Volume extensive properties

For example, the cohesive energy and molar volume (extensive properties) and solubility parameter (an intensive property) of a random copolymer containing two different types of repeat units with mole fractions of irq and m2 can be estimated by using equations 17.7-17.10 ... 

Some properties, such as temperature and melting point, are intensive properties. They do not depend on the amount of sample being examined and are particularly useful in chemistry because many intensive properties can be used to identify substances. Extensive properties depend on the amount of sample, with two examples being mass and volume. Extensive properties relate to the amount of substance present. 

In order to specify fhe size of fhe sysfem, af leasf one of fhese variables ought to be extensive (one that is proportional to the size of the system, like n or the total volume V). In the special case of several phases in equilibrium several extensive properties, e.g. n and Vfor two phases, may be required to detennine the relative amounts of the two phases. The rest of the variables can be intensive (independent of the size of the system) like T,p, the molar volume V = V/n,or the density p. For multicomponent systems, additional variables, e.g. several ns, are needed to specify composifion. 

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

The properties used to identify a substance must be intensive that is, they must be independent of amount The fact that a sample weighs 4.02 g or has a volume of 229 mL tells us nothing about its identity mass and volume are extensive properties that is, they depend on amount. Beyond that substances may be identified on the basis of their—... 

Note that even though mass and volume are extensive properties, the ratio of mass to volume is intensive. Samples of copper weighing 1.00 g, 10.5 g, 264 g,... all have the same density, 8.94 g/mL at 25°C. 

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... 

Properties are also classified according to their dependence on the mass of a sample. An intensive property is a property that is independent of the mass of the sample. For example, temperature is an intensive property, because we could take a sample of any size from a uniform bath of water and measure the same temperature (Fig. A.2). An extensive property is a property that does depend on the mass ( extent ) of the sample. Volume is an extensive property 2 kg of water occupies twice the volume of 1 kg of water. 

Some intensive properties are ratios of two extensive properties. For example, the property density, d, mentioned above, is a ratio of the mass, m, of a sample divided by its volume, V ... 

Unlike mass and volume, density does not vary with the amount of a substance. Notice in Figure 1-20 that all the corks float, regardless of their sizes. Notice also that all the pieces of lead sink, regardless of their sizes. Dividing a sample into portions changes the mass and volume of each portion but leaves the density unchanged. A property that depends on amount is called extensive. Mass and volume are two examples of extensive properties. A property that is independent of amount is called intensive. Density and temperature are intensive properties. 

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. 

Drawing a Conclusion The slope of a straight line is constant. No matter where you measure the slope on the line, the slope is the same. You should find that the slope is equal to the change in mass divided by the change in volume. Use this information to explain why you think density is an intensive or extensive property. 

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 most important new concept to come from thermodynamics is entropy. Like volume, internal energy and mole number it is an extensive property of a system and together with these, and other variables it defines an elegant self-consistent theory. However, there is one important difference entropy is the only one of the extensive thermodynamic functions that has no obvious physical interpretation. It is only through statistical integration of the mechanical behaviour of microsystems that a property of the average macrosystem, that resembles the entropy function, emerges. 

This simple relationship allows us to express all the thermodynamic variables in terms of our colloid concentration. The Helmholtz free energy per unit volume depends upon concentration of the colloidal particles rather than the size of the system so these are useful thermodynamic properties. If we use a bar to symbolise the extensive properties per unit volume we obtain... 

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. 

Properties that do not vary with the amount of mass of a substance - for example, temperature, pressure, surface tension, mole fraction - are termed intensive properties. On the other hand, those properties that vary in proportion to the total mass of substances - for example, total volume, total mass, and heat capacity - are termed extensive properties. 

It should be noted, however, that some extensive properties become intensive properties, in case their specific values - that is, their values for unit mass or unit volume - are considered. For example, specific heat (i.e., heat capacity per unit mass) and density (i.e., mass per unit volume) are intensive properties. 

The objective of this section is to establish a relationship between the time rate of change of an extensive property of a system and the behavior of the associated intensive property within a control volume that surrounds the system at an instant in time. This kinematic relationship, described in terms of the substantial derivative, is central to the derivation of conservation equations that describe fluid mechanics. 

Figure 2.2 calls particular attention to how a fluid system moves relative to a fixed control volume that is, it illustrates convective transport. It is very important to note that an extensive property of the system can change owing to molecular transport (e.g., a... 

In the limit of a vanishingly small time interval, this term represents the rate at which the extensive property N is transported convectively with the fluid motion across the control surfaces out of the control volume. Given that the fluid flow can be described by a vector field V, the convective transport flux across the area A of the control surface can be written as... 

Combining Eqs. 2.22, 2.24, and 2.26 yields the Reynolds transport theorem, which relates the time rate of change (net accumulation) of an extensive property in a flowing system to a fixed control volume that coincides with the system at an instant in time,... 

This equation provides the relationship between the rate of change of an extensive property N for a system (a specific, but possibly flowing, mass) and the substantial derivative of the associated intensive variable r) in an Eulerian control volume 8V that is fixed in space. 

Internal generation rate of extensive property in control volume... 

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 ith cell has extensive properties of entropy Sh energy Uh volume Vb and mass Nh where... 

The first class comprises quantity-type ( extensive ) properties Xb such as the quantity of mass or spatial volume of the system. A distinctive characteristic of these properties is their additivity in subunits of the system, such that each is linearly proportional to overall scale (number of identical subunits), as measured, for example, by total mass. Arbitrary linear combinations of the independent Xb... 

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