Gases, properties

Partition functions based on quantum mechanics can provide a more complete description of the ideal gas than our simple lattice model could. In this section, we compute the properties of ideal gases. 

We derived the ideal gas law from a lattice model in Example 7.1. Now w e derive the gas law from quantum mechanics instead. Equation (11.35) shows that the partition function for a gas is a product of volume V and a volume-independent factor we ll call qi. Substituting q = qiV into Equation (11.46) gives F = -NkTlnV-NkTln eqi/N). Taking the derivatWe that defines pressure in Equation (8.12) gives the ideal gas law, 

206 Chapter ii. The Statistical Mechanics of Simple Gases Solids 

Atomic energy states used to obtain the electronic partition functions 

Atom Electron Configuration Term Symbol Degeneracy g = 2J+ Energy (eV) 

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Calculation of thermophysical properties of gases relies on the principle of corresponding states. Viscosity and conductivity are expressed as the sum of the ideal gas property and a function of the reduced density ... 

This technique for finding a weighted average is used for ideal gas properties and quantum mechanical systems with quantized energy levels. It is not a convenient way to design computer simulations for real gas or condensed-phase... 

The common physical properties of acetyl chloride ate given in Table 1. The vapor pressure has been measured (2,7), but the experimental difficulties ate considerable. An equation has been worked out to represent the heat capacity (8), and the thermodynamic ideal gas properties have been conveniently organized (9). 

This equation indicates that, for small particles, viscosity is the dorninant gas property and that for large particles density is more important. Both equations neglect interparticle forces. 

In order to calculate the distribution function must be obtained in terms of local gas properties, electric and magnetic fields, etc, by direct solution of the Boltzmann equation. One such Boltzmann equation exists for each species in the gas, resulting in the need to solve many Boltzmann equations with as many unknowns. This is not possible in practice. Instead, a number of expressions are derived, using different simplifying assumptions and with varying degrees of vaUdity. A more complete discussion can be found in Reference 34. 

Ideal gas properties and other useful thermal properties of propylene are reported iu Table 2. Experimental solubiUty data may be found iu References 18 and 19. Extensive data on propylene solubiUty iu water are available (20). Vapor—Hquid—equiUbrium (VLE) data for propylene are given iu References 21—35 and correlations of VLE data are discussed iu References 36—42. Henry s law constants are given iu References 43—46. Equations for the transport properties of propylene are given iu Table 3. 

T. E. Taubert and R. P. Daimer, Thjsical and Thermocfynamic Properties of Pure Chemicals, Suppl /, CIO2 Gas Property Section, Hemisphere Publishing Corp., Bristol, Pa., 1991. 

Numerous other methods have been used to predict properties of gases and Hquids. These include group contribution, reference substance, approaches, and many others. However, corresponding states theory has been one of the most thoroughly investigated methods and has become an important basis for the development of correlation and property estimation techniques. The methods derived from the corresponding states theory for Hquid and gas property estimation have proved invaluable for work such as process and equipment design. 

A substance is in the ideal gas state when the volume of its molecules is a zero fraction of the total volume taken up by the substance and when the individual molecules are far enough apart from each other so that there is no interaction between them. Although this only occurs at infinite volume and zero pressure, in practice, ideal gas properties can be used for gases up to a pressure of two atmospheres with little loss of accuracy. Thermal properties of ideal gas mixtures may be obtained by mole-fraction averaging the pure component values. 

Residua] Properties These quantities compare true and ideal gas properties through differences ... 

Additional sources are the Journal of Applied Optics and the Journal of the Optical Society of America, particularly for surface properties the Jour nal of Quantitative Spectroscopy and Radiative Transfer for gas properties the Jour -nal of Heat Tr ansfer andthe Inter national Journal of Heat and Mass Tr ansfer lor broad coverage and the Jour nal of the Institute of Ener gy for applications to industrial furnaces. 

Furthermore, appreeiahle differenees ean arise from simply using different sourees of data on gas properties. There are very few ealeu-lated power requirements for a easeade proeess under praetieal operating eonditions that have been published and, therefore, available for a direet eomparison between the two proeesses. Additionally, published figures on the aetual power requirements for many easeades are aetually for natural gas, whereas the ealeulated figures are based on the liquefaetion of pure methane. 

Because of safety concerns, all combustible and/or toxic gases must be used in outdoor test loops or in a special indoor test building with the required safety monitoring equipment. The gas cost factor makes the problem even more difficult. The problem of known gas properties adds another complication. Despite all the negative aspects just mentioned, most performance tests are closed-loop tested. 

Whilst they will differ depending upon gas properties, the procedures and precautions appropriate for transport of cylinder gases are exemplified for LPG in Table 15.16. 

In velocity and gas property effects, the Reynolds number, Re, is taken into consideration as... 

In Section 3.4, we consider the open gas turbine cycle in which fuel is supplied in a combustion chamber and the working fiuids before and after combustion are assumed to be separate semi-perfect gases, each with Cp(T), c (T), but with R = [Cp T) — Cv( )l constant. Some analytical work is presented, but recently the major emphasis has been on computer solutions using gas property tables results of such computations are presented in Section 3.5. 

Essentially, the analytical approach outlined above for the open circuit gas turbine plants is that used in modem computer codes. However, gas properties, taken from tables such as those of Keenan and Kaye [6], may be stored as data and then used directly in a cycle calculation. Enthalpy changes are then determined directly, rather than by mean specific heats over temperature ranges (and the estimation of n and n ), as outlined above. 

The discussion of the performance of gas turbine plants given in this chapter has developed through four steps reversible a/s cycle analysis irreversible a/s cycle analysis open circuit gas turbine plant analysis with approximations to real gas effects and open circuit gas turbine plant computations with real gas properties. The important conclusions are as follows ... 

In the simplified a/s analysis of Section 4.2 we assumed identical and constant specific heats for the two streams. Now we assume semi-perfect gases with specific heats as functions of temperature but we must also allow for the difference in gas properties between the cooling air and the mainstream gas (combustion products). Between entry states (mainstream gas 3g, and cooling air, 2c) and exit state 5m (mixed out), the steady flow energy equation, for the flow through control surfaces (A + B) and C, yields, for a stationary blade row,... 

The choice of these values is arbitrary. In practice, the cooling fraction will depend not only on the combustion temperature but also on the compressor delivery temperature (i.e. the pressure ratio), the allowable metal temperature and other factors, as described in Chapter 5. But with ip assumed for the first nozzle guide vane row, together with the extra total pressure loss involved (k = 0.07 in Eq. (4.48)), the rotor inlet temperature may be determined. These assumptions were used as input to the code developed by Young [11] for cycle calculations, which considers the real gas properties. 

Typically, in specifying a unit, the suction and discharge pressures, capacity (MMsefd), inlet temperature, and gas properties are given. The actual sizing of the cylinders is left to the manufacturer from his specific combinations of standard cylinders, pistons, and liners. However, once a proposal is received from a manufacturer, sometimes it is beneficial to check the cylinder sizing and make sure that indeed the compressor will perform. Sometimes it is necessary to size a new cylinder for an existing compressor or to verify that an existing compressor will perform in a different service. 

The capacity of the cylinder is a function of piston displacement and volumetric efficiency. This is in turn a function of cylinder clearance, compression ratio, and gas properties. 

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