Availability adiabatic

In thermodynamics, for a given energy a measure of departure from stable equilibrium is the adiabatic availability—the larger the availability, the greater the departure from stable equilibrium. This availability in turn is related to the value of the entropy of the system since the smaller the entropy, the larger the availability. In other words, common sense dictates that entropy is an inherent property of matter in the same sense that energy is an inherent property of matter. Hence, the inconsistency of statistical thermodynamics. 

Theorem. From any state of a system, the maximum energy that can be extracted adiabatically in a CCP process is the work done in a reversible adiabatic process that ends in a stable equilibrium state. Moreover, the energy change of a system starting from a given state and ending at a stable equilibrium state is the same for all reversible adiabatic CCP processes. We call this energy the adiabatic availability. 

In modern separation design, a significant part of many phase-equilibrium calculations is the mathematical representation of pure-component and mixture enthalpies. Enthalpy estimates are important not only for determination of heat loads, but also for adiabatic flash and distillation computations. Further, mixture enthalpy data, when available, are useful for extending vapor-liquid equilibria to higher (or lower) temperatures, through the Gibbs-Helmholtz equation. ... 

This chapter centers on the mathematical aspects of the non-adiabatic coupling terms as single entities or when grouped in matrices, but were it not for the available ab initio calculation, it would have been almost impossible to proceed thus far in this study. Here, the ab initio results play the same crucial role that experimental results would play in general, and therefore the author feels that it is now appropriate for him to express his appreciation to the groups and individuals who developed the numerical means that led to the necessary numerical outcomes. 

Oxidizers. The characteristics of the oxidizer affect the baUistic and mechanical properties of a composite propellant as well as the processibihty. Oxidizers are selected to provide the best combination of available oxygen, high density, low heat of formation, and maximum gas volume in reaction with binders. Increases in oxidizer content increase the density, the adiabatic flame temperature, and the specific impulse of a propellant up to a maximum. The most commonly used inorganic oxidizer in both composite and nitroceUulose-based rocket propellant is ammonium perchlorate. The primary combustion products of an ammonium perchlorate propellant and a polymeric binder containing C, H, and O are CO2, H2, O2, and HCl. Ammonium nitrate has been used in slow burning propellants, and where a smokeless exhaust is requited. Nitramines such as RDX and HMX have also been used where maximum energy is essential. 

Adiabatic flame temperatures agree with values measured by optical techniques, when the combustion is essentially complete and when losses are known to be relatively small. Calculated temperatures and gas compositions are thus extremely useful and essential for assessing the combustion process and predicting the effects of variations in process parameters (4). Advances in computational techniques have made flame temperature and equifibrium gas composition calculations, and the prediction of thermodynamic properties, routine for any fuel-oxidizer system for which the enthalpies and heats of formation are available or can be estimated. 

Adiabatic Frictionless Nozzle Flow In process plant pipelines, compressible flows are usually more nearly adiabatic than isothermal. Solutions for adiabatic flows through frictionless nozzles and in channels with constant cross section and constant friction factor are readily available. 

When the kinetics are unknown, still-useful information can be obtained by finding equilibrium compositions at fixed temperature or adiabatically, or at some specified approach to the adiabatic temperature, say within 25°C (45°F) of it. Such calculations require only an input of the components of the feed and produc ts and their thermodynamic properties, not their stoichiometric relations, and are based on Gibbs energy minimization. Computer programs appear, for instance, in Smith and Missen Chemical Reaction Equilibrium Analysis Theory and Algorithms, Wiley, 1982), but the problem often is laborious enough to warrant use of one of the several available commercial services and their data banks. Several simpler cases with specified stoichiometries are solved by Walas Phase Equilibiia in Chemical Engineering, Butterworths, 1985). 

Inert, Ideal Gas-Filled Vessels The energy available for external work following the rapid disintegration of the vessel is calcuJated by assuming that the gas within the vessel expands adiabatically to atmospheric pressure. 

In the case of thick-walled HP vessels, the strain energy in the vessel shell can contribute to the available energy, but for vessels below about 20 MN/m (200 barg) it is negligible and can be ignored. If a MoUier chart for the gas is available, the adiabatic energy can be measured directly. This is the preferred method, but in many cases the relevant chart is not available. 

Steam Rate Enthalpy data can be obtained from Mollier diagrams or from steam tables (see Sec. 2), from which the theoretical steam rate can be calculated. For example, a throttle inlet condition of 4137 kPa (600 psig) and 399° C (750° F) gives an enthalpy of 3.2 MJ/kg (1380 Btu/lb), and if the end point is at 348 kPa (50 psig), then adiabatic expansion is to 2.69 MJ/kg (1157 Btu/lb). This gives 0.52 MJ/kg (223 Btu/lb) available, and the theoretical steam rate is calculated from the Btu equivalent per Idlowatthour or horsepower-hour ... 

Two standard estimation methods for heat of reaction and CART are Chetah 7.2 and NASA CET 89. Chetah Version 7.2 is a computer program capable of predicting both thermochemical properties and certain reactive chemical hazards of pure chemicals, mixtures or reactions. Available from ASTM, Chetah 7.2 uses Benson s method of group additivity to estimate ideal gas heat of formation and heat of decomposition. NASA CET 89 is a computer program that calculates the adiabatic decomposition temperature (maximum attainable temperature in a chemical system) and the equilibrium decomposition products formed at that temperature. It is capable of calculating CART values for any combination of materials, including reactants, products, solvents, etc. Melhem and Shanley (1997) describe the use of CART values in thermal hazard analysis. 

As stated by inequality (2.81) (see also section 4.2 and fig. 30), when the tunneling mass grows, the tunneling regime tends to be adiabatic, and the extremal trajectory approaches the MEP. The transition can be thought of as a one-dimensional tunneling in the vibrationally adiabatic barrier (1.10), and an estimate of and can be obtained on substitution of the parameters of this barrier in the one-dimensional formulae (2.6) and (2.7). The rate constant falls into the interval available for measurements if, as the mass m is increased, the barrier parameters are decreased so that the quantity d(Vom/mn) remains approximately invariant. 

The adiabatic head that is actually available at the rotor discharge is equal to the theoretical head minus the head losses from the shock in the rotor, the incidence loss, the blade loadings and profile losses, the clearance between the rotor and the shroud, and the secondary losses encountered in the flow passage... 

Electron-tunneling Model. Several models based on quantum mechanics have been introduced. One describes how an electron of the conducting band tunnels to the leaving atom, or vice versa. The probability of tunneling depends on the ionization potential of the sputtered element, the velocity of the atom (time available for the tunneling process) and on the work function of the metal (adiabatic surface ionization, Schroeer model [3.46]). 

Temperature change with altitude has great influence on the motion of air pollutants. For example, inversion conditions result in only limited vertical mixing. The amount of turbulence available to diffuse pollutants is also a function of the temperature profile. The decrease of temperature with altitude is known as the lapse rate. The normal or standard lapse rate in the United States is -3.5" F/1,000 ft. An adiabatic lapse rate has a value of -5.4" F/1,000 ft. Temperature as a function of altitude is expressed by the following equation ... 

The second law of thermodynamics states that energy exists at various levels and is available for use only if it can move from a higher to a lower level. For example, it is impossible for any device to operate in a cycle and produce work while exchanging heat only with bodies at a single fixed temperature. In thermodynamics, a measure of the unavailability of energy has been devised and is known as entropy. As a measure of unavailability, entropy increases as a system loses heat, but remains constant when there is no gain or loss of heat as in an adiabatic process. It is defined by the following differential equation ... 

Theorem.—A process yields the maximum amount of available energy when it is conducted reversibly.—Proof. If the change is isothermal, this is a consequence of Moutier s theorem, for the system could be brought back to the initial state by a reversible process, and, by the second law, no work must be obtained in the whole cycle. If it is non-isothermal, we may suppose it to be constructed of a very large number of very small isothermal and adiabatic processes, which may be combined with another corresponding set of perfectlyJ reversible isothermal and adiabatic processes, so that a complete cycle is formed out of a very large number of infinitesimal Carnot s cycles (Fig 11). 

Both lines are broadened independently and solely by adiabatic phase shift as in Lorentz and Weisskopf theories. They are Lorentzians of width (1 — cosa) and frequency shift (sin a). In general off-diagonal elements of f are not zero though they are less than diagonal elements. Consequently, the spectrum may collapse even in the adiabatic case when A 1/tc. However, adiabatic collapse is hardly ever achieved in the gas phase where l/rc > l/t0 > jS since A > 1/tc > j8 and hence only the resolved doublet limit is available. 

Correlations for E are not widely available. The more accurate model given in Section 9.1 is preferred for nonisothermal reactions in packed-beds. However, as discussed previously, this model degenerates to piston flow for an adiabatic reaction. The nonisothermal axial dispersion model is a conservative design methodology available for adiabatic reactions in packed beds and for nonisothermal reactions in turbulent pipeline flows. The fact that E >D provides some basis for estimating E. Recognize that the axial dispersion model is a correction to what would otherwise be treated as piston flow. Thus, even setting E=D should improve the accuracy of the predictions. 

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