 So, we will redo some of the examples that we did before. So, this was the first example that we did earlier. So, here is a duct air comes in at 50 degree Celsius, one atmosphere 85 percent relative humidity volumetric flow rate is given heat is added here and the air leaves at with the relative humidity of 25 percent and at the same mixture pressure. So, we start by locating the inlet state on a psychrometric chart and that is shown here. So, state 1 is over here. So, state 1 is here. So, any two arrows I mean the incoming arrows denote properties that have been used to locate the state on a psychrometric chart. So, obviously, we need the two properties to or two quantities to fix the the state or locate the state in a psychrometric chart. So, the incoming arrows denote those properties or those quantities and the outgoing arrows indicate property values which have been looked up from the psychrometric chart for that particular state. So, in this case the temperature is given to be 5 degree Celsius relative humidity is 85 percent. So, we use the line of constant I mean line of phi equal to 85 which is this one here and temperature equal to 5 which is this one here to locate the state. Notice that this line corresponds to phi equal to 70. This line corresponds to phi equal to 80. This line corresponds to phi equal to 90. So, phi equal to 85 approximately is in between 80 and 90. So, we may fix the state here like this. Once the state is fixed we retrieve h star corresponding to that state. So, h 1 I am sorry h 1 star and we pick up V a 1. Omega 1 is also retrieved from the table as 4.5. So, this is omega 1. So, phi 1 is 85 percent, omega 1 is also retrieved from the table. So, we have retrieved h 1 star V a 1, omega 1 is also retrieved from the table although the exact value is not required, but anyway because omega 2 equal to omega 1. Now, state 2 may be located by using the fact that phi is equal to 25 and omega 2 equal to omega 1. So, omega is the value that is used to locate the state and phi equal to 25 percent the line is over here and we look up h 2 star for state 2. So, we look up h 2 star for state 2. Now, we proceed with the analysis mass flow rate of dry air may be evaluated as V 1 dot over V a 1 that is nothing, but 100 divided by V a 1 which we have looked up from the chart. So, that is simply 125.786. Application of first lot to the duct gives us this expression and we substitute the values directly we get 39.83. So, you may see now how easy it has become to do these calculations. Earlier we had to use a long expression to calculate V a 1. Remember V a 1 was calculated by saying that V a 1 is equal to r air times T 1 divided by P a 1 or P a 1 which itself is equal to a mixture pressure P minus P v 1 and P v 1 itself has to be evaluated from the given value of phi. So, we have to do all these calculations and then get eventually V a 1 whereas the chart contains all this information in a ready to use fashion all these things have already been done. Remember all these things that we just mentioned. Relative humidity, how to use this all these things are already embedded in the chart. So, it is straightforward to use and we just retrieve the values from the chart and then proceed with the calculations. So, all these intermediate steps or the calculations corresponding to all this are already embedded in the chart. So, we may directly look up the values and then do the calculation. So, this is how the psychrometric chart makes calculations much easier, not necessarily much more accurate. Whatever we did earlier actually is more accurate, but this is much more easy to use. Accuracy probably is compromised a little bit because we have to look it up from the chart and again some approximations have to be made when we are retrieving this from the chart. So, but that is acceptable and you may compare this value with the values that we calculated earlier and you will see that they are about the same not too different from one another. Let us just go back and quickly check. So, this we are getting 39.83 kilowatts. Let us see what we obtained before. So, we obtained 40.458. So, you can see what we what we did here. Partial pressure. So, this partial pressure was evaluated from the definition of relative humidity and so on. Now, all these calculations are conveniently embedded in the psychrometric chart. The values that we are getting are not that different from what we had obtained earlier. Let us go to the next example. So, here we had a duct and there is a cooling coil. So, air at 35 degrees Celsius, one atmosphere, 80 percent relative humidity comes in and heat is removed from the air. So, there is condensation and then the air leaves at 22 degrees Celsius and fully saturated because condensation is taking place. It is fully saturated. So, let us see how we locate the states on a psychrometric chart. So, 35 degrees Celsius, 80 percent relative humidity, state 1, relative humidity phi 1 is 80 percent, 35 degrees Celsius. So, this is T 1, 35 degrees Celsius. This is the line corresponding to phi equal to 80 percent. So, these are the two incoming arrows. So, we have fixed the state here like this and this is H 1 star and this is VA 1. So, we have retrieved VA 1. Notice that this line is parallel to lines of constant specific volume. So, lines of constant specific volume look like this. So, this corresponds to the line of constant specific volume that passes through this state. So, we have retrieved VA 1 also. So, this line corresponds to 0.9 for specific volume of dry air and this line corresponds to 0.9 and this would correspond to 0.92 for 1 meter cube per kg. So, this falls in between. So, we approximate using some interpolation and then retrieve VA 1. So, let us see what we have done here. So, we get VA 1 to be 0.915 based on interpolation and omega 1 is also retrieved. So, you can see that omega 1 is also retrieved from the tables. We point 029 kg vapor. Remember this is in the chart gives the values in grams of vapor per kg dry air. We convert that to kilogram. So, we get 0.029 kg vapor VA and H 1 star all have been retrieved from the chart. Now, the dry bulb temperature of state 2 and the relative humidity are both known which means remember this is the curve that corresponds to phi equal to 100 percent. So, phi 2 is equal to 100 percent and this temperature 22 degree Celsius this is the line for T2. This is T2. So, this is T2. So, the state has been located and this is nothing, but H2 star is nothing, but H2 star. So, we can retrieve H2 star also and omega 2 has also been retrieved from the chart. So, omega 2 basically is 16 about 17 grams of vapor per kg dry air. So, omega 2 is 0.0169 and H2 star is 64 actually. Let me see. So, mass flow rate of dry air is nothing, but V1 dot over VA1 and this is the value that we have retrieved. So, we may get it to be 131.15 kg per minute. So, basically when you want to interpolate for example, for VA1. So, you use a ruler and so, you know the distance here and the ruler gives you fine markings. So, basically you can use that to determine the value for this that is how you interpolate graphically on a chart like this. Similarly, for omega 2 also or omega 1 also for any variable basically you line up your ruler with the lines of a constant, with the two lines which correspond to the contours of the quantity that you are interested in, locate where your state is and then visually interpolate. So, mass balance of water across the control volume basically is water vapor that comes in minus water vapor that goes out. So, that comes out to be 1.5869 kg per minute which agrees well with what we had calculated earlier. Now, SFEA applied to the control volume gives us something like this. This value of course, has to be looked up from the steam table issues. So, we get Q dot to be minus 5755.44 which is about 27.28 tons. So, let us see what we obtained earlier. So, we obtained 27.17 tons. Now, we have 27.28 tons which is close enough for the ease and comfort that we get by using the chart the values are acceptable. Now, let us look at an example that we have not done before. So, here we have two unit processes namely dehumidification and heating together. So, air at 30 degree Celsius one atmosphere 80 percent relative humidity enters an insulated air conditioning duct where it is first cooled and dehumidified. So, we cool the air so the moisture condenses and the air leaves the duct because there is condensation air leaves the duct fully saturated. So, relative humidity goes up but temperature comes down. So, we then heat the air so that the relative humidity comes down and the temperature increases slightly but it does not matter because the relative humidity now is at a comfortable value. So, this is what is done in practical HVAC applications. So, we take the air cool it reduce its temperature. This process increases the relative humidity because the because of the condensation relative humidity becomes 100 percent. Then you heat the air so that the temperature increases slightly but the relative humidity comes down. So, you have a comfortable temperature as well as relative humidity. We will check it by looking at the temperature that we have here how much of how much has the temperature increased as a result of heating. We will take a look at that also. So, this puts together both dehumidification as well as control of relative humidity without adding moisture just by adding heat. So, we are asked to do the calculation for unit volume flow rate of air that enters. So, we have taken volume flow rate to be 1 meter cube per minute. So, let us locate state 1 in the psychrometric chart. State 1 30 degree Celsius and 85 percent relative humidity. So, that state comes here. These are the two incoming arrows. So, we have retrieved H1 star and VA1 has also been retrieved. What is that? This line corresponds to 0.88 for VA1 and this corresponds to 0.90 for VA1. So, we interpolate based on these two. Omega 1 has also been retrieved. Now, if you look at state 3, state 3 temperature and relative humidity are both known. So, 22 degree Celsius and 40 percent relative humidity that we should be able to locate because we have values for two quantities. So, state 3 relative humidity 40 percent, 22 degree Celsius. So, 22 degree Celsius for state 3 and relative humidity 40 percent which is this one. So, let us label that V3. So, that is this line here. So, the state is over here. So, this is H3 star. We have retrieved H3 star and we have retrieved omega 3. Now, if you look at state 2, notice that only one quantity is known at state 2. That is relative humidity. We need one more quantity. But between state 2 and state 3, there is no addition or removal of moisture which means omega 2 equal to omega 3. We have already looked up omega 3. So, that means omega 2 equal to omega 3. So, 100 percent relative humidity is going to be over on this along this curve and omega 2 equal to omega 3. So, we come here. So, these are the two incoming arrows for locating the state. So, this is H2 star and this is T2. Notice that T2, the temperature corresponding to I am sorry the drivable temperature of state 2 is actually I am sorry yeah state 2 is quite small. So, we retrieved these using these values. We retrieved omega 1, VA 1 and H1 star. Mass flow rate for unit volume flow rate of air may be calculated like this. So, we located state 3 on the psychrometric chart and retrieved omega 3 and H3 star. Then argued that omega 2 equal to omega 3 and we retrieved H2 star and T2. Notice that T2 is 7.5 degree Celsius. So, T2 is 7.5 degree Celsius. So, what is happening here is that omega 2 equal to omega 3 and this temperature comes out to be 7.5 degree Celsius. So, we cool the air to 7.5 degree Celsius, but the relative humidity is 100 percent. The air is also very cold. So, we heat the air so that the temperature comes to a comfortable 22 degree Celsius and the relative humidity is also at a comfortable value of 40 percent. So, that is what HVAC is all about. So, once we have these values, we can do mass balance of water in the cooling section and evaluate the mass of water that condenses to be 0.0166 kg per minute. So, this is basically mass of water vapour that comes in minus mass of water vapour that goes out. SFE applied to the cooling section gives us this from which we can get QC dot to be 0.322 tons per unit volume flow rate. Please bear that in mind. And the amount of heat that has to be added in the heating section may be evaluated quite easily that comes out to be 0.2715 kilowatts. So, if you want to scale up the volume flow rate of air, all these quantities can be easily scaled up. So, this is how the knowledge that you gained in the first course can be used for practical applications like this one here. Basically, you have not learned any new concept in this module on psychrometry because we have already dealt with the mixtures of ideal gas or mixture of ideal gases in the previous course itself. You are just using those concepts in a different manner or in a manner well suited for or tailored for this particular application. And these three examples also make clear how the psychrometric chart is extremely useful for doing these calculations for practical applications. Of course, we can do all this in the manner that we did earlier also, but the psychrometric chart simply makes it much easier to do the calculations. So, what we will do in the next lecture is look at a few more applications of psychrometry, not necessarily HVAC applications, but different applications where again psychrometry is very important.