Properties of a Perfect Gas

In several derivations in the text, we use the properties of a perfect gas. All these properties are derived here. 

A perfect gas is one whose pressure, density, and absolute temperature are related by 

Here R is the universal gas constant, whose values in various units are shown in App. A. 9. The density in this equation is the mass density, or mass/volume. If we wish the molar density, moles/volume, we simply drop the M from Eq. D.l and from all the equations in this appendix. There is rarely any question whether the mass density or molar density is being used in any of the equations in this book. 

It is shown in any standard text on thermodynamics that for a perfect gas the enthalpy per unit mass h and the internal energy per unit mass u are functions of temperature alone they do not depend on pressure. (The same is 

---

The thermodynamic properties of a perfect gas are. of course, especially simple. For example, the difference between the molar heal capacities at constant pressure and constant volume is equal to the gas constant R,... 

It can be shown that this relation is also true if the temperature scale is based on the properties of a perfect gas.) From equations (5) and (6) ... 

An examination of the equations shows that two of the variables are independent. The system is therefore divariant, in agreement with the result of applying the phase rule. If the system had not been assumed to have the properties of a perfect gas and of an ideal solution, the equations would have taken a rather more complicated form, but the same conclusion would have been reached. 

Fig.F.9 The model used for discussing the molecular basis of the physical properties of a perfect gas. The pointUke molecules move randomly with a wide range of speeds and in random directions, both of which change when they collide with the walls or with other molecules.

The transport properties, particularly viscosity and diffusion, of a perfect gas are discussed and the concepts of gas dynamics are briefly mentioned. Such methods can be applied to flowing gas in, for example, pipework or nozzles and jets. 

Physical Properties.—Density.—The density corresponds to simple molecules, PHS, but deviations from the laws of a perfect gas are observed. The weight of a normal litre is 1-5293 to 1-5295 gram,5 a value which shows that under these conditions it agrees closely with Avogadro s theory. At pressures of 10 atmospheres or more, however, and at temperatures from 24-6° to 54-4° C. the compressibility is much greater than is allowed by Boyle s law. The following values refer to 24-6° C. —6... 

We have already calculated, in Section 3.5, the changes in thermodynamic properties accompanying the isothermal expansion of a perfect gas. As... 

When a mass of any substance is subject to some physical change, certain properties—mass, chemical composition—remain fixed and invariable, while other properties—temperature, pressure, volume—vary. When the value these variables assume in any given condition of the substance is known, we are said to have a complete knowledge of the state of the system. These variable properties are not necessarily independent of one another. We have just seen, for instance, that if two of the three variables defining the state of a perfect gas are known, the third variable, can be determined from the equation pv = BTt... 

The speed of sound of a perfect gas, as shown above, is a function of the temperature and not of the velocity. Keep in mind that the speed of sound is a property of the matter, not a property of the flow. If the temperature changes as the fluid flows, then the speed of sound will change from point to point but at any point it is the same in a flowing gas as it would be in the same gas standing still at the same temperature. This argument applies equally well to solids and to liquids. Observe also that the magnitudes are c = 3 mi/s for steel, 1 mi/s for water, jand mi/s for air. 

Thermodynamic parameters, excluding the highly precise parameters, of a chromatographic process may be determined if helium, whose properties are those of a perfect gas, is employed as the carrier gas. 

The use of thermodynamics is well accepted and indeed essential in those areas of particle technology which involve heat and/or flow of gases. Properties of a dust-laden gas, for example, deviate from those of a perfect gas as a consequence of the finite particle volume. Internal energy, enthalpy and specific heats of a particulate system, needed in applications involving heat, are the suitably weighted means of the respective properties of the constituents (except that enthalpy of the particulate phase suspended in a gas also depends on the pressure). Another example is the effect of the presence of particles on both the equilibrium and frozen velocities of sound in a gas. 

We note first that, for a homogeneous fluid, the compressibility and its reciprocal are given in terms of the total and direct correlation function by (4.22) and (4.27). An integration over p gives us the pressure since the known properties of the perfect gas at p = 0 supply the boundary conditions. Hie integration requires, however, that we know h(ri2) and c(ri2) as functions of density and so this is not a route to the pressure that we shall find useful in discussing the gas-liquid surface. 

We have seen that a feature of a perfect gas is that for any isothermal expansion the total energy of the sample remains the same and that q = -w. That is, any energy lost as work is restored by an influx of energy as heat. We can express this property in terms of the internal energy, for it implies that the internal energy remains constant when a perfect gas expands isothermally from eqn 1.6 we can write... 

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. 

For the purpose of understanding pressure filtering, attention may be restricted to the single-component, constant-property, nonreacting equations for a perfect gas. Introducing the nondimensional variables into the vector forms of the mass-continuity, constant-viscosity Navier-Stokes, and perfect-gas thermal-energy equations yields the following nondimensional system ... 

Assume that all species are highly dilute in ammonia. For the purpose of this problem, consider the following transport properties as constants n = 2.7 x 10-4 g/cm-s, k = 1.1 x 104 erg/cni S-K, and Dtmg-nh3 = 3 cm2/s. The specific heat for ammonia may be taken as cp = 2600 J/kg-K. Assume that the density may be determined from a perfect-gas equation of state for ammonia alone. 

For a perfect gas the mass-averaged mean properties of the mixture are given as... 

Uranium hexafluoride is probably the most interesting of the uranium fluorides. Under ordinary conditions, it is a dense, white solid with a vapor pressure of about 120 hull ai room temperature. It can readily be sublimed or distilled, and it is by far the most volatile uranium compound known. Despite its high molecular weight, gaseous UFg is almost a perfect gas, and many of the properties of the vapor can be predicted from kinetic theory. 

The properties of the two phases, the properties of the chemical, and the temperature, control the partitioning process. For trace concentrations of chemicals in the ambient atmosphere, the air compartment can be treated as a perfect gas. Methods to predict KPA thus must consider three factors the properties of the plant, the properties of the chemical, and temperature. The temperature dependence of KPA is a function of the chemical and the plant the influence of chemical properties on KPA is a function of temperature and the plant. Understanding and describing these interdependencies quantitatively is a considerable challenge which has been addressed only recently although much progress has been made, much remains to be done. 

So many of the properties of matter, especially when in the gaseous form, can be deduced from the hypothesis that their minute parts are in rapid motion, the velocity increasing with the temperature, that the precise nature of this motion becomes a subject of rational curiosity. Daniel Bernoulli, Herapath, Joule, Kronig, Clausius, etc. have shewn that the relations between pressure, temperature, and density in a perfect gas can be explained by supposing the particles to move with uniform velocity in... 

But if, in these various cases, we can put beyond doubt the existence of the same gas in two distinct polymeric forms, we are indebted to the phenomena of false equilibrium in the conditions of temperature and pressure for which the states of false equilibrium would not be produced, oxygen, taken in definite conditions, would always enclose a determined amount of ozone at a given pressure and temperature its properties would.be perfectly determined but its density taken with respect to a perfect gas would vary with the pressure and with the temperature oxygen would behave, in terms of the variation of density produced by a rise in temperature, just as do sulphur vapor, iodine vapor, acetic acid vapor one may not, therefore, argue from this fact that at a given pressure and temperature each of these gases exists in a perfectly determined state in order to deny, for each of them, the coexistence of two polymers one may nierely conclude there are not produced phenomena of false equilibrium in the conditions of temperature and pressure for which the experiments have been performed. 

---