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  • Good afternoon. Today, we will start a new topic that is, the properties of pure substances.

  • 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

  • handy in calculating problems and representing different thermodynamic cycles. Other planes

  • are also possible; like in the refrigeration cycle we can use a different thermodynamic

  • plane but those we will discuss later on. Mainly for steam properties or for the processes

  • involving steam, to represent the process we will use either a pv diagram or a TS diagram

  • or an hs diagram. Which are the properties we are interested in? Let us say that we will

  • be interested in the specific volume. So what is the specific volume?

  • If we think of any thermodynamic plane, let us say we are interested in the TS plane and

  • in this TS plane we want to represent a process. The end points of the process can be anywhere,

  • either it can be in the liquid region or it can be in the two phase region or it can be

  • in the vapour region. Accordingly, we have to determine the properties in those regions.

  • Let us say, we are interested in one property which is the specific volume, v. If it is

  • in the super heated vapour region then we can determine it knowing other two properties

  • like pressure and temperature. Similarly, if it is in the liquid region we can determine

  • it knowing two independent properties. Let us say, again we take pressure and temperature;

  • these two properties are easily measurable properties. From there we can determine what

  • the specific volume is. But inside the two phase dome what should we do? We can proceed

  • like this. The mass balance if we make, m sample could be m liquid plus m vapour. V

  • sample, total volume of the sample, that could be V liquid plus V vapour. Then one can write

  • m into v. What is this quantity? This quantity is the specific volume multiplied by mass

  • that means it will give the total volume. That could be written as mf into vf plus mg

  • into vg and then we can divide both side by m; so it will be mf by m into vf plus mg by

  • m into vg.

  • Basically, we are getting the specific volume of the mixture is equal to mf by m multiplied

  • by vf plus mg by m multiplied by vg. By definition, the first term in this particular quantity

  • is the dryness fraction or x. Similarly here, what is mf? m minus mg that is your mf divided

  • by m into vf plus mg by m into vg. This will be 1 minus x into vf plus x into vg. One can

  • simplify it slightly. So, one can write vf plus x into vg minus vf. Here, either of these

  • two expressions can be used for denoting the specific volume of the mixture. Either the

  • first expression or the second expression can be used for determining or denoting the

  • specific volume of the mixture. What do we need for determining the specific volume of

  • the mixture? We need the specific volume of the fluid and we need the specific volume

  • of the gas or vapour and at the same time we need the mass fraction of any of this component

  • or we need the quality or dryness fraction.

  • If we go back to

  • this diagram, this is a constant pressure line and we are interested in this pressure.

  • This is a constant dryness fraction line. Let us say, this dryness fraction is 0.75.

  • We are interested in determining, at p bar and at dryness fraction is equal to 0.75,

  • what is the specific volume of the mixture. What we have to determine? First, we have

  • to know what vf is. That vf corresponds to this value of the saturated liquid. We have

  • to know vg. vg corresponds to the specific volume of the saturated vapour at p bar and

  • already it it specified that we have to determine it at x is equal to 0.75. We know the magnitude

  • of this quantity vf here. We know the value of vg here; we know the value of x here. So,

  • that can be plugged in this equation and ultimately we can find out the specific volume of the

  • mixture. This holds good for any other property.

  • If we want to determine enthalpy, we can use similar type of additive formula. If we are

  • interested in determining entropy, we can use similar type of expressions. Sometimes,

  • instead of using vg minus vf their difference is used and then this expression is like this

  • v is equal to vf plus x vfg. That means, this is the difference between vg and vf. So this

  • expression is also used in some of the occasions.

  • For determining the steam properties, we use steam table. This