State extensive properties

Intensive properties that specify the state of a substance are time independent in equilibrium systems and in nonequilibrium stationary states. Extensive properties specifying the state of a system with boundaries are also independent of time, and the boundaries are stationary in a particular coordinate system. Therefore, the stationary state of a substance at ary point is related to the stationary state of the system. 

The energy of a system can be changed by means of thermal energy or work energy, but a further possibility is to add or subtract moles of various substances to or from the system. The free energy of a pure substance depends upon its chemical nature, its quantity (AG is an extensive property), its state (solid, liquid or gas), and temperature and pressure. Gibbs called the partial molar free heat content (free energy) of the component of a system its chemical potential... 

Volume is an extensive property. Usually, we will be working with Vm, the molar volume. In solution, we will work with the partial molar volume V, which is the contribution per mole of component i in the mixture to the total volume. We will give the mathematical definition of partial molar quantities later when we describe how to measure them and use them. Volume is a property of the state of the system, and hence is a state function.1 That is... 

But much of chemistry involves mixtures, solutions, and reacting systems in which the number of moles or mole number, of each species present can be variable. When this happens, the extensive properties, Z = V, S, U, H,A or G become functions of the composition variables, as well as two of the state variables as described earlier.a We can express this mathematically as... 

Excited states play important roles in chemistry. Recall from Chapter 7 that the properties of atoms can be studied by observing excited states. In fact, chemists and physicists use the characteristics of excited states extensively to probe the stmcture and reactivity of atoms, ions, and molecules. Excited states also have practical applications. 

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. 

Several copper enzymes will be discussed in detail in subsequent sections of this chapter. Information about major classes of copper enzymes, most of which will not be discussed, is collected in Table 5.1 as adapted from Chapter 14 of reference 49. Table 1 of reference 4 describes additional copper proteins such as the blue copper electron transfer proteins stellacyanin, amicyanin, auracyanin, rusticyanin, and so on. Nitrite reductase contains both normal and blue copper enzymes and facilitates the important biological reaction NO) — NO. Solomon s Chemical Reviews article4 contains extensive information on ligand field theory in relation to ground-state electronic properties of copper complexes and the application of... 

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. 

Internal Energy is the energy contained within a system. It is an extensive property of the system and the increase or decrease in internal energy between two states is independent of the way the change between states is brought about... 

It is important to distinguish between the intensive (state) properties (functions) and the extensive properties (functions). 

The conservation laws are often based on a rather simple and intuitive concept. They state the rate of accumulation of an extensive property of a system is equal to the net (incoming minus outgoing) transport rate of the property across the surfaces that bound the system plus the net (creation minus destruction) rate of internal generation of the property... 

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. 

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. 

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. 

In view of their extensive property, the state descriptors of each phase must sum to the total value in the system ... 

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. 

The standard free-energy change, A G°, for a reaction is the change in free energy that occurs when reactants in their standard states are converted to products in their standard states. As with AH° (Section 8.10), the value of AG° is an extensive property that refers to the number of moles indicated in the chemical equation. For example, AG° at 25°C for the reaction... 

As stated in the introduction to this chapter, the methods used and the equations developed in the previous sections are formally applicable to all extensive properties. However, there are two classes of properties those... 

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. 

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). 

The properties of natural silk are affected by numerous factors, such as nutrition, temperature, hydration state, extension rate, reeling speed (ICnight et al., 2000 Madsen et al., 1999 Riekel et al., 1999 Vollrath and ICnight, 1999 Vollrath et al., 2001), and spinning medium during the manufacture (Chen et al.,... 

The extent of reaction is an extensive property, and it can apply not only to chemical reactions but also as the extent of change to all physicochemical processes such as diffusion, melting, boiling, and solid state transformation. 

The compilations by Wagman et al. and Robie et al. are quite extensive, including many solids as well as ionic solutes in aqueous solution. Since a compound may be written as the product of a chemical reaction that involves only chemical elements as reactants, and since pP for an element is equal to zero, pP for a compound can be considered to be a special example of ArG° for a reaction that forms the compound from its constituent chemical elements. Thus pP values also are termed standard Gibbs energies of formation and given the symbol AfG°. In addition to p° (or AfG°) values, Wagman et al. and Robie et al. list H° and S° for many substances. These Standard-State thermodynamic properties are related to ArH° and ArS° in Eq. 1.42 15... 

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