Extensive property: defined

Considering any extensive property K, the partial molar quantity is defined by... 

International plastics selector , 9th edition, Int. Plastics Selector, San Diego, CA (1987). Thermoplastics, thermosets, elastomers, and key property areas critical to plastics are extensively specification defined. 

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... 

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. 

All members of this pigment family share good lightfastness, combined with poor solvent and migration resistance. These properties define and limit their application. Monoazo yellow pigments are used extensively in air-dried alkyd resin and in emulsion paints, and certain inks used in flexo and screen printing. Other applications are in letterpress and offset inks, as well as in office articles. 

Heat capacity is an extensive property (Section 1.4), so its value depends on both the size of an object and its composition. To compare different substances, it s useful to define a quantity called specific heat, the amount of heat necessary to raise the temperature of 1 g of a substance by 1°C. The amount of heat necessary to raise the temperature of a given object, then, is the specific heat times the mass of the object times the rise in temperature ... 

Properties such as internal energy, volume and entropy are called extensive because their values for a given phase are proportional to the mass or volume of the phase. The value of an extensive property of an entire system is the sum of the values of each of the constituent phases. The molar value of an extensive property is that for a properly defined gram-molecular weight or mole of material. The specific value of an extensive property is that per unit weight (eg, one gram of material). A property is called intensive if its value for a given phase is independent of the mass of the phase. Temp and pressure are examples of such intensive properties... 

The subject of partial molar quantities needs to be developed and understood before considering the application of thermodynamics to actual systems. Partial molar quantities apply to any extensive property of a single-phase system such as the volume or the Gibbs energy. These properties are important in the study of the dependence of the extensive property on the composition of the phase at constant temperature and pressure e.g., what effect does changing the composition have on the Helmholtz energy In this chapter partial molar quantities are defined, the mathematical relations that exist between them are derived, and their experimental determination is discussed. 

We now move the two surfaces a and b toward each other so that they coincide at some position c to give one two-dimensional surface lying wholly within the real surface. The system is thus divided into two parts, and we assume that the properties of each of the two parts are continuous and identical to the properties of the bulk parts up to the single two-dimensional surface. Certain properties of the system are then discontinuous at the surface. The extensive properties of the two-dimensional surface are defined as the difference between the values of the total system and the sum of the values of the two parts. Thus, we have for the energy, entropy, and mole number of the c components ... 

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. 

This shows that the natural variables of G for a one-phase nonreaction system are T, P, and n . The number of natural variables is not changed by a Legendre transform because conjugate variables are interchanged as natural variables. In contrast with the natural variables for U, the natural variables for G are two intensive properties and Ns extensive properties. These are generally much more convenient natural variables than S, V, and k j. Thus thermodynamic potentials can be defined to have the desired set of natural variables. 

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... 

Extensive properties of multicomponent phases (solutions) are related to the amount of material in the phase, but may not be just the sum of the properties of the constituent components. Probably the best known example of this difference is the observation that mixing 1.0 L of ethanol with 1.0 L of water at standard temperature and pressure (STP) produces 1.93 L of water-ethanol solution. We define the difference between an extensive property of the solution and the sum of the properties of its pure components as the property change of mixing for the solution ... 

Properties like mass m and volume Vare defined by the system as a whole. Such properties are additive, and are called extensive properties. Separation of the total change for a species into the external and internal parts may be generalized to any extensive property. All extensive properties are homogeneous functions of the first order in the mass of the system. For example, doubting the mass of a system at constant composition doubles the internal energy. 

The pressure P and temperature T define the values at each point of the system and are therefore called intensive properties, some of which can be expressed as derivatives of extensive properties, such as the temperature... 

For the entropy and internal energy, the canonical variables consist of extensive parameters. For a simple system, the extensive properties are S, U, and V. and the fundamental equations define a fundamental surface of entropy S = S(U,V) in the Gibbs space of S, U, and V. 

Since the temperature is not uniform for the whole system, the total entropy is not a function of the other extensive properties of U, V, and N. However, with the local temperature, the entropy of a nonequilibrium system is defined in terms of an entropy density, sk. 

Note that CO(g) is a reactant in Equation (10.2), so Equation (10.3) must be reversed, since CO(g) is a product in the reaction as written. When a reaction is reversed, the sign of AG° is also reversed. In Equation (10.4), CO2(g) is a product, as it is in Equation (10.2), but only one molecule of C02 is formed. Thus Equation (10.4) must be multiplied by 2, which means the AG° value for Equation (10.4) must also be multiplied by 2. Free energy is an extensive property since it is defined by two extensive properties, H and 5. 

Partial Molar Quantities. — The thermodynamic functions, such as heat content, free energy, etc., encountered in electrochemistry have the property of depending on the temperature, pressure and volume, i.e., the state of the system, and on the amounts of the various constituents present. For a given mass, the temperature, pressure and volume are not independent variables, and so it is, in general, sufficient to express the function in terms of two of these factors, e.g., temperature and pressure. If X represents any such extensive property, i.e., one whose magnitude is determined by the state of the system and the amounts, e.g., number of moles, of the constituents, then the partial molar value of that property, for any constituent i of the system, is defined by... 

An intensive property may be defined as a property that is unchanged when the size of the system is increased by adding to it any number of systems that are identical to the original system. An extensive property is one that increases in proportion to the size (for example, volume) of the system in such a process. Thus an intensive property may be formed from any extensive property through division by any other extensive property. 

Since the partial molar value (with respect to i) of any extensive property X is defined as (5//3N ) equation (6) shows that is the partial... 

Define or explain the following terms energy, system, closed system, nonflow system, open system, flow system, surroundings, property, extensive property, intensive property, state, heat, work, kinetic energy, potential energy, internal energy, enthalpy, initial state, final state, point (state) function, state variable, cyclical process, and path function. 

Since the energy content of a system obviously depends on the quantity of material contained in the system, it is apparent that the energy is an extensive property, as defined in 4d. If the mass of the system is altered, the energy content will be affected in the same proportion. Similarly, the value of AE for any process depends upon the amount of material contained in the system which imdergoes the change. 

Define the following terms, and illustrate each with a specific example (a) weight (b) potential energy (c) kinetic energy (d) endothermic process (e) extensive property. 

Liquid solutions are most readily dealt with by excess properties, which are defined for extensive properties and in this case for the Gibbs free energy by the difference between the real solution property G and the ideal solution property G. Eq. (7) is the excess Gibbs free energy. 

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