Extensive thermodynamic quantities

The subscripts used to denote a chemical process, listed under (i) above, should be used as subscripts to the A symbol to denote the change in an extensive thermodynamic quantity associated with the process. 

In general, any extensive thermodynamic quantity X may be written as the sum of the contributions from the adsorbent, the adsorbate, and the adsorptive ... 

Let E be any extensive thermodynamic quantity expressed as a function of the variables T, P, and N (where N is the total number of molecules in the system). Viewing the same system as a mixture of quasi-components, we can express E as a function of the new set of variables T, P, and N. For correctness, consider a QCDF based on the concept of CN. The two possible functions mentioned above are then... 

Note that in (3.139), E stands for the energy, whereas in previous expressions in this section, we have used E for any extensive thermodynamic quantity. Since the normalization condition for is... 

Changes in extensive thermodynamic quantities X due to an event y should be represented by yX ... 

Molar Gibbs Energy Other extensive thermodynamic quantities are dealt with in the same way. In the case of pure substances, they are considered a function of T, p, n, and for a substance in a mixture with other substances, as a function of T, p, n, n, n",. The Gibbs energy G is especially interesting in this context because in the conventional thermodynamic calculations, it is very closely connected with the chemical potential. In the case of a pure substance at fixed T and p, G is proportional to the amount of substance n. Therefore, G itself does not serve as the substance-specific characteristic, but the quotient G/n ... 

Extensive thermodynamic quantities Z(p, 7, ni,..., rik) of the type given by Eq. (47), such as volume V, entropy S, enthalpy //, heat capacity C, and Gibbs energy G, yield partial molar quantities ... 

FIGURE 1 Determination of partial molar quantities Z2 and apparent molar quantities z from measurements of extensive thermodynamic quantities Zpj n n2) (also AZ2 from AZ see Section III.B). 

Extensive thermodynamic quantities such as A//, A5, and AG are almost always normalized per mole of substance involved to produce intensive, molar-based values for these quantities. This is because it is often useful to quantify energy changes due to a reaction on a per-mole basis. Thus, when you encounter these quantities in this textbook, they almost always refer to the specific (per-mole) value. 

Many compounds cannot be directly synthesized from their elements. In some cases, the reaction proceeds too slowly, or side reactions produce substances other than the desired compound. In these cases A// can be determined by an indirect approach, which is based on Hess s law of summation for extensive thermodynamic quantities. 

Hess s law states that the overall enthalpy change in a reaction is equal to the sum of enthalpy changes for individual steps in the overall reaction. Hess s law holds for any extensive thermodynamic quantity. 

Thus far, we have used the symbol E to designate any extensive thermodynamic quantity. In this respect, relations (5.96) and (5.100) provide general formal connections between thermodynamics and QCDF s (or singlet GMDF s). Note that for each thermodynamic quantity, we can have different representations of the form (5.96) or (5.99), depending on the choice of QCDF. For example, the average volume can be written as... 

Extensive thermodynamic quantities are always expressed as molar quantities, i.e. the extensive quantity divided by the total amount (number of moles) of substanee molar volume V, molar internal energy U, molar enthalpy H, molar entropy S, molar Gibbs energy G, ete. 

The thermodynamic analysis of solutions is facilitated by the introduction of quantities that measure how the extensive thermodynamic quantities (V, E, H, G,. ..) of the system depend on the state variables T, P, and nj. This leads to the definition of partial molar quantities where, if we let Y be any extensive thermodynamic property, we can define the partial molar value of Y for the ith component as ... 

Thermodynamics studies two forms of energy transfer heat and work. Heat can be defined as transfer of energy caused by the difference in temperatures of two systems. Heat is transferred spontaneously from hot to cold systems. It is an extensive thermodynamic quantity, meaning that its value is proportional to the mass of the system. The SI (Systeme International de Unites) unit of the heat is the joule (J). The earlier unit of calorie is not in use any more. 

The physical properties of the binary mixtures are expressed by the general symbol Y that may represent extensive thermodynamic quantities such as molar... 

The basic thermodynamic framework for interfacial thermodynamics was developed by J. W. Gibbs in the late nineteenth century. Central to this formalism is the concept of the dividing surface, which is a mathematical surface to which all excess interfacial thermodynamic quantities are assigned. Once such a dividing surface is defined, the extensive thermodynamic quantities of the two-phase system can be written as the sum of contributions from the two bulk phases (calculated as if each bulk phase were uniform up to the dividing surface) and an excess contribution that is due to the presence of the interface. For a liquid-solid interface of a general multi-component system this procedure gives... 

As mentioned above, the boundary between two thermodynamic phases has to be a vague transition zone for any physical quantity because nature does not like sharp steps. Hence, in principle, any real phase boundary extends in three dimensions — the interphase (cf O Fig. 4.2a). This apparently innocent comment has the important result that all extensive thermodynamic quantities, such as concentrations, energies, entropy etc., will depend on position across the interphase. This causes trouble when it comes to an exact description of a thermodynamic system with more than one phase, because there is virtually no experimental access to the spatial dependence of thermodynamic quantities across the phase boundary. Moreover, the beauty of usual thermodynamics is very much due to the assumption that parameters remain constant across a phase. 

Moreover, the balance of any extensive thermodynamic quantity, Y, in the two-phase system is no longer... 

By analogy with a D-face, new excess quantities have to be introduced for all extensive thermodynamic quantities with respect to the TL. Details are not given here. For brevity, only a result of consideration of the Helmholtz free energy for a three-phase system in thermodynamic equilibrium under the influence of gravity is mentioned. It leads to a condition for the mechanical equilibrium at the TL on a solid with an arbitrary surface profile (roughness) ... 

Euler s theorem would describe Equation (E6.6F) by saying that the extensive thermodynamic quantity K is a first-order, homogeneous function of Differentiating Equation (E6.6F) by... 

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