As extensive property

If a system is split into subsystems the properties of state may either remain unchanged in every subsystem and then they are denoted intensive properties. The properties of state in the splitted subsystems may otherwise be altered with respect to the unsplit system, in which case they are classified as extensive properties. Pressure and temperature are intensive properties. Energy and mass are extensive properties. 

On the other hand, properties that depend on the total amount of material present, such as volume, are referred to as extensive properties. 

Equation (A2.1.23) can be mtegrated by the following trick One keeps T, p, and all the chemical potentials p. constant and increases the number of moles n. of each species by an amount n. d where d is the same fractional increment for each. Obviously one is increasing the size of the system by a factor (1 + dQ, increasing all the extensive properties U, S, V, nl) by this factor and leaving the relative compositions (as measured by the mole fractions) and all other intensive properties unchanged. Therefore, d.S =. S d, V=V d, dn. = n. d, etc, and... 

Since Cy and E are bodi extensive properties (ocN), the root-inean-square energy fluctuations are smaller, by a factor 1/y, than typical average energies E. As the system size increases, the relative magnitude of... 

Another way to improve the error in a simulation, at least for properties such as the energy and the heat capacity that depend on the size of the system (the extensive properties), is to increase the number of atoms or molecules in the calculation. The standard deviation of the average of such a property is proportional to l/ /N. Thus, more accurate values can be obtained by running longer simulations on larger systems. In computer simulation it is unfortunately the case that the more effort that is expended the better the results that are obtained. Such is life ... 

Any list of copolymer applications would be as extensive as the applications of polymers in general. We shall only consider a few items in which the two-component nature of the copolymer plays an explicit role in determining the properties of the polymer. In addition, we shall examine several additional concerns which come up when applications technology is considered. 

Published data and shortcut estimating methods can be used to calculate the approximate manufacturing cost of a new product. However, most companies have extensive data on various items of cost such as overheads, property taxes, etc. These data should be used whenever possible to give the estimate that is most vahd for a particular company. 

The bulk properties of a polymer ean often be altered considerably by the incorporation of additives. Probably the most well-known examples of this occur in rubber technology where variations in the choice of additives can produce such widely differing products as tyres, battery boxes, latex foam upholstery, elastic bands and erasers. It is also possible to achieve variations as extensive as this amongst plastics materials, in particular with PVC from which rigid rainwater piping, baby pants, conveyor belting, footballs and domestic insulating flex may all be prepared. 

A balanced equation for every extensive property in each control volume may be written as ... 

Main-group elements, 153t Malleability The ability to be shaped, as by pounding with a hammer characteristic of metals, 244 Maltose, 618-619 Manometer, 104 Maple syrup, 277-278 Mass An extensive property reflecting the amount of matter in a sample, 7. See also Amount, critical, 525... 

Only differences in A can be calculated because of its relationship to U in equation (1.20). As with the other extensive properties, the molar (intensive)... 

The third observation is that the equations apply as well when the extensive properties are replaced by the corresponding intensive molar properties.0 For... 

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... 

Organic matter and rocks are the building materials of soils, which both undergo extensive transformations within soil. These transformations include changes in physical as well as chemical properties and result in unique new soil characteristics. Weathering is one type of... 

Classify each of the following as an intensive or extensive property of the wood samples a. color b. smell c. grain pattern of the wood d. mass e. volume and f. density. Provide justification for your classification. 

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. 

It is thus seen that heat capacity at constant volume is the rate of change of internal energy with temperature, while heat capacity at constant pressure is the rate of change of enthalpy with temperature. Like internal energy, enthalpy and heat capacity are also extensive properties. The heat capacity values of substances are usually expressed per unit mass or mole. For instance, the specific heat which is the heat capacity per gram of the substance or the molar heat, which is the heat capacity per mole of the substance, are generally considered. The heat capacity of a substance increases with increase in temperature. This variation is usually represented by an empirical relationship such as... 

The flow patterns in liquid-liquid systems have not been as extensively studied as those in gas-liquid systems. However, Russell et al. (R6), and Charles et al. (C3) have studied the flow of oils and water in horizontal pipes and have presented flow-pattern charts for the various oil-water systems. It is very difficult to predict the flow pattern for a liquid-liquid system, unless the liquids have physical properties similar to those of water and the oils used by Govier and co-workers. The Baker chart might be used to give a first estimate of the flow pattern for a liquid-liquid system, but the viscosity of the less-dense phase is not included in the coordinate parameters, and the feasibility of such an approach has never been investigated. 

When two or more monomers are polymerized into the same molecular chain they produce a copolymer, The distribution of monomers, in terms of their relative concentrations and placements, is responsible for controlling a copolymer s properties. Figure 5.8 illustrates five possible comonomer distributions for a copolymer comprising equal numbers of two types of monomer. The relative concentrations of the different monomers and the lengths of the various blocks can be varied widely. Relatively small changes in comonomer concentration and placement can result in significant changes in physical and chemical properties. Properties that can be modified include such diverse characteristics as extensibility, elastic recovery, modulus, heat resistance, printability, and solvent resistance. 

We can express the use of all the different units in evolution in the language of thermodynamics. While the genome is defined by a DNA sequence so that each base has a singular intensive property as in a computer code of symbols, by way of contrast, the protein content of a cell is an extensive property being concentration dependent and therefore varies under circumstances such as temperature and pressure although... 

---