thermod chapter3 ideal gas

8/3/2019 ThermoD Chapter3 Ideal Gas

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Energy revisited ,

forms of energy:

associated with the forces between themolecules.

Molecular Kinetic energy: It is

of individual molecules.

Intramolecular energy: It is associated with molecular and atomic structure and

2

related force


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Low Density Gas t very ow ens t es, t e

average distances betweenmo ecu es are very arge an

intermolecular potential energycan e neg ecte .

In such cases, particles are-

is referred to as anIdeal Gas.

Ideal Gas Equation of StateIdeal Gas Equation of State

Thesimplestandbestknownequation istheIdealgasEquationofState.


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The universal gas constantThe universal gas constant

RMR

KkmolkJ /.31458

Rlbmollbt /1545

M = Molecular weight, kg/M = Molecular weight, kg/kmolkmol

Ideal Gas Equation of StateIdeal Gas Equation of State

==

The as that obe s this relation iscalled an Ideal Gas.

different constant for each

.

The value for R for a number ofsu s ance s g ven n a e .


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Ideal Gas Equation of StateIdeal Gas Equation of State,

equation is used in thermodynamiccalculations, wherever possible.

It is applicable to actual gases at lowdensit .

At low pressure and high temperature, theens y o gas ecreases an gas e aves

as an ideal gas under these conditions

Non-Ideal or Real GasLow Temperature

g ressure

compared to space between

par c es

significant


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Deviations from the Ideal Behavior

Vapor at saturated state deviates

behavior.

At hi her ressures, articularlin the vicinity of CP andsaturated va our lineunacceptable error (over 100%).

Deviations from the Ideal Behavior

s e s a e o e su s ance sfurther removed from the

,behavior comes closer to ideal gas.

pressure ower an a,water vapour may be assumed as

. .

So, high T and low P favor idealgas e av or.


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The Compressibility Factor (Z)

The concept of Compressibility

assessment of the deviation from.

It is a measure of deviation fromideal gas behavior.

It i fin a Pv

RT

or ea gas, = 1.

The deviation of Z from unityis a measure of deviation from

ea gas e av or.


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Compressibility Chart for NitrogenCompressibility Chart for Nitrogen

Observations from the

om ressi ilit hartAt all temperatures, as P0, Z 1At temperatures of300 K and above

(the room temp) the Z1 uptoressure o 10 a => ea gas

equation of state can be used for N2

considerable accuracy.

At lower temperatures or at very highpressures, Z deviates significantlyfrom the ideal gas value (Z = 1).


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Compressibility Chart

other pure substances, we find diagramsare similar in characteristic as N2.

The compressibility diagrams for all puresubstances are ualitativel similar

Quantitatively they are different, sincet ey ave w e y er ng r t ca o nts.

Substance TC,OC PC, MPa

Water 374.14 22.09CO2 31.05 7.39

O2 -118.35 5.08

General Compressibility Chart

Is there any way in which we can putall these substances on a commonbasis?

We can put all the pure substances

reduced properties.


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General Compressibility Chart

Reduced pressure, Pr = P/Pc

Reduced temperature, Tr = T/Tc

Reduced ro ert for a ivenstate is the value of this property in

of this same propertyat the criticalpoint.

General Compressibility ChartGeneral Compressibility Chart

In fact, when such Z versus Prdiagrams (general compressibilitydiagrams) are plotted for differentsubstances, they all nearly coincide.

The Z factor for all gases is

Reduced Pressure and Temperature.


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If the lines of constant T are plottedon Z versus Pr diagram, we obtain a

GeneralizedGeneralized Com ressibilitCom ressibilit ChartChart.

.


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Simple Fluid Compressibility Chart

ome o serva ons are ma e rom genera zecompressibility chart.

At Pr 2, the gases can be assumedas an ideal gas to a Pr as high as 4 or 5.

The deviation of gas from ideal-gas behavior isgreatest in the vicinity of Critical Point.


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InterpolationMakesureyou2 0.3424

samegrouping

.7

3 1.7334

theequation

Alwaysputassociateddataentriesdirectlyaboveeachother

3424.0???3424.07334.1

.


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DoubleInterpolation tofinddependson2variables.

P = 1.0 P = 1.5 P = 2.0

10 56 51 48

20 65 62 59

40 76 71 65Find v at P = 1.75 and T = 25

P=1.75

T P = 1.0 P = 1.5 P = 2.0

10 56 51 48

20 65 62 59

T=25


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we can still deal with this via linear

inter olation .... but we have to do it 3 times!

= . = .20 62 59

25 ?1? ?2?

,

newinterpolated

entries

for

vat = an = . an =

Thenyouusethesetwonewknown

=

1.75 . . .20 62 59

25 63 ?3? 60

?3? = 61.5

thermod chapter3 ideal gas

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