Thermodynamic representation

The horizontal line at the bottom of the pressure-volume diagram of Figure 4 traces the other tv o strokes of the four-stroke cycle. On the exhaust stroke, from 5 to 6, the rising piston expels most of the remaining combustion products from the cylinder. On the intake stroke, from 6 to 7 (= 1), the descending piston inducts a fresh charge for repetition of the cycle. The net thermodynamic work developed in this cycle is proportional to the area enclosed by the pressure-volume diagram. In the ideal case, both the exhaust and intake strokes occur at atmospheric pressure, so they have no effect on the net output work. That justifies their exclusion from the thermodynamic representation of the ideal Otto... 

The above form of the thermodynamic representation of the condition for the occurrence of a spontaneous process or of equilibrium is frequently used. 

Thermodynamic representation of transitions often represents a challenge. First-order phase transitions are more easily handled numerically than second-order transitions. The enthalpy and entropy of first-order phase transitions can be calculated at any temperature using the heat capacity of the two phases and the enthalpy and entropy of transition at the equilibrium transition temperature. Small pre-tran-sitional contributions to the heat capacity, often observed experimentally, are most often not included in the polynomial representations since the contribution to the... 

Non-stoichiometry in solid solutions may also be handled by the compound energy model see for example a recent review by Hillert [16]. In this approach the end-member corresponding to vacancies is an empty sub-lattice and it may be argued that the model loses its physical significance. Nevertheless, this model represents a mathematically efficient description that is often incorporated in thermodynamic representations of phase diagrams. 

Cruz, Jose-Luis and H. Renon, "A New Thermodynamic Representation of Binary Electrolyte Solutions Nonideality in the Whole Range of Concentrations," AIChE J., 1978, 24, 817. 

This chapter will begin, very briefly, with the thermodynamic representation of Gibbs energy for stoichiometric compounds before concentrating on the situation when mixing occurs in a phase. 

Mock B, Evans LB, Chen CC. Thermodynamic representation of phase equilibria of mixed-solvent electrolyte systems. AIChE J 1986 32 1655-1664. 

Fig. 14. Two thermodynamic representations of a liquid hydrocarbon (benzene) dissolution into water, assuming constant heat capacity change. (Left) Free energy of transfer and underlying contributions as a function of temperature. (Right) Solubility function ( "GVT) and underlying contributions as a function of In T. Dotted lines are drawn at respective maxima, TH and Ts. Shaded regions show triangular relations as discussed in the text.

SCHEME 4.1 Thermodynamic representation of radical cation cycloaddition reaction acceleration. 

In order to predict accurately chemical reactions in a concentrated solution, we need to account for this reduction in effective concentration. This is done using a concentration term known as activity that is independent of electrostatic interactions. Activity is the formal thermodynamic representation of concentration and it describes the component of concentration that is free to take part in chemical reactions. Activity is related to concentration by an activity coefficient (y). 

The V denotes activity the formal thermodynamic representation of concentration (see Section 2.6). 

We start the chapter by explaining the graphical thermodynamic representations for ternary mixtures known as Residue Curve Maps. The next section deals with the separation of homogeneous azeotropes, where the existence of a distillation boundary is a serious obstacle to separation. Therefore, the choice of the entrainer is essential. We discuss some design issues, as entrainer ratio, optimum energy requirements and finite reflux effects. The following subchapter treats the heterogeneous azeotropic distillation, where liquid-liquid split is a powerful method to overcome the constraint of a distillation boundary. Finally, we will present the combination of distillation with other separation techniques, as extraction or membranes. 

Cruz JL, Renon H (1978) A new thermodynamic representation of binary electrolyte solutions nonideality in the whole range of concentrations. AIChE J 24 817-830... 

The standard Helmholtz energy is defined as follows First we write the chemical potentials of A and B, in their thermodynamic representation, as... 

Figure 5.4. Thermodynamic representation of the standard state (SS) for an adsorption process.

---