Perfect-gas equation

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

Where W is weight and Rj is a specific constant for the gas involved. This is the perfect gas equation. Going one step further, by making W, in pounds, equal to the molecular weight of the gas (one mole), the formula becomes ... 

The perfect-gas equation of state for multicomponent mixtures depends on the species composition. Representing the composition as either mass fraction Yk or mole fraction Xk leads to... 

Finally, the perfect-gas equation of state in the nondimensional variables is... 

Assume that the flow enters the tube with a certain mass flow rate m = pU, Ac, a pressure pi, and a composition 5/. Assume isothermal flow and a perfect-gas equation of state. Based on a summary of the governing differential equations, discuss the mathematical characteristics, including a suitable set of boundary conditions for their solution. 

The system of equations becomes complete with a perfect-gas equation of state that provides the mass density, given the mean pressure, the local temperature, and the local i... 

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. 

Develop a system of equations to describe the flow and temperature field in the annular space between the two cylinders. Assume a perfect-gas equation of state. To achieve a tubular flow in the similar form, discuss the approximations that must be made and the limitations of the assumptions. 

The columns of cells below row 16 contain the values of the dependent variables at the node points. They will all be iterated until a final solution is achieved. The formula in each cell represents an appropriate form of the difference equations. Each column represents an equation. Column B represents the continuity equation, column C represents the radial momentum equation, column D represents the circumferential momentum equation, and column E represents the thermal energy equation. Column F represents the perfect-gas equation of state, from which the nondimensional density is evaluated. The difference equations involve interactions within a column and between columns. Within a column the finite-difference formulas involve the relationships with nearest-neighbor cells. For example, the temperature in some cell j depends on the temperatures in cells j — 1 and j + 1, that is, the cells one row above and one row below the target cell. Also, because the system is coupled, there is interaction with other columns. For example, the density, column F, appears in all other equations. The axial velocity, column B, also appears in all other equations. 

This equation relates the state variables of the system. This equation is called the ideal gas equation or perfect gas equation. A gas, which obeys this relationship over a range of states of interest, is said to behave ideally in the range. A gas, which obeys this relationship in all possible states, is called an ideal gas or a perfect gas. 

There are a number of equations of state for gases which attempt to account for the deviations found from the ideal (perfect) gas equation (4.1). These have the following features ... 

A similar example is the introduction of the universal gas constant, R, which ensures that in the perfect gas equation of state p V = n R T the already fixed secondary... 

In every case yet worked out, the adsorbed films of soluble substances are of the gaseous type there are always corrections, except in very dilute solutions, to the perfect gas equation due to the area actually occupied by the adsorbed molecules and in many cases also there are corrections due to the lateral adhesion between them. 

The proportionality of surface tension lowering to the concentration thus indicates that the adsorbed film is gaseous, with negligible corrections to the perfect gas equation. 

Equation 1-14 expresses the equality of AG with the surface excess free energy, oA7. If, as is customary, the film pressure, ir, is used for —Ay, and the vapor can be considered to be a perfect gas, Equation 7 can be rewritten in its more familiar form... 

In the following sections of this chapter these three laws are formulated and applied in the solution of some problems. It is also shown that they can be combined into a single equation, which is called the perfect-gas equation. 

If the number of moles in a sample of gas, n, remains constant and the temperature T remains constant, the perfect-gas equation simplifies to... 

The volume occupied by one mole of gas at standard conditions is seen from the perfect-gas equation to be just the product of R and the temperature 0° C on the absolute scale. The value of R can hence be found by dividing 22.4 by 273 ... 

Some of the ways in which the perfect-gas equation can be used in the solution of chemical problems are discussed in the following paragraphs. 

Real gases differ in their behavior from that represented by the perfect gas equation for two reasons. First, the molecules have finite size, so that each molecule prevents others from making use of a part of the volume ot the gas container. This causes the volume of a gas to be larger than that calculated for ideal behavior. Second, the molecules even when some distance apart do not move independently of one another, but attract one another slightly. This tends to cause the volume of a gas to be smaller than the calculated volume. 

It is striking that the equation is identical in form with the perfect-gas equation van t Hoff emphasized the similarity of a dissolved substance and a gas. 

It is important to stress that there is a fundamental difference between the van t Hoff formula and the perfect gas equation... 

The mostly measurable input data on the density po(T) at ambient pressure have been used below to develop the predictable model. For the vapor pressure at low temperatures it is proposed to use the perfect-gas equation ... 

That is, the osmotic pressure obeys the generalised gas law, which includes Boyle s Law, Gay-Lussac s, and the Avogadro Hypothesis It will be observed that the R is numerically identical with the R of the perfect gas equation That is, the osmotic pressure of a dilute solution is related to the molecular volume, or the inverse of this the molecular concentration quantitatively as the pressure of a perfect gas is related to the volume For substances in dilute solution R = i 985 calones per gram-mole It may be noted that in the particular case in which V - v the osmotic pressure is identical with the gas pressure... 

The state of a perfect gas can be defined by specifying P, V, and T. As PV = nRT for a fixed mass of gas we need specify only two of P, V, and T since this will be sufficient to fix the remaining variable. Indeed such is the case for any pure substance (or mixture of fixed composition) even though it may not follow the perfect gas equation. We may write T f(P, V). Such an equation which links P, Ff and T is called an equation of state. 

---