principle, because the surroundings can be idealized as composed of reservoirs, each with uniform intensive properties. 

The conflicting serial/parallel models for IVR/VP are not readily distinguished until time resolved experiments can be performed on the systems of interest. Both models can relate the relative intensities of the emission features to the various model parameters, but the serial process seems more in line with a simple, conventional [Fermi s Golden Rule for IVR (Avouris et al. 1977 Beswick and Jortner 1981 Jortner et al. 1988 Lin 1980 Mukamel 1985 Mukamel and Jortner 1977) and RRKM theory for VP (Forst 1973 Gilbert and Smith 1990 Kelley and Bernstein 1986 Levine and Bernstein 1987 Pritchard 1984 Robinson and Holbrook 1972 Steinfeld et al. 1989)], few parameter approach. Time resolved measurements do distinguish the models because in a serial model the rises and decays of various vibronic states should be linked, whereas in a parallel one they are, in general, unrelated. Moreover, the time dependent studies allow one to determine how the rates of the IVR and VP processes vary with excitation energy, density of states, mode properties, and isotropic substitution. 

This thermodynamic constraint arises because the intensive properties that describe an equilibrium state of a single phase (e.g., T, P, and component activities) cannot all be varied independently. Equation 3.33 can be written in the compact form ... 

In the above equation the exergy is written as an intensive property, e.g. per mol of fuel. The subscript "1" represents the original thermodynamic state, the subscript "o" describes the state when thermodynamic equilibrium with the environment is established. In these considerations it is arbitrarily assumed that any reaction product is in equilibrium with the environment when it has a temperature of T = 300K and a pressure of P = lbar. 

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