 So, welcome back, after understanding all the different regions in the phase diagram of water, I would like to again concentrate on properties of the subcooled or compressed liquid. And therefore, I will again take you to the this region above the LV line or saturated liquid vapor line and they will try to understand some property approximation. It is a very characteristic property approximation of which we have deliberated in a little bit manner earlier in the first lecture, but I would like to understand make you understand again what is this approximation related to subcooled or compressed liquid properties. Then I will briefly summarize all the states that we have seen on the phase diagram and also introduce you to a new term called quality of the mixture or quality, all right. So, let us look at properties of subcooled or compressed liquid, this is a very special region for which we had referred to in table 3 and let us again try to analyze how to retrieve properties of subcooled or compressed liquid region. So, this is our PT diagram ratio on the y axis, temperature on the x axis and what you see here is a LV line or saturated liquid vapor line which is drawn from TP to CP that means triple point to critical point. Now, let us look at a specific pressure case which is 0.15 MPa, one can take any pressure case, but I have just taken 0.15 MPa just for an example corresponding to this if I want to find out what is the T-SAT value I will just refer to table number 2 and get corresponding temperature value and this temperature value happens to be 111.349, all right. So, this could be any pressure corresponding to this pressure I have taken T-SAT P which is 111.349 and I will just draw this line vertically because I would like to see the effect of various pressures on this line in the subcooled or compressed liquid region. This is the subcooled or compressed liquid region I am sure now everybody of you know. Now, what I am going to do is I am going to this compressed liquid further and further and see the effect of increased pressure I can go from 0.15 to 0.2 to 0.3 to 1, 2, 3, 4 and go beyond even critical pressure just to understand what happens to the properties of this compressed liquid or subcooled liquid how do they change, all right. So, let us look at this first point which is on a LV line or a saturated point which is this is a P-SAT corresponding to this what we have is a P-SAT P. What are the properties that we look? We look at four different pressures we will try to look at specific volume, thermal energy, enthalpy and entropy and I would like to look at these properties or the property changes rather for different pressures in this subcooled or compressed liquid region, all right. So, first point is basically the saturation point for which I have got some values over here. Now, I would like to show the table from which we have taken these values just for the benefit of those who have not seen the table so often just try to go to that table and have a look at that and let us try to see how did I get these values. So, I have got a value at say 0.15 and then I will go to let us say 1 MPa also and let us try to get those property values from there just try to understand this and we will come back to this table again, all right. So, this is the table and this is 0.15 MPa corresponding to 0.15 MPa we have got T-SAT value as 111.349 which is what we had just seen. So, if I want to take the properties this is table 3 which is therefore you have got a pressure on the top and corresponding values from 0 to 1000 degree centigrade. So, if I can bring your attention to this point, all right, this is the top point and the bottom point and these are the values we are taking for saturated vapor region, saturated liquid region. How will you identify this? We will see when we come back to the table again. So, this is my properties at 0.15 MPa and let us see I look at some other pressure 1 MPa may be look at this, this is 1 MPa, corresponding to this what you have is I want to see the same pressure. As I said that I want to increase the pressure keeping the temperature the same. So, if I go back to 111 point point some temperature 111 you can see that I may have to interpolate between these values 110 to 115. So, I may have to interpolate these properties in order to get all the properties at 111 degree centigrade, all right. So, I am what I am doing I am keeping the temperature the same, but I am compressing the liquid from 0.15 MPa to 1 MPa to 2 MPa and in this way going from one pressure to another pressure diagram or table I will try to retrieve all these values. Once I get all these values I will come back to compare these values and what I said that we wanted to see that the property changes that happen because of the pressure increase in the compressed liquid region, okay. Let us come back to the table again, right. We were at this point and you can see at 0.15 MPa I have got these values which are given in red and these values which are given in blue and you identify from here which values are meant for gas and which values are meant for liquid. As you can see that the different values related to specific volume thermal energy enthalpy and entropy for vapor region are more than that for the gas or for the vapor region. As you know the enthalpy is 2693 while the enthalpy for the liquid region will be 467 and we can see the difference between these two values actually is Hfg, this is Sfg, this is delta U or Ufg, this difference and this difference could be delta V or Vfg, all right. Now what we are concerned about is the liquid properties that means I will consider only this blue properties or the properties which are given in blue color, all right. Coming back to our argument that now I would like to increase the pressure from 0.15 to further higher pressures and the next pressure therefore is could be 1 MPa and I had just shown you that table from where I can take those values by interpolation and I am putting up those values in this table. So at 1 MPa now you can see that these values of specific volumes thermal energy enthalpy and entropy and if you actually see those values you can see there is hardly any change. For example in the value of specific volume you can find that it has changed in 7th decimal point there is hardly any change even in thermal energy, little bit change in enthalpy and very little change in entropy, all right. So 0.15 to 1 MPa you can see that changes are very very little may be less than 1%. If I go further now compressing this liquid I go now to compress to 5 MPa, all right. So these are the properties and again you see that the property changes are minimum in this cases but in case of enthalpy you can see now this is little bit more increase in this property may be around 1% now while for these cases again the property changes are minimum. If I go on further compressing this liquid to 10 MPa I got still more properties I will go to 20 MPa and I got this property changes. So you can see that at 20 MPa again I have got now property changes that is happening in 1, 2, 3, 4, 5 fifth decimal place, all right. So it was in 7th then may be in 6th decimal and now we have got property changes as far as basic volume is concerned it is in the 5th decimal place while U has changed from 466 to around 460 and just above 1%. While you can see that enthalpy has changed from 467 to 481 which is little bit more as compared to V, U and when S, S value is also changed from 1.4 to 1.41 which is not very much as such changes in this property. Now if I take the next pressure which is above the critical pressure, critical pressure as you know is 22 MPa if I take the next property as 25 MPa you can find that this changes now is in 5th decimal place here, all right. So 5 has become 4 and 4 has become 3 now similarly the values in U little bit still less however in enthalpy there is substantial change that way in comparison to other values while in entropy again the changes are not so much. If I compare this property changes if I do property at 0.15 minus property value at 25 divided by the original property and if I just compute the percentage change that has happened over here in the last row we can see that comparing this 25 properties at 25 MPa to the properties at 0.15 MPa for the subcooled region taking the liquid properties now the percentage changes for V is hardly 1.21, percentage change for U is hardly 1.65, percentage change for H is minus 3.89 which is little bit more and percentage change in entropy is just 1.45. It means that even if I got liquid compressed from 0.15 to 25 if you see the pressure ratio this pressure ratio is of the order of 200. So even if the pressure ratio has increased from 0.15 to 25 MPa the property changes as far as specific volume thermal energy and entropy are considered this property values changes are very very small while there is some change and let us say significant change of minus 3.89 percent that has occurred as far as enthalpy is concerned. This is a very significant discussion that we are having as far as we are talking about subcooled or compressed liquid the reason for this will be talked in the next method. Thank you very much.