Entropy absolute, defined

We can measure all entropy values against the absolute zero of entropy as defined by the third law. Table 17.2 lists values of standard entropies at 25 °C for selected substances. A more complete list can be found in Appendix IIB. Standard entropy values are listed in units of joules per mole per kelvin (J/mol K). The units of mole in the... 

The chemical potential, plays a vital role in both phase and chemical reaction equiUbria. However, the chemical potential exhibits certain unfortunate characteristics which discourage its use in the solution of practical problems. The Gibbs energy, and hence is defined in relation to the internal energy and entropy, both primitive quantities for which absolute values are unknown. Moreover, p approaches negative infinity when either P or x approaches 2ero. While these characteristics do not preclude the use of chemical potentials, the appHcation of equiUbrium criteria is faciUtated by the introduction of a new quantity to take the place of p but which does not exhibit its less desirable characteristics. 

The work done by an expanding fluid is defined as the difference in internal energy between the fluid s initial and final states. Most thermodynamic tables and graphs do not presentbut only h, p, v, T (the absolute temperature), and s (the specific entropy). Therefore, u must be calculated with the following equation ... 

The second law of thermodynamics also consists of two parts. The first part is used to define a new thermodynamic variable called entropy, denoted by S. Entropy is the measure of a system s energy that is unavailable for work.The first part of the second law says that if a reversible process i f takes place in a system, then the entropy change of the system can be found by adding up the heat added to the system divided by the absolute temperature of the system when each small amount of heat is added ... 

Deals with the concept of entropy, which serves as a means of determining whether or not a process is possible. Defines the zero entropy state for any substance in a single, pure quantum state as the absolute zero of temperature. 

Just as the intrinsic energy of a body is defined only up to an arbitrary constant, so also the entropy of the body cannot, from the considerations of pure thermodynamics, be specified in absolute amount. We therefore select any convenient arbitrary standard state a, in which the entropy is taken as zero, and estimate the entropy in another state /3 as follows The change of entropy being the same along all reversible paths linking the states a and /3, and equal to the difference of the entropies of the two states, we may imagine the process conducted in the following two steps ... 

In summary, the Carnot cycle can be used to define the thermodynamic temperature (see Section 2.2b), show that this thermodynamic temperature is an integrating denominator that converts the inexact differential bq into an exact differential of the entropy dS, and show that this thermodynamic temperature is the same as the absolute temperature obtained from the ideal gas. This hypothetical engine is indeed a useful one to consider. 

Chapter 4 presents the Third Law, demonstrates its usefulness in generating absolute entropies, and describes its implications and limitations in real systems. Chapter 5 develops the concept of the chemical potential and its importance as a criterion for equilibrium. Partial molar properties are defined and described, and their relationship through the Gibbs-Duhem equation is presented. 

The entropies of individual ions in solution are determined by setting the entropy <>1 II in water equal to 0 and then defining the entropies of all other ions relative to this value hence a negative entropy is one that is lower than the entropy of H in water. All absolute entropies are positive, and no sign need he given all entropies of ions are relative to that ot H+ and are listed here with a sign (either + or —). 

There is no single criterion for the system alone that applies to all processes. However, if we restrict the conditions to constant temperature and pressure, there is a state function whose change for the system predicts spontaneity. This new state function is the free energy (G), which was introduced by the American J. Willard Gibbs and is defined by Equation G = H - T S As usual, H is enthalpy, T is absolute temperature, and S is entropy. 

The connection between the multiplicative insensitivity of 12 and thermodynamics is actually rather intuitive classically, we are normally only concerned with entropy differences, not absolute entropy values. Along these lines, if we examine Boltzmann s equation, S = kB In 12, where kB is the Boltzmann constant, we see that a multiplicative uncertainty in the density of states translates to an additive uncertainty in the entropy. From a simulation perspective, this implies that we need not converge to an absolute density of states. Typically, however, one implements a heuristic rule which defines the minimum value of the working density of states to be one. 

The available energy (A) is defined as the difference between the total energy (U or H = U + pV) and the product of the absolute temperature (T) by the entropy (S), which measures the amount of the thermal energy that cannot be used at that temperature to produce work ... 

Boltzmann, following Clausius, considered entropy to be defined only to an arbitrary constant, and related the difference in entropy between two states of a system to their relative probability. An enormous advance was made by Planck who proposed to determine the absolute entropy as a quantity, which, for every realizable system, must always be positive (third law of thermodynamics). He related this absolute entropy, not to the probability of a system, but to the total number of its possibilities. This view of Planck has been the basis of all recent efforts to find the statistical basis of thermodynamics, and while these have led to many differences of opinion, and of interpretation, we believe it is now possible to derive the second law of thermodynamics in an exact form and to obtain... 

It is more problematical to define the third law of thermodynamics compared to the first and second laws. Experimental work by Richards (1902) and Nemst (1906) led Nemst to postulate that, as the temperature approached absolute zero, the entropy of the system would also approach zero. This led to a definition for the third law of thermodynamics that at a temperature of absolute zero the entropy of a condensed system would also be zero. This was further refined by Planck (1911) who suggested this be reworded as the entropy of a pure element or substance in a perfect crystalline form is zero at absolute zero. 

How can the absolute entropy be determined Equation 1 defines entropy in terms of the transfer of heat so it can be used to calculate only changes in the entropy of a substance. In 1877, the Austrian... 

Values of AG°f at 25°C for some common substances are listed in Table 17.3, and additional values are given in Appendix B. Note that AG°f for an element in its most stable form at 25°C is defined to be zero. Thus, solid graphite has AG°f = 0 kj/mol, but diamond, a less stable form of solid carbon at 25°C, has AG°f = 2.9kJ/mol. As with standard enthalpies of formation, AH°f, a zero value of AG°f for elements in their most stable form establishes a thermochemical "sea level," or reference point, with respect to which the standard free energies of other substances are measured. We can t measure the absolute value of a substance s free energy (as we can the entropy), but that s not a problem because we are interested only in free-energy differences between reactants and products. 

H, F and G) can be defined only with reference to some standard state. Entropy, however, can be defined in absolute terms with the help of the third law... 

The reaction entropy ACS is a result of the different opportunities of the species to save thermal energy between the absolute zero level of temperature and the temperature level of the reactor. Concerning the energy balance of a fuel cell (Figure 2.1), the heat <2FCrev has to be transferred reversibly from the fuel cell to the environment. 0FCrev is defined as a positive value if the reversible change in entropy is... 

The thermodynamic functions have been defined in terms of the energy and the entropy. These, in turn, have been defined in terms of differential quantities. The absolute values of these functions for systems in given states are not known.1 However, differences in the values of the thermodynamic functions between two states of a system can be determined. We therefore may choose a certain state of a system as a standard state and consider the differences of the thermodynamic functions between any state of a system and the chosen standard state of the system. The choice of the standard state is arbitrary, and any state, physically realizable or not, may be chosen. The nature of the thermodynamic problem, experience, and convention dictate the choice. For gases the choice of standard state, defined in Chapter 7, is simple because equations of state are available and because, for mixtures, gases are generally miscible with each other. The question is more difficult for liquids and solids because, in addition to the lack of a common equation of state, limited ranges of solubility exist in many systems. The independent variables to which values must be assigned to fix the values of all of the... 

In Equation (8.22) fi°[T,P0] is the molar Gibbs energy of the substance in its standard state defined at the temperature T and the arbitrary pressure P0. The change of the Gibbs energy with temperature cannot be determined, because the absolute value of the entropy is not known, as stated before. 

The energy and entropy functions have been defined in terms of differential quantities, with the result that the absolute values could not be known. We have used the difference in the values of the thermodynamic functions between two states and, in determining these differences, the process of integration between limits has been used. In so doing we have avoided the use or requirement of integration constants. The many studies concerning the possible determination of these constants have culminated in the third law of thermodynamics. 

We have therefore used the Third Law of Thermodynamics to define absolute zero for a scale of standard entropy, thus ... 

Since the equations of thermodynamics which derive from the first and second laws do not permit calculation of absolute values for enthalpy and entropy, and since all we need in practice are relative values, the reference-state conditions T0 and P0 are selected for convenience, and values are assigned to H 0a and S 9 arbitrarily. The only data needed for application of Eqs. (6.45) and (6.46) are ideal-gas heat capacities and PVT data. Once V, H, and S are known at given conditions of T and P, the other thermodynamic properties follow from defining equations. 

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