Thermo Chap II

7/28/2019 Thermo Chap II

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PURE SUBSTANCE

A pure substance is identified as a substance which has a

fixed chemical composition throughout its mass ie

Homogenous.

It can be a mixture of two or more substances as long as

the mixture is homogenous. For example Air

It can be of different physical appearance as long as the

chemical composition is same. For example

Water and Steam is a pure substance (H2O)

Oil and Steam is not a pure substance as they have

different chemical composition and do not mix to become

homogenous. On the other hand Salt and water could be

considered a pure substance if salt dissolves

homogenously in water.

Further the composition must not change with time eg

Mixture of Air and Fuel Vapor is Homogenous as long as

they do not react. Once reaction starts then the

composition changes and it is not a pure Substance

Now it may be possible that once Reaction is completedthen the products could form a homogenous mixture and

could be considered a pure substance.

It is important for us to identify the pure substance and

then analyse it.


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PHASES OF A PURE SUBSTANCE

We have seen in daily life that material as well as pure

substances can exist as Solids, Liquids and Gas. One

lid)example is H2O which can be found as

Ice( Solid) , Water(Liquid) and Gas ( Steam)

Furthermore a Pure Substance can have different

appearance in its Principal Phase:-

Carbon in its solid phase can exist as Graphite as well as

Diamond. They are made of the same molecules but their

molecular structure is different.

Iron has three solid phases

Ice has seven solid phases at High Pressures

Why do we have different phases?

The answer lies in their molecular structure and thebonding between the molecules.

Molecular Bonds are the strongest in Solids and are the

weakest in gases. When we heat a solid , it melts because

the molecular bonds are weakened by heat and the

substance becomes a liquid and on further heating

becomes a Gas.

Heat has a profound effect on change of phase, alongwith

pressure.

Lets look at the three phases in details.


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SOLIDS

The molecules in a solid are arranged in a fixed pattern,

and remain in these fixed positions by the strong inter-

molecular bonds.

So in solid phase Molecules oscillate about their fixed

positions.

These oscillations become faster as the temperature of

the substance rises. The effect of high temperature is to

weaken the molecular bonds , and the molecules break

away.

THIS IS WHAT IS KNOWN AS MELTING PROCESS

LIQUIDS

In liquids , the molecules are no longer in fixed positionsrelative to each other. Group of molecules float abouteach other , but the group of molecules maintain anorderly structure among themselves, and remain fixed intheir groups.Inter molecular distances are larger than those in solidsand bonds are also weaker compared to solids.GASES

Here the molecular distances are large , and there is no

fixed molecular pattern. Molecules are moving randomly,

and continuously collide with each other. Bonds are very

weak and molecules in the gaseous phase have high

energy levels.Thus we a Gas condenses or freezes, it

releases a large amount of Energy, mostly in the form of

heat.


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PHASE CHANGE

Now we are aware that pure substances have different

phases , and also two or three phases of a pure

substance can co-exist in equilibrium.

Water and ice can exist as two phases at a particular

Temperature and pressure

Water and Steam can also exist as two phases.

Now we also know that phase change can take place but

not all the time. It requires a specific condition.

Lets look into this in more detail by investigating the phase

change of water.

Lets take water at 1 atm and 20 oC, in a piston cylinder

arrangement. We heat the water at CONSTANT PRESSURE.

If we keep heating until the temperature is 100 oC , and if

we keep heating we find that the temperature reaches

100 oC , and further heat will cause vaporization.

A liquid about to vaporize is known as

SATURATED LIQUID.

1 Atm20 oC

As we heat the water we see that itstemperature rises, but it remains aliquid.

This state is known as

COMPRESSED LIQUID or

SUB COOLED LIQUID


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Now if we keep on heating the water starts boiling and

steam starts to form, but

THE TEMPERATURE DOES NOT RISE

Here both Liquid and Gas phase co-exist and their mixture

is known as SATURATED MIXTURE

Because of heat addition , all the water will vaporize into

steam.

HERE THE VAPOR IS SATURATED VAPOR

This is because if we remove heat , at point the vapor will

condense. Lets see this on a Temperature and specific

volume diagram:-

State 1-2 is compressed liquid

State 2-4 is saturated state, a mixture of Saturated Liquid

and Saturated Vapor

Once the liquid is completely vapor, ADDITION OF HEAT

WILL CAUSE TEMPERATURE OF VAPOR TO RISE

This is known as SUPERHEATED VAPOR

T

v

20 o

100 o

Compressed Liquid

Saturated Mixture

1

2 3

4

5

SuperHeated

Vapor

180 o


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So if we have steam at 1 atm and 180 oC, and if we

remove heat , the process will move in reverse direction,

but condensation will take place at 100 oC.

So we see that at a pressure of 1 atm between

20 100 oC Temp of water changes but it remains as

water. Phase does not change.

At 100 oC Temp. does not change. Phase Changes

100 180 oC Temp of vapor changes but it remains as

vapor. Phase does not change

SATURATION TEMPERATURE AND PRESSURE

We have seen that at 1 atm , the change of phase takes

place at 100oC.

If the pressure was not allowed to remain constant , then

the phase would be at a different temperature.THUS CHANGE OF PHASE OCCURS AT A FIXED

TEMPERATURE FOR A FIXED PRESSURE.

This combination of Pressure and Temperature is known

as Saturation Pressure and Saturation Temperature

For water we have

TSat inoC PSat in kPa T Sat in

oC PSat in kPa

-10 0.26 100 101.3

0 0.61 150 475.8

10 1.23 200 1554

30 4.25 300 8581

LATENT HEATS


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To change phase we need to either add Heat or remove

Heat. This energy is known as LATENT HEAT.

When we change from solid to liquid ( MELTING)

or change from liquid to solid ( FREEZING)

Then the heat required for melting of heat removed for

freezing is called as LATENT HEAT OF FUSION

When we change from liquid to gas ( VAPORIZATION)

or change from gas to liquid ( CONDENSATION)

Then the heat required for VAPORIZATION of heat

removed for condensation is called as LATENT HEAT OF

VAPORIZATION.

The Latent Heats have specific value for each

combination of Saturation Temperature and Pressure. We

will see how to evaluate these values at a later stage.

LIQUID VAPOR SATURATION CURVES


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We have seen that TSatand PSathave a fixed relationship

for each pure substance. ( )SAT SAT T f P= . So if we plot it

for a pure substance we get

Thus if Saturation pressure drops Saturation temperature

also reduces.

Thus at high altitudes Water boils at less than 100oC,

because of low pressures at high altitude

Sometimes one wants to cook at high temperature , so we

use pressure cookers. This allows Boiling temperature to

increase.

PSat

TSat

LIQUID-VAPOR SATURATION CURVE


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Property Diagrams

We can draw P-v-T diagrams of phase change by keeping

one property constant. If we want to make a T-v diagram

we keep Pressure Constant , and then make it for water.

We will observe the following trend

We see that at each pressure there is a temperature

where the liquid changes to gas and then again the

temperature increases. Now as the pressure increases

the phase change line becomes shorter and shorter. At a

pressure of 22.09 MPa the phase change becomes a

T

v0.1 MPa

1.0 MPa

8 MPa

15 MPa

22.09 MPa

25 MPaCritical Point374.14


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point. At this point the temperature is 374.14 oC. This point

is known as CRITICAL POINT. Here Saturated Liquid and

Saturated vapor States are identical.

At this point the we have Critical Pressure, Critical

temperature and critical specific volume. For water

Critical Pressure is 22.09 Mpa

Critical temperature is 374.14 oC

Critical specific volume is 0.003155 m3/kg

For helium it is

Critical Pressure is 0.23 Mpa

Critical temperature is -267.85oC

Critical specific volume is 0.01444 m3/kg

At pressures above PCritical the phase change will not be

distinct. A sudden change will take place and it cannot bepredicted.

Generally we refer to any substance as SUPERHEATED

VAPOR above its Critical Temperature. and as

COMPRESSED LIQUID below Critical Temperature.

Now in the above diagram we connect the saturated

states points we get the following:-


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Similarily we can get a P-v diagram keeping the

temperature constant.

In P-v diagrams the constant temperature line are nearly

straight.We will learn about how to use these diagrams at

a later stage in the course

Saturated Liquid Line

SaturatedVapor Line

T

v

Critical Point

Saturated Liquid andSaturated Vapor Region


SaturatedVapor Line

P

v

Critical Point



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SOLID PHASE. We have uptill looked at equilibrium

states of liquid , vapor and liquid- vapor states. We will

now look at the Solid Phase. So if we reduce pressure

and temp. we get into solid phase. Lets make a P-v

diagram

SOLID

SOLID+LIQUI

D

LIQUID

TRIPLE LINE

LIQUID + VAPOR

SOLID + VAPOR

CHANGE FROMSOLID TO VAPOR

CHANGE FROMVAPOR TO SOLID


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This is a P-v diagram of a substance which contracts on

freezing. There are substances which expand on freezing

like water. This entails a slightly P-v diagram .

The Triple Line is the point where Vapor + Liquid + Solid

can exist together. At Triple Line the Pressure and

Temperature is fixed. The specific volume can change.

The change from Solid to Vapor is known as

SUBLIMATION

The triple point data of a few substances is as follows

Substance Pressure T.Point TemperatureT.PointWATER 0.6113 kPa 0.01 oC

OXYGEN 0.1502 kPa -218.81 oC

TITANIUM 0.0053kPa 1668.0 oC

We can also make a P-T diagram and it will look like this


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At triple point all three phases co exist.

P-v-T SURFACES.

We had earlier stated the two property rule. So we can fix

the state of a substance by two Independent Intensive

Properties. Then other properties will become dependent

on these two properties. We can thus relate P-v-T and

present it on a 3-Dimensional graph. These are shown in

Fig 2-26 and 2-27.

VAPOR

Liquid

Solid

Expands onFreezing

Sublimation

Melting

Vaporization

TRIPLE POINT

Contracts onFreezing


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Vapor Pressure and Phase Equilibrium

A gas exerts pressure . This pressure is due to the force

exerted by the moving molecules in the gas. In fact

( ) ( )

( )

F Avg Velocity of molecules No of molecules per unit volume

so P f T and density

=

If a gas has five individual pure substances then

( )

Total a b c d e aP p p p p p where p are the partial pressures

so p No of molecules Moles

= + + + +


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Now atmospheric air consists of Dry air and water vapor

so atm dry air water vapor w v P p p p is known as vapor pressure= +

Pw v is generally about 3 % of Patm

The vapor pressure is due to the molecules of water vapor

in atmospheric air. However air can only absorb a certain

amount of water vapor. We thus define a term called

Relative Humidity which is defined as

.

. .

Actual amount of water vapor in air at temp T

Max amount of which can be held in air at temp T =

varies from 0 to 100 %

0 % is called dry air

100 % is moist air or Rain

Now the vapor pressure of water vapor is a max when the

water vapor present exerts a pressure equal to its

saturation pressure at the existing temperature. It has

been found that @v Sat T P P= so

if =60 % and T=25oC then at 25oC the value of

Psat=3.17 kPa so Pv=0.6(3.17)=1.9 kPa


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Since Psat increases with increase of Temperature so at

high Temperatures air can hold more moisture. So

wherever we have high humidity area ie moist climates we

have FOG(suspended droplets) when temperature drops

or DEW(Liquid Water) on cold surfaces.

PHASE EQUILIBRIUM

Now if we take liquid water in open air , we find that it will

start evaporating.

In DRY AIR evaporation is faster , because air has more

capacity to hold water vapor.

Now as the vapor goes into atmosphere it increases the

quantity of vapor in the air. A time will come when the air

will not accept any more water vapor. This is because the

air has become saturated with water vapor.This is the point of phase equilibrium. This is governed by

the fact that :

THE VAPOR PRESSURE IN THE AIR IS EQUAL TO

THE SATURATION PRESSURE OF WATER AT THE

TEMPERATURE OF THE AIR.

w vapor Sat of water Water p P at T=

This is valid for water exposed to air.

If pvapor in air is less than Psat of waterat water temperature ,

then water will evaporate in open air. The larger the


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difference between PSat of water and pvapor , the greater the

evaporation.

Evaporation will cool the water and water temperature will

reduce. As a reduction in water temperature will reduce

PSat of water , so evaporation will reduce until a balance is

achieved. This is phase equilibrium between the vapor

and liquid water.

We can however increase the evaporation , by increasing

the water temperature. Hence hot water will evaporate

faster than cold water in the same environment. We will

study about this when we study air conditioning in the next

semester.

PROPERTY TABLES AND CHARTS

Since systems require values of properties for their state

identification , so we need to know how to evaluate the

properties. This is done by

A. Generating mathematical functions to relate

properties

B. Do experiments and develop experimental data

C. Both


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Also sometimes we combine certain properties to get a

new property . We will see a lot of these but at present we

look at one very important combination called ENTHALPY

ENTHALPY is a property made up by combining Internal

energy , Pressure and Volume and given symbol H

.

/

, int

H U PV with units of Joules called Enthalpy

If we divide by mass

H U PV then we have h u Pv J kg

m m m

h specific enthalpy u specific ernal energy

and v specific volume

= +

= + = +

= =

=

( )32

We check the units U is in Joules

NPV m N X m Joules

m= =

s

So Enthalpy is a property which is representative of

energy.

SATURATED LIQUID AND SATURATED VAPOR STATE

Lets us look at these phases


SaturatedVapor Line

T

v

Critical Point


f g


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On the saturation line points left of Critical point are

Saturated Liquid points.(f)

Points right of Critical point are Saturated vapor points.(g)

So volume at Sat. Liquid line is denoted by vfand volume

of saturated by vg

Similarily all properties related to saturated liquid will be

indicated by subscript f . Thus uf , hf ,

And Similarily all properties related to saturated vapor will

be indicated by subscript g . Thus ug , hg ,

vf-g= vg vf= Difference of Sat vapor and Sat Liquid

Specific volumes at the same saturation conditions.

hf-g= hg hf= Difference of Sat vapor and Sat Liquid

Specific enthalpies at the same saturation conditions.

uf-g= ug uf= Difference of Sat vapor and Sat LiquidSpecific internal energies at the same saturation

conditions.

hf-g is called Enthalpy of Vaporization or

LATENT HEAT OF VAPORIZATION

hf-g decreases at Psatand TSat increases

hf-g =0 at Critical Point

For water these properties are given in what is known as

Steam tables and these are given in your book as table

4,5,and 6. Lets look at few examples like 2-2,2-3 and 2-4.


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SATURATED LIQUID-VAPOR MIXTURE REGION


SaturatedVapor Line

T

v

Critical Point


f g


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In the saturated liquid-vapor region both exist in

equilibrium. So here mass of mixture is equal to the

mass of liquid + mass of vapor.

At this point we define the quality of the mixture as

Vapor g

Total f g

m mx

m m m= =

+

If all the mass is liquid then0

00f

xm

= =

+

If all the mass is vapor then 10

g

g

mx

m= =

+

So quality varies from 0 to 1.00 for Saturated mixture with

Saturated Liquid has x = 0 and

Saturated Vapor has x = 1.00

What happens if we are not at saturated conditions.

So we are at point 1 then here V1 = mtotal(v1)


SaturatedVapor Line

T

v

Critical Point


f g

1

2


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( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

1 1

1

1

( )( )

(1 )

(1 )

(1 )

f g Total f f g g

g gTotal g f

Total Total

f g f g f

f g f g f

f g f g f

V V V or m v m v m v

m vm m vv

m m

v x v x v v x v v

This is also valid for other properties

u x u x u u x u u

h x h x h h x h h

= + = +

= +

= + = +

= + = +

= + = +

SUPERHEATED VAPOR

All vapor having Temperature greater than TSat for its

existing pressure is called SUPERHEATED VAPOR

Point 2 is in superheated region . For their properties we

have separate table namely Table A-6

COMPRESSSED LIQUID.


SaturatedVapor Line

T

v

Critical Point


f g

1

2

3


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All liquid have temp less than Tsat for its pressure.

Generally very less data is kept for compressed liquid as it

is Independent of Pressure. Generally vComp. Liquid= vfat its

temp ,

uComp. Liquid= ufat its temp and hComp. Liquid=hfat its temp

This is valid for low pressures like point 3

For high pressure h=hf + vf(P Psat) only as enthalpy is

sensitive to pressure.

REFERENCE STATE

Generally the value of u and h are calculated with

respect to a reference state where h and u of the

substance is considered zero.

For water this is 0.01 oc as Tsat

For refrigerant 134-A it is -40o

CThe calculation of these properties will be learnt in

semester III

IDEAL GAS EQUATION OF STATE

We have seen that properties of water is found

experimentally, and presented in tables. We will now look

at Ideal Gases.

Any Equation that relates Pressure,Volume and

Temperature is called as EQUATION OF STATE.

The other properties can then be defined by further

equations like H = U+PV. This can also be called an


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Equation of State. However for our studies we will refer to

only that equation which links P,V and T.

Before we look at the IDEAL GAS EQN. OF STATE we

need to be clear about what is a Gas and what is a vapor.

A SUBSTANCE IS A GAS WHEN IT IS ABOVE ITS

CRITICAL TEMPERATURE.

It is a vapor when it is below its critical temperature . A

vapor is easily condensable , while a gas is not easily

condensable.

The EQUATION OF STATE OF AN IDEAL GAS is given

by PV=mRT where P= Pressure in Pa

T=Absolute Temperature in oK , V=Volume in m3

R=Gas Constant in Joules per kg peroK

m= mass in kgR= Gas Constant and is different for each gas.

Now PV=mRT can be written as Pv=RT by dividing both

sides by the mass and designating v= specific volume.

tan 8314uU o

R JoulesR where R Universal Gas Cons t

M k mol K = = =

The value of RU is the same for all Gases.

M=Molar Mass and it is equal to mass of one Mole of gas.


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Mole of a gas is the Molecular weight( Mass of Molecules)

of the gas expressed in grams or kilograms. generally

K.Mol is used.

So if we have Oxygen then its molecular weight is 32 so

1 K.mol of Oxygen has a mass of 32 kg/K.mol

Hydrogen has molecular weight of 2 so 1 K.mol of

hydrogen has mass of 2kg/k.mol

The number of molecules in a mole is given by the value

of N. Generally if m=mass then m=MN

so if we have 93 kg of oxygen then since for oxygen

M=32 kg/K.mol so

93 kg= 32 kg/K.mol(N) so N=2.906 K.mol

If we now have to find R of other gases we can do the

following

2

2

22

.

8314.

4157

2.

o

oU

H o

Ho

kgH has M

K mol K

Joules

R JoulesK mol K so R

kgM kg K

K mol K

=

= = =

2

2

232

.

8314.

259.8

32.

o

oU

H o

Ho

kgO has M

K mol K

Joules

R JoulesK mol K so R

kgM kg K

K mol K

=

= = =

Now Pv=RT then the units will be as follows


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( )

3

2

3

2

, o

o o o

N mP v and T is in K

m kg

N m

N mPv Joulesm kgsoT K kg K kg K

= =

= = =

2

8314188.95

44

8314286.7

29

CO o

Air o

JoulesNow R

kg K

JoulesR

kg K

= =

= =

Values of R and M of several gases are given in Table A-1

3

.

UU

U U

RV mv and m MN so PV MNRT MN T NR T

M

Vor P R T we write this as Pv R T

N

mv is defined as Molar Specific Volume with units of

K mol

= = = = =

= =

Now if an ideal gas goes from one state to another state


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IDEAL GASES ARE NOT FOUND IN NATURE.

However most gases found in our world ( known as Real

Gases) behave like ideal gases with great degree of

accuracy.

Most gases behave in an Ideal Manner at

LOW PRESSURES AND HIGH TEMPERATURES.

Water Vapor behaves like an ideal gas below 10 kPa even

if temperature is Low. ( Area of low density)

At High Pressures Water vapor does not behave like an

ideal gas.( Area of high density)

Since most gases may not behave as an ideal gas for

accuracy , so we must have some way of dealing with

non-ideal gases with accuracy. This is done by looking at

the concept of Compressibility Factor.

COMPRESSIBILITY FACTOR

1

2

Then at state 1 P1v

1=RT

1and

at state 2 P2v

2= R T

2and since

R remains constant so we say


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Most gases deviate from Ideal gas behaviour near the

Saturation Region and near the Critical point. To account

for this deviation we use the concept of COMPRSIBILITY

FACTOR(Z) where

actual

ideal

vPvZ or Pv ZRT so Z

RT v= = =

For Ideal Gas Z=1.00

Now we had earlier said that most gases behave ideally atLow Pressures and High Temperatures.

But what is Low Pressures and High Temperatures?

at -100oC N2 and Air behave as ideal gases. Now

we see that for N2 CP Temp is -147oC and

for Air is -140oC

Most gases will liquefy at these temperatures. So to

determine the region of Ideal gas behavior we define two

quantities

Re Pr

Re

R

CR

R

CR

Pduced essure P

P

Tduced Temperature T T

= =

= =

THIS IS CALLED AS

PRINCIPLE OF CORRESPONDING STATES

In Fig 2-57 Z is plotted against PR for various TR


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Most gases have same Z at the same PR and TR

Real gases obey the Principle of Corresponding states.

The charts are known as generalized charts and are given

in Figures A-29 a,b,c. If we look at these charts we see

a. At very low pressures PR>2, Ideal gas behaviour is

experienced regardless of Pressure except when

PR>>1

c. Z has very low values at PR=1 and TR=1. Very poor

ideal gas behaviour.

If P and v are given or T and v are given then we can still

use the compressibility chart . For this we define

actualR

CR

CR

vv

RT

P

=. Lines of constant vRare also plotted on

compressibility charts.

Other Scientists have also worked on generating

Equations of state for real gases. These are as follows:-


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VAN DER WALLS

( )2a

P v b RT v

+ =

this equation accounts for

a. Intermolecular forces accounted by a/v2

b. Volume occupied by molecules themselves accounted

by b

The value of a and b is found experimentally and they are

( )22

27

64 8

CR CR

CR CR

R T RTa bP P

where a and b can be evaluated from CP data

= =

BETTIE-BRIDGEMAN EQUATION

has five constants and is accurate upto 0.8 CR

( )2 31UR T c AP v B

vT vv

= +

BENEDICT-WEBB-RUBIN

has eight constants and is accurate upto 2.5 CR

Eqn given in book (2-27)

VIRIAL EQN. OF STATE

Expressed in series.

Eqn given in book( 2-28)

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Thermo Chap II