Properties extensive property

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. 

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. 

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. 

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... 

Mathematically equation (A2.1.25) is the direct result of the statement that U is homogeneous and of first degree in the extensive properties S, V and n.. It follows, from a theorem of Euler, that... 

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... 

The last part of the file presented here is a properties block, which can contain miscellaneous properties extensively described in Refs. [50, 51]. In most cases, however, this block is empty, except for a terminating line (line 18 in Figure 2-25). 

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 ... 

Low Temperature Properties. The property of solvent resistance makes fluorosihcone elastomers usefiil where alternative fluorocarbon elastomers cannot function. The abiHty to retract to 10% of their original extension after a 100% elongation at low temperature is an important test result. Eluorosihcones can typically pass this test down to —59°C. The brittle point is approximately —68°C. 

P rtl IMol r Properties. The properties of individual components in a mixture or solution play an important role in solution thermodynamics. These properties, which represent molar derivatives of such extensive quantities as Gibbs free energy and entropy, are called partial molar properties. For example, in a Hquid mixture of ethanol and water, the partial molar volume of ethanol and the partial molar volume of water have values that are, in general, quite different from the volumes of pure ethanol and pure water at the same temperature and pressure (21). If the mixture is an ideal solution, the partial molar volume of a component in solution is the same as the molar volume of the pure material at the same temperature and pressure. 

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

Balaneed equations for eaeh extensive property of die system (e.g., mass, energy, or individual speeies). 

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

At 6 30 A.M. on June 21, 1970, fifteen railroad cars, including nine cars carrying liquefied petroleum gas (LPG), derailed in the town of Crescent City, Illinois. The derailment caused one of the tanks to be punctured, then release LPG. The ensuing fire, fed by operating safety valves on other cars, resulted in ruptures of tank cars, followed by projectiles and fireballs. No fatalities occurred, but 66 people were injured. There was extensive property damage. 

Most fire accidents involve a large loss of life and extensive property diuiiage. Frequently, a fire is preceded by an explosion, E.xplosions are usually more letlial than fires (see Section 7.4). Some major fires in industrial plants liave been described in detail in tlie literauire. ... 

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... 

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—... 

Properties of gold. The color of gold is an intensive property. The quantity of gold in a sample is an extensive property. The fact that gold can be stored in the air without undergoing any chemical reaction with oxygen in the air is a chemical property. The temperature at which gold melts (1063°C) is a physical property. 

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. 

Experimental yield The amount of product actually obtained in a reaction, 65 Exponential notation, 643-645 Extensive property A property of a... 

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... 

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... 

Entropy is an extensive property and Sm the molar entropy is often used. 

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... 

FIGURE A.2 Mass is an extensive property, but temperature is intensive. These two samples of iron(ll) sulfate solution were taken from the same well-mixed supply they have different masses but the same temperature. 

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 ... 

Physical properties are those that do not involve changing the identity of a substance. Chemical properties are those that involve changing the identity of a substance. Extensive properties depend on the mass of the sample intensive properties do not. The precision of a measurement controls the number of significant figures that are justified by the procedure the accuracy of a measurement is its closeness to the true value. 

Heat capacity is an extensive property the larger the sample, the more heat is required to raise its temperature by a given amount and so the greater is its heat capacity (Fig. 6.10). It is therefore common to report either the specific heat capacity (often called just specific heat ), Cs, which is the heat capacity divided by the mass of the sample (Cs = dm), or the molar heat capacity, Cm, the heat capacity divided by the amount (in moles) of the sample (Cm = C/n). For example, the specific heat capacity of liquid water at room temperature is 4.18 J-(°C) -g, or 4.18 J-K 1-g and its molar heat capacity is 75 J-K -mol1. 

Doubling the number of molecules increases the number of microstates from W to W2, and so the entropy changes from k In W to k In W2, or 2k In W. Therefore, the statistical entropy, like the thermodynamic entropy, is an extensive property. 

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