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Compressibility factor- a measure of deviation from ideal gas behavior

Gases deviates from ideal gas behavior significantly at states near the saturation region and the critical point.

This deviation from ideal gas behavior at a given temperature and pressure can accurately be accounted for my

introducing of a correction factor called compressibility factor Z

Pv = ZRT

Z It can also be expressed as Z =

Z =1for ideal gas

Farther away Z is form unity, the more the gas deviates from ideal gas behavior

= =

reduced pressure, reduced temperature,

critical pressure, critical temperature,

The Z factor all gases approximately the same at the same reduced pressure and temperature. This is called the

principle of corresponding states. The gases seem to obey the principle of corresponding states reasonably well. By

curve-fitting all the data, we obtain generalized compressibility chart that can be used for all gases.

At very low pressures all the gases approach ideal gas behavior (regardless of their temperature)

Observations from the compressibility chart:

1. At very low pressures ( ) the gas behave as an ideal gas regardless of temperature.2. At high temperatures ( ) ideal- gas behavior can be assumed with good accuracy regardless of pressure

(except when 1)3. The deviation of a gas from ideal gas behavior is greatest in the vicinity of the critical point.

Pseudo- reduced specific volume,

=

is defined differently from and . It is related to and instead of . Lines of constant are aisoadded to the compressibility charts and this enables one to determine T and P without having to resort to time

consuming iterations.

Other equation of state:

It is the desirable to have equations of state that represent the PVT behavior of substances accurately over

alarge region with no limitations. There are some equations namely.

[2 constant]vander waals berthelet redlich-kwang, [5 constant]Beattie-bridgemann, [8 constant] Benedict-webb-

rubin, [16 constant] Strobridge, [depend on no of terms] Virial. several equations of state been proposed throughout

history

Vander waals equation of state:

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This is one of the earliest equation proposed in 1873,and it has two constants that are determined from the

behavior of a substance at the critical point.

Vander waals included two effects that are not considered in the ideal gas equation of state. The inter

molecular attractoion forces and the volume occupied by the molecules themselves.

Inter molecular forces.

baccounts for the volume occupied by gas molecules.

Theconstants a and b can be determined for any substance from the critical point data alone.

a

& b=

Properties of mixtures of gases-Daltons law of partial pressure:

Let us imagine a homogenious mixture of inert gases at a temperatures T,a pressure P and a volume V. Let

us suppose there are molecules of gas, and moles of gasand up to moles of gas. Since there isno chemical reaction.the mixture is in a state of equilibrium with the equation of state.

Pv = RTWhere =8.3143 KJ/kg mol k

P=

The expression

represents the pressure that the gas would exert if it occupied the volume V alone at

temperature T. this is called the partial pressure of the gas and is denoted by .Thus

=

, =

=

Now P =

Also v = (

v =

The partial pressure of gas is

Substitute the value of V in (1)

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Total no of moles in s gas

Thus for each gas from (1-m)

From equation

In a mixture of gases, if all but one mole fraction is determined, the last can be calculated from the above equation

(A)

In the terms of mass

Using Doltons low

PV = (

Where P =

Assume is the gas constant of the mixture then

Pv =

Total mass of gas mixture is

If denotes the equivalent molecular weight of the mixture having n total number of moles.

n

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A quantity called the partial volume of a component of a mixture is the volume that the component alone would

occupy at the pressure & temperature of the mixture.

Here V = The total volume (V) is the sum of the partial volumes (

The specific volume of the mixture, v is given by

v =

=

denote the specific volume occupied by each components.

v =

There fore the density of the mixture.

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