Intensive thermodynamic properties defined

We have defined solutions as homogeneous phases, with uniform concentrations throughout. Clearly, the surface of a solution provides a different environment than its bulk, and we should expect intensive properties (concentrations as well as intensive thermodynamic properties) to vary in this region. The mechanical and thermal variables, P and T, however, can be taken as uniform throughout the solution. It should be emphasized that the surface region of the solution is very thin, just a few molecular diameters thick. Bulk properties of the solution will, thus, only be affected by the surface if the solution is composed of very small droplets. 

Write the exact differential for any intensive thermodynamic property in terms of partial derivatives of specified independent, intensive properties. For example, given h= h T P), write dh. Define what is meant by independent properties and dependent properties. 

The inequalities of the previous paragraph are extremely important, but they are of little direct use to experimenters because there is no convenient way to hold U and S constant except in isolated systems and adiabatic processes. In both of these inequalities, the independent variables (the properties that are held constant) are all extensive variables. There is just one way to define thermodynamic properties that provide criteria of spontaneous change and equilibrium when intensive variables are held constant, and that is by the use of Legendre transforms. That can be illustrated here with equation 2.2-1, but a more complete discussion of Legendre transforms is given in Section 2.5. Since laboratory experiments are usually carried out at constant pressure, rather than constant volume, a new thermodynamic potential, the enthalpy H, can be defined by... 

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... 

In nonequilibrium systems, the intensive properties of temperature, pressure, and chemical potential are not uniform. However, they all are defined locally in an elemental volume with a sufficient number of molecules for the principles of thermodynamics to be applicable. For example, in a region A , we can define the densities of thermodynamic properties such as energy and entropy at local temperature. The energy density, the entropy density, and the amount of matter are expressed by uk(T, Nk), s T, Nk), and Nk, respectively. The total energy U, the total entropy S, and the total number of moles N of the system are determined by the following volume integrals ... 

Wyman (5,6,7) introduced the binding potential, which he represented by the Russian L for linkage. This is a molar thermodynamic property that is defined by a Legendre transform that introduces the chemical potential of the ligand as an independent intensive property. The binding potential is given by... 

The value of G(A) is equal to the work of thinning the film in a reversible, isobaric, and isothermal process from infinity to a finite thickness A, with TT(A) = —(dG/ dh)T pL ij vgi vs- Derjaguin et al. (1987) point out that the choice of 11(A) as the basic thermodynamic property is not a mere change of notation, but 11(A) has advantages in cases where Gibbs thermodynamic theory is not well defined, such as, when interfacial zones overlap to the extent that the film does not retain the intensive properties of the bulk phase. The use of the disjoining pressure is advantageous from an experimental point of view because of the relative ease to account for different contributions (e.g., electrostatic effects). 

Integral and differential thermodynamic relationships between the different excess quantities defined by Eq, (2) and the set of experimental variables (P, r,y,) or (T,nf) can be derived analogously to those for conventional bulk-phase thermodynamic properties [9], However, an additional intensive property called the surface potential (cf>, ca /g) is necessary to completely define the Gibbsian adsorbed phase. The surface potential can be calculated by using the relationship [9] ... 

Phases in thermodynamic systems are then macroscopic homogeneous parts with distinct physical properties. For example, densities of extensive thermodynamical variables, such as particle number N of the fth species, enthalpy U, volume V, entropy S, and possible order parameters, such as the nematic order parameter for a liquid crystalline polymer etc, differ in such coexisting phases. In equilibrium, intensive thermodynamic variables, namely T,p, and the chemical potentials pi have to be the same in all phases. Coexisting phases are separated by well-defined interfaces (the width and internal structure of such interfaces play an important role in the kinetics of the phase transformation (1) and in other... 

Before describing these thermodynamic variables, we must talk about their properties. The variables are classified as intensive or extensive. Extensive variables depend upon the amount while intensive variables do not. Density is an example of an intensive variable. The density of an ice crystal in an iceberg is the same as the density of the entire iceberg. Volume, on the other hand, is an extensive variable. The volume of the ocean is very different from the volume of a drop of sea water. When we talk about an extensive thermodynamic variable Z we must be careful to specify the amount. This is usually done in terms of the molar property Zm, defined as... 

The chemical potentials sought are intensive properties of the system, in the usual thermodynamic language [26]. Furthermore, AUa is a quantity of molecular order of magnitude. Specifically, the AUa defined by (9.13) should be system-size independent for typical configurations of thermodynamically large systems. Because of... 

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... 

Salvador [100] introduced a non-equilibrium thermodynamic approach taking entropy into account, which is not present in the conventional Gerischer model, formulating a dependence between the charge transfer mechanism at a semiconductor-electrolyte interface under illumination and the physical properties thermodynamically defining the irreversible photoelectrochemical system properties. The force of the resulting photoelectrochemical reactions are described in terms of photocurrent intensity, photoelectochemical activity, and interfacial charge transfer... 

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. 

In addition to being a function of T, the partition function is also a function of V, on which the quantum description of matter tells us that the molecular energy levels, , depend. Because, for single-component systems, all intensive state variables can be written as functions of two state variables, we can think of q(T, V) as a state function of the system. The partition function can be used as one of the independent variables to describe a single-component system, and with one other state function, such as T, it will completely define the system. All other properties of the system (in particular, the thermodynamic functions U, H, S, A, and G) can then be obtained from q and one other state function. 

This is the defining equation for the fundamental material function Lx, the spectral intensity, it describes the directional and wavelength dependence of the energy radiated by a body and has the character of a distribution function. The (thermodynamic) temperature T in the argument of Lx points out that the spectral intensity depends on the temperature of the radiating body and its material properties, in particular on the nature of its surface. The adjective spectral and the index A show that the spectral intensity depends on the wavelength A and is a quantity per wavelength interval. The Si-units of Lx are W/(m2/um sr). The units pm and sr refer to the relationship with dA and dec. 

It is possible to subdivide the properties used to describe a thermodynamic system (e.g., T, P, V,U,...) into two main classes termed intensive and extensive variables. This distinction is quite important since the two classes of variables are often treated in significantly different fashion. For present purposes, extensive properties are defined as those that depend on the mass of the system considered, such as volume and total energy content, indeed all the total system properties (Z) mentioned above. On the other hand, intensive properties do not depend on the mass of the system, an obvious example being density. For example, the density of two grams of water is the same as that of one gram at the same P, T, though the volume is double. Other common intensive variables include temperature, pressure, concentration, viscosity and all molar (Z) and partial molar (Z, defined below) quantities. ... 

In the study of thermodynamics, extensive and intensive properties are constantly employed. In this chapter we discuss the dependence of extensive properties on the mass of the system and demonstrate how to define a set of intensive properties related to a given extensive property. We shall describe experimental methods for the measurement of these sets of intensive properties. Finally, we present a list of a number of commonly used composition variables and show how these may be related to each other. 

Assume the existence of two phases separated by a phase boundary or interface. Phases, in this sense, can exist in any of the three states of matter gaseous, liquid or solid. Their only requirement for existence is that their intensive properties such as pressure and free energy (see below) are the same everywhere within the phase. This assumes that the phases are large in size since the free energy of phases near surfaces will be different. The two phases constitute a system in the thermodynamic sense. At equilibrium, for the conditions of constant temperature and pressure, the following state functions are defined as ... 

In thermodynamics we encounter various properties, for example, density, volume, heat capacity, and others that will be defined later. In general, property is any quantity that can be measured in a system at equilibrium. Certain properties depend on the actual amount of matter (size or extent of the system) that is used in the measurement. For example, the volume occupied by a substance, or the kinetic energy of a moving object, are directly proportional to the mass. Such properties will be called extensive. Extensive properties are additive if an amount of a substance is divided into two parts, one of volume W and one of volume V2, the total volume is the sum of the parts, Vi + V2. In general, the total value of an extensive property in a system composed of several parts is the sum of its parts. If a property is independent of the size of the system, it will be called intensive. Some examples are pressure, temperature, density. Intensive properties are independent of the amount of matter and are not additive. 

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