Thermodynamics state functions and

It should be emphasized that the criterion for macroscopic character is based on independent properties only. (The importance of properly enumerating the number of independent intensive properties will become apparent in the discussion of the Gibbs phase rule, Section 5.1). For example, from two independent extensive variables such as mass m and volume V, one can obviously form the ratio m/V (density p), which is neither extensive nor intensive, nor independent of m and V. (That density cannot fulfill the uniform value throughout criterion for intensive character will be apparent from consideration of any 2-phase system, where p certainly varies from one phase region to another.) Of course, for many thermodynamic purposes, we are free to choose a different set of independent properties (perhaps including, for example, p or other ratio-type properties), rather than the base set of intensive and extensive properties that are used to assess macroscopic character. But considerable conceptual and formal simplifications result from choosing properties of pure intensive (R() or extensive QQ character as independent arguments of thermodynamic state functions, and it is important to realize that this pure choice is always possible if (and only if) the system is macroscopic. 

However, a phase melts when the Gibbs energy of the solid phase, which is a thermodynamic state function and which controls the phase stability, is higher than that of the liquid phase [see e.g. Denbigh (1971) and chapter by Pelton in Volume 5 of MST]. The Gibbs energy G of a phase is given by... 

Statistical thermodynamics therefore gives expressions for all of the basic thermodynamic state functions, and they all depend on the partition function q. 

The terms AG, AH, and AS are state functions and depend only on the identity of the materials and the initial and final state of the reaction. Tables of thermodynamic quantities are available for most known materials (see also Thermodynamic properties) (11,12). 

In the broadest sense, thermodynamics is concerned with mathematical relationships that describe equiUbrium conditions as well as transformations of energy from one form to another. Many chemical properties and parameters of engineering significance have origins in the mathematical expressions of the first and second laws and accompanying definitions. Particularly important are those fundamental equations which connect thermodynamic state functions to real-world, measurable properties such as pressure, volume, temperature, and heat capacity (1 3) (see also Thermodynamic properties). 

Define a state function. Name three thermodynamic quantities that are state functions and three that are not. 

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... 

First, we shall explore a conceptual relation between kinetics and thermodynamics that allows one to draw certain conclusions about the kinetics of the reverse reaction, even when it has itself not been studied. Second, we shall show how the thermodynamic state functions for the transition state can be defined from kinetic data. These are the previously mentioned activation parameters. If their values for the reaction in one direction have been determined, then the values in the other can be calculated from them as well as the standard thermodynamic functions. The implications of this calculation will be explored. Third, we shall consider a fundamental principle that requires that the... 

These two features of state functions are more important for scientists than for cross-counhy travelers like the Daltons. Chemists determine values of state function changes by doing careful experiments using convenient paths. These values are collected in tables, just as distances between cities are collected in an atlas. Energy is one such state function, and chemists use tabulated energy values to analyze chemical processes from a thermodynamic point of view. 

A change in any thermodynamic state function is independent of the path used to accomplish that change. This feature of state functions tells us that the energy change in a chemical reaction is independent of the manner in which the reaction takes place. In the real world, chemical reactions often follow very complicated paths. Even a relatively simple overall reaction such as the combustion of CH4 and O2 can be very complicated at the... 

Why do some reactions go virtually to completion, whereas others reach equilibrium when hardly any of the starting materials have been consumed At the molecular level, bond energies and molecular organization are the determining factors. These features correlate with the thermodynamic state functions of enthalpy and entropy. As discussed In Chapter 14, free energy (G) is the state function that combines these properties. This section establishes the connection between thermodynamics and equilibrium. 

Clearly, the differential obtained, namely, d S = SqJT is exact and S, the entropy, is a thermodynamic state function, that is, it is independent of the path of integration. While Eq. (88) was obtained with the assumption of an ideal gas, the result is general if reversible conditions are applied. 

The enthalpy of formation of a compound is a so-called thermodynamic state function, which means that the value depends only on the initial and final states of the system. When the formation of crystalline NaCl from the elements is considered, it is possible to consider the process as if it occurred in a series of steps that can be summarized in a thermochemical cycle known as a Born-Haber cycle. In this cycle, the overall heat change is the same regardless of the pathway that is followed between the initial and final states. Although the rate of a reaction depends on the pathway, the enthalpy change is a function of initial and final states only, not the pathway between them. The Born-Haber cycle for the formation of sodium chloride is shown as follows ... 

A fundamental thermodynamic state function (symbolized by S), and as such, not dependent on the path by which a particular state is reached. For a reversible process, the differential change in entropy, dS, is equal to the amount of energy absorbed by the system, dq, divided by the absolute temperature, T. Thus,... 

The first law of thermodynamics, which can be stated in various ways, enuciates the principle of the conservation of energy. In the present context, its most important application is in the calculation of the heat evolved or absorbed when a given chemical reaction takes place. Certain thermodynamic properties known as state functions are used to define equilibrium states and these properties depend only on the present state of the system and not on its history, that is the route by which it reached that state. The definition of a sufficient number of thermodynamic state functions serves to fix the state of a system for example, the state of a given mass of a pure gas is defined if the pressure and temperature are fixed. When a system undergoes some change from state 1 to state 2 in which a quantity of heat, Q, is absorbed and an amount of work, W, is done on the system, the first law may be written... 

The thermodynamic state functions obtained by non-linear regression in both experiments are identical within the error limits and are considered reliable contrary to the parameters of higher complexation that suffer from dramatically increased errors and their cross correlation. 

Thus, the deposition temperature and the thermodynamic state function of the adsorption are combined and they can easily be determined from each other. The retention time for a short-lived radioactive species is calculated as the radioactive lifetime of the nuclide ... 

Equation (1.60) illustrates a very important thermodynamic property in which the quantity dqrev / T becomes zero when the cyclic process is completed regardless of the paths taken from the initial to final states. Such a property is known as a state function, as are P, V, T, E, and H. Clausius suggested defining a new thermodynamic state function, called entropy and denoted as S, where dqrev / T = dS, so that... 

A, E, G, H, T, and S are thermodynamic state functions, independent of the path of a process. Changes in A and G from one state to another at constant temperature can be written by ... 

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