Enthalpy function, defined

Since dq is not a state function, c will depend on the path. The problem can be simplified by introducing the enthalpy function, defined as... 

Perhaps tlie most iinportant thermodynamic function tlie engineer works with is the entluilpy. The enthalpy is defined by... 

Students often ask, What is enthalpy The answer is simple. Enthalpy is a mathematical function defined in terms of fundamental thermodynamic properties as H = U+pV. This combination occurs frequently in thermodynamic equations and it is convenient to write it as a single symbol. We will show later that it does have the useful property that in a constant pressure process in which only pressure-volume work is involved, the change in enthalpy AH is equal to the heat q that flows in or out of a system during a thermodynamic process. This equality is convenient since it provides a way to calculate q. Heat flow is not a state function and is often not easy to calculate. In the next chapter, we will make calculations that demonstrate this path dependence. On the other hand, since H is a function of extensive state variables it must also be an extensive state variable, and dH = 0. As a result, AH is the same regardless of the path or series of steps followed in getting from the initial to final state and... 

For processes taking place at constant pressure it is convenient to introduce the enthalpy function, H, defined as... 

We introduced the enthalpy function particularly because of its usefulness as a measure of the heat that accompanies chemical reactions at constant pressure. We will find it convenient also to have a function to describe the temperature dependence of the enthalpy at constant pressure and the temperature dependence of the energy at constant volume. Eor this purpose, we will consider a new quantity, the heat capacity. (Historically, heat capacity was defined and measured much earlier than were enthalpy and energy.)... 

Application to Macromolecular Interactions. Chun describes how one can analyze the thermodynamics of a particular biological system as well as the thermal transition taking place. Briefly, it is necessary to extrapolate thermodynamic parameters over a broad temperature range. Enthalpy, entropy, and heat capacity terms are evaluated as partial derivatives of the Gibbs free energy function defined by Helmholtz-Kelvin s expression, assuming that the heat capacities integral is a continuous function. 

The internal energy per unit mass e is an intensive (state) function. Enthalpy h, a compound thermodynamic function defined by Equation 1.8, is also an intensive function. 

Early chemists thought that the beat of reaction, —AH. should be a measure of the "chemical affinity" of a reaction. With the introduction of the concepl of netropy (q.v.) and ihe application of the second law of thermodynamics lo chemical equilibria, it is easily shown that the true measure of chemical affinity and Ihe driving force for a reaction occurring at constant temperature and pressure is -AG. where AG represents the change in thermodynamic slate function, G. called Gibbs free energy or free enthalpy, and defined as the enthalpy, H, minus the entropy. S. times the temperature, T (G = H — TS). For a chemical reaction at constant pressure and temperature ... 

The only two functions actually required in thermodynamics are the energy function, obtained from the first law of thermodynamics, and the entropy function, obtained from the second law of thermodynamics. However, these functions are not necessarily the most convenient functions. The enthalpy function was defined in order to make the pressure the independent variable, rather than the volume. When the first and second laws are combined, as is done in this chapter, the entropy function appears as an independent variable. It then becomes convenient to define two other functions, the Gibbs and Helmholtz energy functions, for which the temperature is the independent variable, rather than the entropy. These two functions are defined and discussed in the first part of this chapter. 

The enthalpy function for the surface is obtained from the defining equation... 

Suppose now that we decide to combine a secondfactor, in addition to the enthalpy change, AH0 in the search for an overall parameter (G) the change in which (AG°) will indicate to us whether a given reaction or process is likely to take place spontaneously. Suppose we call this second factor, the entropy change ( AS0) which will be based on the change in a function defined as entropy (S). Then, from the evidence above, it seems likely that ... 

Two systems at rest may have the same amount of internal energy, and, if they are at different pressures, they have different capacities to perform PV work. (This is one demonstration of why "energy is the capacity to perform work" is a poor definition of energy. See Physics Lecture 3.) Enthalpy is a man-made property that accounts for this extra capacity to do PV work. Unlike functions such as pressure, volume, and temperature, enthalpy is not a measure of some intuitive property. Enthalpy is defined as an equation rather than as a description of a property. Enthalpy H is defined as ... 

The first step is to formulate the equation of internal energy in terms of enthalpy. The enthalpy function is defined by (e.g., [89] [87]) ... 

For the understanding of thermal analysis, it is necessary to recognize that most encountered polymeric systems are not in equilibrium, may be micro- or nanophase separated, and could even be not homogeneous. In order to describe such situations, one has to turn to nonequdibrium, irreversible thermodynamics. Functions of state such as entropy and free enthalpy are defined for systems in global equilibrium. Some others, such as mass, volume, and total energy, on the other hand, are largely indifferent to equilibrium. They need special treatment to be used for the description of nonequilibrium situations which arise when deviating from the free enthalpy minimum characteristic for equilibrium, as shown in Fig. 2.79. The four possible functional forms of the free enthalpy lead to stable, metastable, neutral, and labile equilibria. 

But what if we do the experiment at constant pressure instead It would be useful to have a function that would be equal to the heat flow under constant pressure conditions. This function, known as enthalpy, is defined as... 

Enthalpy (AH) (9.5) A state function defined as + PV, and equal to the heat flow at constant pressure. 

To avoid impractical conditions when expressing intensive variables as differential quotients as, for example, in Equation 3.9, auxiliary functions are introduced. These are the enthalpy H, defined as... 

In equilibrium, the interfacial region, which according to the Gibbs convention is assumed to be contracted in a volumeless dividing plane, may be considered as an independent phase. Now, as we did for bulk phases (see Equations 3.11 through 3.13), auxiliary functions of state may be defined for the interfacial phase. Thus, the interfacial enthalpy, is defined as... 

For three-dimensional systems, the enthalpy is defined in terms of internal energy, pressure and volume. In the case of adsorbed layers it is necessary to decide whether defining the enthalpy as a function of internal energy is compatible with defining it as a function of Gibbs free energy and entropy, or in other words whether the relation E — E - -pV is compatible with B = G -1- TS. 

Based on these definitions and the data provided, we compute the enthalpy of the air at the inlet and outlet of the column (Figure 3.20). Alternatively, we can use the functions defined in the exercise for mixtures of air streams to estimate absolute humidity and enthalpy. 

The advantage is that the temperature of this stream is known. Alternatively, we can define modules for each of the functions defining the enthalpy of flow. We leave it to the reader as an exercise. 

Though it is most useful in thermochemistry, enthalpy as defined in (2.4.3) is a function of state which can be related to quantities other than heats of reaction. Since the change in enthalpy corresponds to the heat exchanged in a process at constant pressure. 

For many engineering applications it is convenient to reformulate the equation of internal energy in terms of enthalpy or fluid temperature and heat capacity. To be able to transform the internal energy equation into a suitable form we need to apply some important thermodynamic relations which are discussed step by step in the following paragraphs. The first step is to formulate the equation of internal energy in terms of enthalpy. The enthalpy function is defined by (e.g., [89, 91]) ... 

A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

Themodynamic State Functions In thermodynamics, the state functions include the internal energy, U enthalpy, H and Helmholtz and Gibbs free energies, A and G, respectively, defined as follows ... 

Equation (5-43) has the practical advantage over Eq. (5-40) that the partition functions in (5-40) are difficult or impossible to evaluate, whereas the presence of the equilibrium constant in (5-43) permits us to introduce the well-developed ideas of thermodynamics into the kinetic problem. We define the quantities AG, A//, and A5 as, respectively, the standard free energy of activation, enthalpy of activation, and entropy of activation from thermodynamics we now can write... 

If the definition of work is limited to mechanical work, an interesting simplification is possible. In this case, AE is merely the heat exchanged at constant volume. This is so because if the volume is constant, no mechanical work can be done on or by the system. Then AE = q. Thus AE is a very useful quantity in constant volume processes. However, chemical and especially biochemical processes and reactions are much more likely to be carried out at constant pressure. In constant pressure processes, AE is not necessarily equal to the heat transferred. For this reason, chemists and biochemists have defined a function that is especially suitable for constant pressure processes. It is called the enthalpy, H, and it is defined as... 

Other thermodynamic functions described above in that the change in free energy AG is determined solely by the initial and final states of the system. The maximum work, or maximum available energy, defined in terms of the Gibbs free energy G, which is now called the free enthalpy, is... 

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