Perfect gas law, 2.3,15.4

The deviation from the perfect gas law is not great at ordinary pressures and temperatures. At the highest pressure normally encountered commercially, 41 MPa (6000 psig), the compressibiUty factor of nitrogen is 1.3629 at 25°C (12). 

The gas usually deviates considerably from the perfect-gas laws, and in many cases temperature or other limitations necessitate a thor-... 

Compressibility of Natural Gas All gases deviate from the perfect gas law at some combinations of temperature and pressure, the extent depending on the gas. This behavior is described by a dimensionless compressibility factor Z that corrects the perfect gas law for real-gas behavior, FV = ZRT. Any consistent units may be used. Z is unity for an ideal gas, but for a real gas, Z has values ranging from less than 1 to greater than 1, depending on temperature and pressure. The compressibihty faclor is described further in Secs. 2 and 4 of this handbook. 

Ideal gas obeys the equation of state PV = MRT or P/p = MRT, where P denotes the pressure, V the volume, p the density, M the mass, T the temperature of the gas, and R the gas constant per unit mass independent of pressure and temperature. In most cases the ideal gas laws are sufficient to describe the flow within 5% of actual conditions. When the perfect gas laws do not apply, the gas compressibility factor Z can be introduced ... 

Charles and Gay-Lussac, working independently, found that gas pressure varied with the absolute temperature. If the volume was maintained constant, the pressure would vary in proportion to the absolute temperature [I j. Using a proportionality constant R, the relationships can be combined to form the equation of state for a perfect gas, otherwi.se known as the perfect gas law. 

A term may now be added to Equation 2.1 to correct it for deviations from the ideal gas or perfect gas law. 

Classes II and III include all tests in which the specified gas and/or the specified operating conditions cannot be met. Class II and Class III basically differ only in method of analysis of data and computation of results. The Class II test may use perfect gas laws in the calculation, while Class III must use the more complex real gas equations. An example of a Class II test might be a suction throttled air compressor. An example of a Class III test might be a CO2 loop test of a hydrocarbon compressor. Table 10-4 shows code allowable departure from specified design parameters for Class II and Class III tests. 

The use of a gas mixture presents a two-part problem. If the state of the mixture is such that it may be considered a mixture of perfect gases, classical thermodynamic methods can be applied to determine the state of each gas constituent. If, however, the state of the mixture is such that the mixture and constituents deviate from the perfect gas laws, other methods must be used that recognize this deviation. In any case, it is important that accurate thermodynamic data for the gases are used. 

About 1902, J. W. Gibbs (1839-1903) introduced statistical mechanics with which he demonstrated how average values of the properties of a system could be predicted from an analysis of the most probable values of these properties found from a large number of identical systems (called an ensemble). Again, in the statistical mechanical interpretation of thermodynamics, the key parameter is identified with a temperature, which can be directly linked to the thermodynamic temperature, with the temperature of Maxwell s distribution, and with the perfect gas law. 

It is convenient to calculate a TNT equivalent of a physical explosion to use the military results of Figures 9.1-4 and 5. Baker et al. (1983) give a recipe for the rupture of a gas filled container assuming expansion occurs isothermally and the perfect gas laws apply (equation 9.1-25), where W is... 

Figures 2-38A and 2-38B are based on the perfect gas laws and for sonic conditions at the outlet end of a pipe. For gases/vapors that deviate from these laws, such as steam, the same application will yield about 5% greater flow rate. For improved accuracy, use the charts in Figures 2-38A and 2-38B to determine the dowmstream pressure when sonic velocity occurs. Then use the fluid properties at this condition of pressure and temperature in ...

Based on air and perfect gas laws, vessel uninsulated, and vessel will not reach rupture conditions. Review for specific design. situations [33a]... 

Yo = initial concentration of component (oxidant) under low pressure, mol fraction Z = compressibility factor, deviation of actual gas from perfect gas law. Usually Z = 1.0 at low pressure below 300 psig. 

Compressibility is expressed as the multiplier for the perfect gas law to account for deviation from the ideal. At a given set of conditions of temperature and pressure ... 

The ideal gas law or perfect gas law is a combination of Boyle s and Charles laws for any compressible fluid (gas/vapor). 

Equations of state (e.g., perfect gas laws, Van der Waals equation, etc.). 

Ideal (or perfect) gas behavior is approached by most vapors and gases in the limit of low pressures and elevated temperatures. Two special forms of restricted utility known as the Boyle s law and the Charles law preceded the development of the perfect gas law. 

A combination of the above two statements results in the equation of state termed the ideal (or perfect) gas law ... 

The mole is particularly useful when working with gas mixtures. It is based on Avogdro s law that equal volumes of gases at given pressure and temperature (pT) conditions contain equal number of molecules. Since this is so, then the weight of these equal volumes will be proportional to their molecular weights. The volume of one mole at any desired condition can be found by the use of the perfect gas law. 

Volatility is the weight of vapor present in a unit volume of air, under equilibrium conditions, at a specified temperature. It is a measure of how much material (agent) evaporates under given conditions. The volatility depends on vapor pressure. It varies directly with temperature. We express volatility as milligrams of vapor per cubic meter (mg/m3). Calculate it numerically by an equation derived from the perfect gas law. This equation follows ... 

The vapor density pc was expressed in terms of pG and T0 through the perfect gas law ... 

The role of approximate mechanisms in organic chemistry is somewhat like that of the perfect gas laws in physical chemistry. The fact that an approximate mechanism has some value does not of course mean that precise mechanisms are not still better. 

For methane at 25 °C or 298 K, cp = 2.24 J/gK. Note that on substituting for the temperatures in this steady state example it makes no difference whether K or °C units are used. This follows from the conservation of mass. However, for unsteady applications of Equation (3.40), since we have used the perfect gas law in which T is in K, we should be consistent and use it through the equations. When in doubt, use K without error. Substituting ... 

The conditions that apply for the saturated liquid-vapor states can be illustrated with a typical p-v, or (1 /p), diagram for the liquid-vapor phase of a pure substance, as shown in Figure 6.5. The saturated liquid states and vapor states are given by the locus of the f and g curves respectively, with the critical point at the peak. A line of constant temperature T is sketched, and shows that the saturation temperature is a function of pressure only, Tsm (p) or psat(T). In the vapor regime, at near normal atmospheric pressures the perfect gas laws can be used as an acceptable approximation, pv = (R/M)T, where R/M is the specific gas constant for the gas of molecular weight M. Furthermore, for a mixture of perfect gases in equilibrium with the liquid fuel, the following holds for the partial pressure of the fuel vapor in the mixture ... 

By assuming that a perfect gas law applies for the vapor, including the saturation state, it can be seen that... 

The introduction of the perfect gas law to the Clausius-Clapeyron equation (Equation (6.14)) allows us to obtain a more direct approximation to p p(T) in the saturation region. We use the following ... 

Purely phenomenological as well as physically based equations of state are used to represent real gases. The deviation from perfect gas behaviour is often small, and the perfect gas law is a natural choice for the first term in a serial expression of the properties of real gases. The most common representation is the virial equation of state ... 

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