A pure substance can remain at a particular phase or can remain as a mixture of different

phases. By phase, we mean the state of the substance; it can be solid, it can be a liquid

phase and it can be either in vapour or in gas phase. There is a subtle different between

vapour and gas phase which we will know when we discuss further. Out of this particularly

when we will see the different engineering systems of our interest, we will find that

the working medium could be either in the liquid phase or in the vapour phase or gas

phase, or it could be a mixture of liquid and vapour phase. In engineering thermodynamics

or the branch of engineering thermodynamics which we are studying, there we will be concerned

with the determination of thermodynamic properties of liquids, vapours and gasses and the mixture

of liquid and vapour. There could be some properties of a solid material which are also

thermodynamic properties but we are not interested in that. Generally, a metallurgist or physicist

will discuss those properties and that is not within the discussion of the present course.

Let us take one example.

Let us say, we take a certain vapour in a piston cylinder arrangement and the piston

is loaded by a constant load like W. Inside this piston cylinder arrangement some vapour

is there and we are transferring heat to this vapour at a slow rate, so that at any instant the

temperature of the vapour mass anywhere inside this piston cylinder arrangement is uniform

and constant. But, it is changing with time. That means as we are giving or supplying more

and more heat the temperature of the vapour mass as a whole is changing but it is not

changing from point to point. If we do this experiment and then if we try to measure its

different properties then what will we find? If we transfer heat and there is an expansion

of this vapour mass, there will be a change in volume. But, we are applying a constant

weight on the piston so the pressure remains constant. It is a constant pressure process.

The volume changes and there could be change in temperature. If we note down the change

of volume then, one can find out the change in volume with the application of heat. Similarly one can think of a process

in which we are plotting the change of volume.

Either we can think of specific volume or we can think of total volume and this side

we have got pressure. We can think of the change of pressure and volume while the temperature

is kept constant; so the process will be something like this. Let us say, we are going for a

cooling process. The process will be something like this. Here, what we have done is, we

have kept the temperature constant. At this point let us say we are coming to the saturated

state of the vapour. We have started at any arbitrary pressure, volume and temperature

of a vapour. Then we are cooling it. That means, we are extracting heat from the vapour

mass, keeping the temperature constant.

We are plotting the pressure and volume at different stages. At one stage we will reach

the saturated vapour condition. After that, if we extract more heat what will we find?

We find that temperature will remain constant and pressure will also remain constant till

this saturated vapour completely gets converted into saturated liquid. At this point we are

getting a saturated liquid. After this if we extract more heat then, we will find that

there is a rise in pressure but during this process there is very less change in volume.

Here we are having a liquid state and in the liquid state it is almost incompressible,

so the change in volume will be small. Let us say this is at temperature T1. We can repeat

this process for another temperature. Let us repeat this process for another temperature

and we will get something like this. We are getting basically three regions of the curve.

In this region, we are getting super heated vapour, in this region this is the saturated

vapour point, here we are getting vapour liquid mixture, this is the saturated liquid point

and here we call it sub-cooled liquid. This is liquid, this is vapour and in between we

have a zone where mixture of liquid and vapour exists. If we do this experiment for different

temperatures, we will have different points for saturated vapour. Similarly, we will have

different points for saturated liquid. If we combine all these points by some sort of

a smooth curve, then you will get some sort of a dome like this.

Let us say, this is the line which passes through points of all the saturated vapour

and this is the line which passes through all the points of saturated liquid. If they

are extended they will join at a particular point which is known as critical point. Let

me denote this point as C or critical point. If somebody does the same experiment or same

type of curves are plotted then, through the critical point one will get a curve like this.

Beyond critical point the nature of the curve will be something like this. Let me write

down. This side we are having liquid which is denoted by L. Inside the dome we are having

liquid plus vapour and this side we are having vapour. L denotes liquid and v denotes vapour.

If we have the dome, on the left hand side of the dome and on the right hand side of

the dome we have got single phase regions, while inside the dome we have got a two phase

region or mixture of two phases.

For a pure substance if it is in single phase, then if we have know two independent thermodynamic

properties, then any third property can be determined. In this region or in the vapour

region if we have know two independent thermodynamic properties, let us say, if we know pressure

and temperature we can determine volume, we can determine enthalpy, we can determine entropy

or any other properties for that matter. Similarly, in the liquid region, if, say pressure and

temperature are known, other thermodynamic properties can be determined. In the two phase

region we need any three independent properties for determining another thermodynamic property.

We will see how to determine the thermodynamic properties and what the important thermodynamic

properties are. Mainly our working substance will be either in the gaseous phase or vapour

phase or it will be in the liquid phase or it will be a mixture of liquid and vapour.

Common working medium with which our engineering cycles run are like steam; it can be a refrigerant.

Basically, steam is used in number of engineering cycles and it is a medium which is extensively

used for the production of power. We will study the properties of pure substance with

reference to properties of steam. For steam, the diagram which I have shown you is known

as pV diagram. For steam this is the pV diagram. Here, these are constant temperature lines.

This is a constant temperature heating line. Earlier I have shown a constant temperature

cooling line. This point is known as the critical point. This line is known as saturated vapour

line and this line is known as saturated liquid line.

Similarly, one can have another thermodynamic plane for representing the pure substance.

This is a TS plane or temperature entropy plane. In this temperature entropy plane we

can have constant pressure lines like this. This is a constant pressure line, so we can

call it p is equal to constant. Another line we can have; let us say, this P1 is constant

where P1 is greater than P. Here also we are having the critical point here at the top

of the dome. C is the critical point. Then, if I have these two lines A to C or line AC,

this is the saturated liquid line and BC is saturated vapour line. Here, we can see a dome type structure within which

there is both liquid plus vapour. On the left hand side of the dome we have the liquid and

on the right hand side of the dome we have got vapour. At the critical point one cannot

make any demarcation between the liquid phase and the vapour phase and at the top of the

critical point we have got gaseous phase of the matter.

This holds good for both pV diagram and for the TS diagram. That means, at the critical

point we do not have any demarcation between liquid phase and vapour phase and above the

critical point or at the top of the critical point we have got gaseous phase. I have mentioned

that for any pure substance if it is in single phase, we need two independent properties

for determining the third property or for determining any other thermodynamic property.

Inside this dome we have got a mixture. Though it is a pure substance here two different

phases are existing together; liquid and vapour. Here, we need one additional information for

determining the property values. That information is known as quality or dryness fraction.

Let us say, we take a sample of a two phase mixture. The mass of the sample is M. As it is a mixture of two phases, it is made

up partly with liquid and partly with vapour. Conventionally, liquid is expressed with a

subscript f and vapour is denoted with a subscript g. M total will be Mf plus Mg. The quality

or dryness fraction is denoted as x. So, x is mass of vapour divided by the mass of the

sample. In this case it will be Mf by M or it will be Mf by Mf plus Mg. This quality

or dryness fraction will be used as another property inside the two phase dome. If we

go back to our earlier diagram we can write at the saturated vapour line, x is equal to

1; saturated liquid line x is equal to zero and in between values of x that will lie between

these two lines. In other words we will have different curves for different values of x

inside the dome. These are constant x values or constant x lines; so we can write x is

equal to constant. A similar thing is there in this TS diagram; x is equal to 1, here

x is equal to zero and in between there are number of lines. Let us say, this is one typical

line where x is equal to constant. As I have mentioned in the beginning, we are not much

concerned with the property of solids. Let us see the total scenario on a PT diagram,

pressure temperature diagram.

This is a PT plane for any thermodynamic substance. Here, the transformation of phases can be

denoted by lines like this. This side we will have solid, this is liquid, this is vapour

and this is gas; this is extended. If we give different names, this point is C and this

is TP. S denotes solid, L denotes liquid, V denotes vapor and G denotes gas. C denotes

critical point and TP denotes triple point. This is a very important diagram. It shows

depending on the values of pressure and temperature, what will be the phase of a particular substance?

Whether it will be in solid phase or it will be in liquid phase or it will be in vapour

or gaseous phase?

This line indicates the transformation between solid and liquid; so this line indicates either

melting process or solidification process. This line indicates the transformation between

solid and vapour. So, this is indicative of sublimation and de-sublimation process and

this line indicates transformation between liquid and vapour, so it is boiling and condensation.

Here we can see the critical point beyond which or at which there is no physical demarcation

between the liquid phase and the vapour phase. If we compare between this PV diagram and

the PT diagram of a substance where all the three phases are shown, this is the saturated

liquid line and this is the saturated vapour line. These two lines are coincident in this

line where there is a transformation between vapour and liquid phase. In between there

is a point which is known as triple point. This point is a very important one and at

this pressure and temperature, all the three phases can coexist. These lines show the coexistence

of two phases but this point shows the coexistence of three phases; all the three phases can

coexist at triple point. This is for the general information, but for the branch of engineering

thermodynamics in which we are interested, we are interested in this line only where

transformation between vapour phase and liquid phase is taking place.

Let us recapitulate once again what we have learnt so far and then we will go for determination

of different properties. What we have seen so far is that, a pure substance can remain

in different phases like solid, liquid and gas or vapour. As far as engineering thermodynamics

is concerned, we are interested in liquid phase and vapour phase and sometimes in gaseous

phase. In a pure substance when there is transformation between liquid to vapour phase and vapour

to liquid phase, we are interested in those processes and those processes can be expressed

on different thermodynamic plane. Two thermodynamic planes I have shown. One is a pV plane and

another is a TS plane. In all these planes we can see that there are three regions; one

is a liquid region another is a mixture of vapour and liquid region and third one is

the vapour region. The mixture of liquid and vapour region is bounded by two lines. In

any diagram like this one, on one side we have got saturated liquid line and on the

other side we have got saturated vapour line.

This saturated liquid line and saturated vapour line intersect at one point which is known

as critical point. At the critical point, there is no demarcation between liquid and

vapour and above critical point we have got gaseous region. These are the important things.

There is another important information which I have provided. Inside the two phase region,

we need another property for determining any thermodynamic property of the mixture and

that property which we take generally is dryness fraction or quality. By definition this is

the ratio of the mass of vapour divided by the total mass.

Let me draw the thermodynamic plane which we generally use for discussing the change between

the liquid phase and vapour phase. One is a pv plane, as I have shown; this is the pv

plane. Another is a TS plane. The third one is hs plane. The hs plane looks like this.

In the hs plane also we have got the critical point. This is critical point c and you will

have different values of x like this. This is x and it is equal to constant and this

line is your saturated vapour line. This hs diagram, where enthalpy and entropy are taken

as the coordinates, has got another name that is known as Mallier diagram or sometimes it

is called Mallier chart. This diagram is very useful in solving problems because directly

one can get the enthalpy values and changes in entropy in different processes, from this

chart. As in different steady state steady flow processes, changes of enthalpy is a very

important quantity and it has to be computed number of times. This Mallier chart is very