Ideality, thermodynamic

When both phases form ideal thermodynamic solutions, ie, no heat of mixing, no volume change on mixing, etc, Raoult s law apphes ... 

As you may know, the ideal thermodynamic efficiency of a heat engine is given by... 

The thermal state of the melt in the extruder is frequently compared with two ideal thermodynamic states. One is where the process may be regarded as... 

The electrical conductivity is proportional to n. Equation 1.168 therefore predicts an electrical conductivity varying as p. Experimental results show proportionality to p and this discrepancy is probably due to incomplete disorder of cation vacancies and positive holes. An effect of this sort (deviation from ideal thermodynamic behaviour) is not allowed for in the simple mass action formula of equation 1.167. 

Nonideal Physicochemical behavior that does not conform to ideal thermodynamic predictions. 

Curve P in Fig. 2 represents the ideal thermodynamic limit for conversion efficiency and cuarve C sets an approximate limit for the efficiency of conversion to stored chemical energy. There are, however, other loss factors to be considered which vaary according to the device. These loss factors have been considered in considerable detail for photovoltaic devices (15, 19) and estimates for the ultimate achievable conversion efficiency to electricity vaary from 25 - 2 8% however, only recently have efficiencies been considered for conversion to stored chemical energy (5). In this case... 

Ideally, thermodynamic activities of the reactants should be used in the equation, but since concentrations are normally easier to measure these are often used instead. The use of the activity of water (which can be measured fairly easily) and the concentrations of the other reactants has been recommended for studies of enzyme catalyzed reactions in organic media (Hailing, 1984). In order to increase the synthesis of the ester, the water concentration (or activity) should be reduced. This can be achieved by replacing part of the water with a water miscible solvent. 

It follows that retention measurements on silica based stationary phases for the purpose of obtaining thermodynamic data is fraught with difficulties. Data from solutes of different molecular size cannot be compared or related to other Interacting variables ideally, thermodynamic measurements should be made on columns that contain stationary phases that exhibit no exclusion properties. However, the only column system that might meet this requirement is the capillary column which, unfortunately introduces other complications wmcn will be discussed later. 

Corner s Equation of State. At the high temps pressures encountered in explosives technology, the perfect gas law is not applicable. The calculation of pressures developed by expls therefore requires the adoption of a suitable equation of state. Furthermore, in calculating the explosion products it is necessary to correct the ideal thermodynamic equilibria of the relevant chem reactions for the effect of the gas imperfection. This correction also depends on the equation of state adopted. Most equations of state, whether empirical or theoretical, are not suitable for application at the high temps pressures developed by expls. Comer has recently discussed a theoretical equation of state applicable to propellent expls (Ref 3)... 

Finally, let us show the ideal thermodynamic cycle description that elucidates the advantages of 3S compared to TET in achieving low temperatures. 

The silver-silver Ion electrode. Of the reversible metal electrodes, silver has been most often employed. There is only one stable oxidation state of silver above 300°C there is no danger of oxide formation because Ag20 is unstable.57 The metal has no observable tendency to dissolve in molten silver salts and is highly reversible in mixed chloride and nitrate eutectics. The Ag(I) ion can be introduced into the melt by either adding silver nitrate to a nitrate melt (AgCl to a chloride melt) or by anodizing a silver electrode. The potentials of silver nitrate concentration cells show ideal thermodynamic behavior up to 0.5 mol % in (Na,K)N03 eutectic and in NaN03.58... 

It should be stressed that there is nothing wrong with these practices. In fact, column performance is best compared under ideal thermodynamic conditions CL). Hence, test systems should be chosen to produce the best column performance, since most workers like to see how well a column really can perform. However, it should be recognized that when considering the number of plates specified for a column, it is necessary to examine the test conditions used to generate that number. 

Real gases are usually non-ideal. Thermodynamics describes both ideal and non-ideal gases with the same type of formulas, except that for non-ideal gas mixtures the fugacity f is substituted in place of the pressure pi and that the activity at is substituted in place of the molar fraction xi or concentration c, of constituent substance i. We have already seen that in the ideal gas of a pure substance the chemical potential is expressed by Eq. 7.5. By analogy, we write Eq. 7.9 for the non-ideal gas of a pure substance i ... 

Fig. II.A.2 Ideal thermodynamic processes in the combustion chamber and nozzle of a rocket motor...

Mujtaba and Macchietto (1994) presented an industrial case study in which dynamic optimisation method of Mujtaba and Macchietto (1993) is utilised for the development of the optimal operation of an entire batch distillation campaign where 100 batches of fresh charge have to be processed with secondary reprocessing of intermediate off-cuts. The process involved a complex separation of a five-component mixture of industrial interest, described using non-ideal thermodynamic models. In addition, the operation of the whole production campaign was subject to a number of resource constraints, for example -... 

In this separation, there are 4 distillation tasks (NT-4), producing 3 main product states MP= D1, D2, Bf) and 2 off-cut states OP= Rl, R2 from a feed mixture EF= FO. There are a total of 9 possible outer decision variables. Of these, the key component purities of the main-cuts and of the final bottom product are set to the values given by Nad and Spiegel (1987). Additional specification of the recovery of component 1 in Task 2 results in a total of 5 decision variables to be optimised in the outer level optimisation problem. The detailed dynamic model (Type IV-CMH) of Mujtaba and Macchietto (1993) was used here with non-ideal thermodynamics described by the Soave-Redlich-Kwong (SRK) equation of state. Two time intervals for the reflux ratio in Tasks 1 and 3 and 1 interval for Tasks 2 and 4 are used. This gives a total of 12 (6 reflux levels and 6 switching times) inner loop optimisation variables to be optimised. The input data, problem specifications and cost coefficients are given in Table 7.1. 

A thermodynamic system is a part of the physical universe with a specified boundary for observation. A system contains a substance with a large amount of molecules or atoms, and is formed by a geometrical volume of macroscopic dimensions subjected to controlled experimental conditions. An ideal thermodynamic system is a model system with simplifications to represent a real system that can be described by the theoretical thermodynamics approach. A simple system is a single state system with no internal boundaries, and is not subject to external force fields or inertial forces. A composite system, however, has at least two simple systems separated by a barrier restrictive to one form of energy or matter. The boundary of the volume separates the system from its surroundings. A system may be taken through a complete cycle of states, in which its final state is the same as its original state. 

The water electrolysis rest potential is determined from extrapolation to ideal conditions. Variations of the concentration, c, and pressure, p, from ideality are respectively expressed by the activity (or fugacity for a gas), as a = yc (or yp for a gas), with the ideal state defined at 1 atmosphere for a pure liquid (or solid), and extrapolated from p = 0 or for a gas or infinite dilution for a dissolved species. The formal potential, measured under real conditions of c and p can deviate significantly from the (ideal thermodynamic) rest potential, as for example the activity of water, aw, at, or near, ambient conditions generally ranges from approximately 1 for dilute solutions to less than 0.1 for concentrated alkaline and acidic electrolytes.91"93 The potential for the dissociation of water decreases from 1.229 V at 25 °C in the liquid phase to 1.167 V at 100 °C in the gas phase. Above the boiling the point, pressure is used to express the variation of water activity. The variation of the electrochemical potential for water in the liquid and gas phases are given by ... 

This is a term used to describe the effective concentration of a solute. In dilute solutions, solutes can be considered to behave according to ideal (thermodynamic) principles, i.e. they will have an effective concentration equivalent to the actual concentration. However, in concentrated solutions (> 0.5molL" ), the behaviour of solutes is often non-ideal, and their effective concentration (activity) will be less than the actual concentration [C]. The ratio between the effective concentration and the actual concentration is called the activity coefficient (y) where... 

Relative to the ideal thermodynamical efficiency (3.22), the practical efficiency is diminished by the electrochemical losses through the system (3.23), discussed above for each step in the process. Furthermore, as also mentioned in the preceding subsections, not all the hydrogen fuel is utilised and there is a hydrogen content in the outflow from the fuel channel. When cells are combined to form a fuel cell stack, a fuller utilisation may be achieved by... 

The gas thermometer has never been used at a temperature higher than 1,550 C. Above 1,500°C. the temperature scale is defined by means of the Stefan-Boltzmann or Wien-Planck radiation laws. These laws have a theoretical significance, and experimental evidence is such as to lead to the conclusion that the scales defined by these two radiation laws are in mutual agreement and that they represent the ideal thermodynamic scale. 

Limitations to the spectroscopic measurement of the temperatures from line intensities lie in possible deviations from ideal thermodynamic behavior in real radiation sources, but also in the poor accuracy of transition probabilities. They can be calculated from quantum mechanics, and have been determined and compiled by Corliss and Bozman at NIST [10] from measurements using a copper dc arc. These tables contain line energy levels, transition probabilities and the so-called oscillator strengths for ca. 25000 lines between 200 and 900 nm for 112 spectra of 70 elements. Between the oscillator strength f (being 0.01-0.1 for non-resonance and nearer to 1 for resonance lines) there is the relationship [11] ... 

Figure 3.6. Ethanol-water vapor-liquid diagram for ideal thermodynamics.

When modeling mass transfer equipment, there are two key points to remember (1) thermodynamics is important and (2) convergence is difficult. The corollary is that you have to compare your thermodynamic predictions with experimental data. Also, you may start with ideal thermodynamics and obtain a solution. This solution can then be used as the initial guess when the thermodynamic model is more realistic. Process simulators do not always work, so you need to be flexible about how you approach a problem. 

An ideal thermodynamic cell which could be used to study the adsorption of adsorbate A at mercury is the following ... 

With negligible liquid holdup, negligible pressure drop, constant vapor and liquid flow rates from tray to tray, time-invariant vapor flow rate, and ideal thermodynamics, the batch distillation problem for product k may be stated as follows (Farhat et al., 1990) ... 

The separation cost is often related directly to the degree of dilution for the component of interest in the initial mixture. This cost includes the fact that most separations use 50 times the minimum energy requirement based on the ideal thermodynamic requirements. To put the energy consumption in perspective, the chemical and petroleum refining industries in the US consume approximately 2.9 million barrels per day of crude oil in feedstock conversion [1], One method to visualize this cost factor is with the Sherwood plot shown in Figure 1.2. 

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