Real Gas Relationships

Essentially there are four methods of getting or predicting real gas properties  

Even if experimental data are available, the other three techniques still may be quite useful for certain types of calculations. Of course, under conditions such that part of the gas liquefies, the gas laws apply only to the gas-phase portion of the system—you cannot extend these real gas laws into the liquid region any more than you can apply the ideal gas laws to a liquid. 

Physical properties and/or the equations used to predict physical properties can be stored on spreadsheets. No programming experience is required, and simple calculations are easy to carry out using the spreadsheet software. Numerical data such as tables can be typed into cells, where they are easily seen. Equations can also be typed into cells and are introduced as needed. Labels and units as well as remarks can be added as needed. 

Your objectives in studying this section are to be able to  

Cite two reasons for using equations of state to predict p, V, T properties of gases. 

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The thermal efficiency of the Brayton cycle can be calculated using classical thermodynamic analysis. The compression ratio of the working fluid and the temperatures of heat addition and heat rejection are very important parameters. The results of such an analysis are shown in Fig. 6.53. These calculations are based on an ambient temperature of 59°F (15 C), actual component efficiencies, and real gas relationships. The results are plotted as thermal efficiency versus specific work for two different firing temperatures. 

Density is the most commonly measured property of a gas, and is obtained experimentally by measuring the specific gravity of the gas (density of the gas relative to air = 1). As pressure increases, so does gas density, but the relationship is non-linear since the dimensionless gas compressibility (z-factor) also varies with pressure. The gas density (pg) can be calculated at any pressure and temperature using the real gas law ... 

It would be useful to have an equation that describes the relationship between pressure and volume for a real gas, just as P V — n R T describes an ideai gas. One way to approach real gas behavior is to modify the ideal gas equation to account for attractive forces and molecular volumes. The result is the van der Waals equation, ... 

The application of the second law method to gas-phase reactions is less problematic than for reactions in solution. As described, a, = pt jp° can be used when the perfect gas model is valid (at low enough pressures). For higher pressures, the real gas model implies a, =f/p°. Either one of these relationships can be... 

That is, as the pressure approaches zero, the fugacity approaches the pressure. Figure 10.5 indicates the relationship between P and/for ideal and real gases. The standard state for a real gas is chosen as the state at which the fugacity is equal to 0.1 MPa, 1 bar, along a line extrapolated from values off at low pressure, as indicated in Figure 10.5. The standard state for a real gas is then a hypothetical 0.1 MPa standard state. 

The relationship to the earlier discussion of real gas properties (Section 2.4.1) can be demonstrated by re-expressing the Van der Waals equation in terms of Z. To obtain Zvdw for the Van der Waals gas, we first rewrite (2.13) in expanded form as... 

The first term on the right-hand side is the idea gas limit, and the remaining -logarithmic terms express the successive virial corrections for the real gas behavior. It is evidently most convenient for this problem to choose the standard state pressure as P° = 0, where all gases are ideal. With this choice, we can write the relationship between fugacity and pressure as... 

The thermodynamics of a l-d Fermi system can be perfectly mapped onto the thermodynamics of a two-component classical real gas on the surface of a cylinder. The relationship between these two infrared problems (cf. Zittartz s contribution) is exploited as follows. We treat the classical plasma by a modified Mayer cluster expansion method (the lowest order term corresponding to the Debye Hiickel theory), and obtain an exponentially activated behavior of the specific heat (cf. Luther s contribution) of the original quantum gas by simply reinterpreting the meaning of thermodynamic variables. 

These relationships may be used to obtain cone flow results from the flat-plate results of the section on uniform free-stream conditions. Real-gas solutions for air obtained in this manner are given in Ref. 17. 

The steady two-dimensional diabatic flow is described by the equations for mass, momentum and energy in conservation form (Schnerr and Dohrmann [7], Dohrmann [8]). Real gas effects are not yet included and inviscid fluids are assumed. Here the classical nucleation theory of Volmer [9] is used which gives a good qualitative representation of the behavior of condensing in the supersaturated state (Wegener [iO]). Oswatitsch [11] introduced this theory into the calculation of flow processes, a summary of all basic relationships for compressible flows with heat addition is given by Zierep [12]. To compute the nucleation rate J per unit time and volume, we take... 

Fugacity is used to replace the pressure of an ideal gas by a corrected pressure / of a real gas i, to produce a universally valid relationship. At zero pressure a real gas behaves like an ideal gas, and... 

In this chapter, I introduce you to gases at both the microscopic and macroscopic levels. I show you one of science s most successful theories — the Kinetic Molecular Theory of Gases. And 1 explain the macroscopic properties of gases and show you the important interrelationships among them. I also show you how these relationships come into play in reaction stoichiometry. This chapter is a real gas ... 

Equation of state (EOS) n. For an ideal gas, if the pressure and temperature are constant, the volume of of the gas depends on the mass, or amount of gas. Then, a single property called the gas density (ratio of mass/volume). If the mass and temperature are held constant, the product of pressure and volume are observed to be nearly constant for a real gas. The product of pressure and volume is exactly for an ideal gas. This relationship between pressure and volume is called Boyle s Law. Finally, if the mass and pressure are held constant, the volume is directly proportional to the temperature for an ideal gas. This relationship is called Charles and Gay-Lussac s law. The gas laws of Boyle and Charles and Gay-Lussac can be combined into a single equation of state PV = nRT, where P is pressure, V volume, Tabsolute temperature, n number of moles and R is the universal gas constant. Ane-rodynamicists us a different form of the equation of state that is specialized of air. Regarding polymers and monomers, equation of state is an equation giving the specific volume (v) of a polymer from the known temperature and pressure and, sometimes, from its morphological form. An early example is the modified Van der Waals form, successfully tested on amorphous and molten polymers. The equation is ... 

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