 So, welcome back, having understood the concept of dryness fraction or the quality and x that we calculated earlier, we had done the formulation of that, let us now see how to calculate this dryness fraction. We know by definition the quality of the mixture is equal to dryness fraction, sometimes referred as x and in most of the books you will find it is referred to as x, which is equal to the ratio of the mass of vapor to the total mass. The definition should be absolutely clear. Now let us look at any two phase mixture which has got some vapor and some liquid, saturated liquid and saturated vapor that is a two phase mixture that will have which will lie on the saturated liquid vapor line. So volume of this two phase mixture is equal to the volume of saturated liquid plus the volume of saturated vapor alright, so Vf and Vg and the saturated liquid and saturated vapor will have its own properties which are given on the in the steam table. So, I can now compute this Vf and Vg and then derive an expression to calculate the value of x. So if I write this total volume in terms of specific volume, I will have to multiply specific volume by total mass. So the total mass is Mf plus Mg mass of liquid plus mass of vapor into the specific volume of two phase mixture alright is equal to the total volume of saturated liquid which is Mf into Vf, Mf is the mass of saturated liquid and Vf is specific volume of the saturated liquid plus the mass of the vapor which is the total mass, the mass of the vapor multiplied by the specific volume of the vapor. Both Vf and Vg are computed at the same pressure and temperature and these values can directly be obtained from the steam tables. Now if I divide this equation by Mf plus Mg, I will get the next expression as V is equal to Mf upon Mf plus Mg Vf plus Mg upon Mf plus Mg into Vg. What is this bracket? This bracket is nothing but x value alright and what is this bracket? Mf upon Mf plus Mg is 1 minus x alright so because Mg represents x, Mf will represent 1 minus x when it is divided by total mass. So if I could write this equation therefore as V is equal to that is the specific volume of a two phase mixture is equal to 1 minus x Vf plus x into Vg and if I rewrite this equation now I will get V is equal to Vf plus x into Vg minus Vf very important expression here. So specific volume of any two phase mixture at a given pressure and temperature is equal to the specific volume of saturated liquid at the same pressure and temperature this can directly be obtained from the steam table because they are P sat and P sat values over here and Vg minus Vf you have got both these values available on the steam table which is what we call as delta V or Vfg alright. So I can calculate this property specific volume by this formulation and if I rewrite in terms of calculation of x now I will get an expression x is equal to V minus Vf upon Vg minus Vf so this is actually the same as what we have got here in terms of mass this is now in terms of specific volume V is the actual specific volume of the given mixture given mixture of gas and liquid alright. So it is a two phase mixture that exists if I know this value I can compute what is x if I know x and if I do not know this value I can still compute the value of V now in that case provided I know Vg and Vf from the steam tables of course I know the Vg and Vf if I know pressure and temperatures and this will be more clear when we solve the problems or tutorials. Now if I carry out further I can apply the same thing for different properties for enthalpy for example for thermal energy for entropy and I will get a similar expression now. So x would remain the same but the values of x can be calculated from any properties for example x is equal to U minus Uf upon Ug minus Uf thermal energy of the two phase mixture minus thermal energy of saturated liquid for the same pressure and temperature divided by Ufg for the delta U value for the same pressure and temperature similarly x is equal to h minus hf upon hg minus hf clear I am just extrapolating the same expressions for enthalpy and for entropy also although the value of delta V and delta U are not given in the steam table this value is directly given and you know that hg minus hf is nothing but hfg which can be directly read from the steam table similarly I can read the value of sfg also directly from the steam table and that is why because these expressions are more widely used these values are also given in the steam tables hfg and sfg. The basic is if I know the entropy of the or the enthalpy of a two phase mixture immediately I can calculate the dryness fraction or the value of the quality of the mixture immediately alright. So once I know these expressions once I know the value of x at a given pressure and temperature I can now compute enthalpy entropy thermal energy or specific volume or the properties of any two phase mixture now can be obtained using this dryness fraction the rest of the properties what I need is basically the saturated liquid value or the saturated vapor value. So I can therefore compute thermal energy of a mixture is equal to Uf plus x Ufg enthalpy of a two phase mixture is equal to hf plus x times hfg and similarly the entropy of a given two phase mixture is equal to sf plus x times sfg. If you can see that these values sfg hfg Uf and Ufg can be obtained from the steam table what I need to know is just the dryness fraction if I know the dryness fraction I can calculate all the properties of a given two phase mixture and this is something which you remember when I said the state of the mixture earlier I did not know how to calculate this but with this formulation and using the steam table I will be calculating all the properties of a given two phase mixture. Since summary I can say now state of a mixture could be given by these formulations alright so what is important to be known is the value of x rest everything is can be obtained from the steam tables if I know the pressure and temperature for a given two phase mixture. So what we have learnt till now we have seen the concept of quality of the mixture that is the dryness fraction that is the value of x alright we have developed an expression for that thing we can calculate the dryness fraction now and therefore based on calculation I can calculate all the properties of a given mixture I can say the enthalpy entropy thermal energy and specific volume of a given two phase mixture can all be calculated from this. Thank you very much.