Gas, perfect

Since the molar volume of the liquid, V, is very small compared with that of the vapour, and if the vapour fi behaves as a perfect gas, then Equation (3.16) becomes... 

Here d/l is the additional wall area exposed when the uptake diminishes by dn moles through evaporation from the capillary p." is the chemical potential of the capillary condensate and p° that of the bulk liquid adsorptive. The negative sign is necessary because the area A exposed increases as the uptake diminishes. If the adsorptive vapour behaves as a perfect gas,... 

Equation (3.73) is the basis of the method proposed by Kiselev for the evaluation of surface area from the Type IV isotherm. If perfect gas behaviour is assumed it becomes... 

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). 

These equations are consistent with the isentropic relations for a perfect gas p/po = (p/po), T/To = p/poY. Equation (6-116) is valid for adiabatic flows with or without friction it does not require isentropic flow However, Eqs. (6-115) and (6-117) do require isentropic flow The exit Mach number Mi may not exceed unity. At Mi = 1, the flow is said to be choked, sonic, or critical. When the flow is choked, the pressure at the exit is greater than the pressure of the surroundings into which the gas flow discharges. The pressure drops from the exit pressure to the pressure of the surroundings in a series of shocks which are highly nonisentropic. Sonic flow conditions are denoted by sonic exit conditions are found by substituting Mi = Mf = 1 into Eqs. (6-115) to (6-118). 

The temperature obeys the adiabatic flow equation for a perfect gas. 

With flashes carried out along the appropriate thermodynamic paths, the formalism of Eqs. (6-139) through (6-143) applies to all homogeneous equihbrium compressible flows, including, for example, flashing flow, ideal gas flow, and nonideal gas flow. Equation (6-118), for example, is a special case of Eq. (6-141) where the quahty x = and the vapor phase is a perfect gas. 

The critical pressure ratio r can be obtained from the following theoretical equation, which assumes a perfect gas and a frictionless nozzle ... 

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. 

The turboexpander in combination with a compressor and a heat exchanger functions as a heat pump and is analyzed as follows In Fig. 29-44 consider the compressor and aftercooler as an isothermal compressor operating at To with an efficiency and assume the working fluid to be a perfect gas. Further, consider the removal of a quantity of heat by the tumoexpander at an average low temperature Ti-This requires that it dehver shaft work equal to Q. Now, make the reasonable assumption that one-tenth of the temperature drop in the expander is used for the temperature difference in the heat exchanger. If the expander efficiency is and this efficiency is mul-... 

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 ... 

With incompressibile fluids, the value of the acoustic speed tends toward infinity. For isentropic flow, the equation of state for a perfect gas can be written ... 

This equation can be rewritten for a thermally and calorifically perfect gas in terms of total pressure and temperature as follows ... 

Momentum equation for a caloricaly and thermally perfect gas, and one in which the radial and axial velocities do not contribute to the forces generated on the rotor the Adiabatic Energy (ifad) per unit mass is given as follows (Euler Turbine Equation) ... 

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. 

The specific gravity, SG, is the ratio of the density of a given gas to the density of dry air at the same temperature and pressure. It can be calculated from the ratio of molecular weights if the given gas is a perfect gas. 

It has played a dual role, one in Equation 2.18 on specific heat ratio and the other as an isentropic exponent in Equation 2.53. In the previous calculation of the speed of sound. Equation 2.32, the k assumes the singular specific heat ratio value, such as at compressor suction conditions. When a non-perfect gas is being compressed from point 1 to point 2, as in the head Equation 2.66, k at 2 will not necessarily be the same as k at 1. Fortunately, in many practical conditions, the k doesn t change very... 

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. 

Nomenclature axial, 226 centrifugal, 192 Non-perfect gas. t i Nozzle velocity, id Nozzles, axial compicssnr, fitting prchlciiis, 2-i"... 

Partial pressure, 18 Particle size, 484 Perfect gas equation, 15, 32 Performance curve, 3 axial, 232... 

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. 

The volumetric flowrate depends on the temperature and changes as the temperature changes. Assuming a perfect gas behavior. 

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... 

Absolute zero The temperature at which a perfect gas kept at constant volume exerts no pressure it is equal to -273.16 °C (0 K). 

The initial analysis [5] is presented by reference to closed a/s cycles using a perfect gas as a working fluid in an externally heated plant. As for the uncooled cycles. studied in Chapter 3, it is argued subsequently that many of the conclusions reached in this way... 

A useful rule of thumb is that the turbine work in a STIC plant is increased by a factor of about (1 + 25), since the specific heat of the steam is about double that of the specific heat of the dry gas. This is in agreement with the example given above and with the earlier detailed calculations by Fraize and Kinney [3]. (Their work was based on the assumption that the mixture of air and steam in the turbine behaved as a semi-perfect gas, with specific heats being determined simply by mass averaging of the values for the two components.)... 

The rea.son for this choice of low pressure ratio is illustrated by an approximate analysis [12], which extends the graphical method of calculating gas turbine pierformance described in Chapter 3. If the gas turbine higher plant is assumed to ojjerate on an air standard cycle (i.e. the working fluid is a perfect gas with a constant ratio of specific heats, y), then the compressor work, the turbine work, the net work output and the heat supplied may be written as... 

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