 So, in this lecture, we are going to discuss psychrometry, so what do we mean by the word psychrometry? Basically, psychrometry is the study of the changes in the state and content of moist or humid air. And the primary application where psychrometry is applied is in heating ventilation and air conditioning that is HVAC. If you are going to say any big building or even for that matter in automobiles today, you have excellent temperature control, so you adjust the temperature and you are ensured that not only is the temperature set to the level you want, the humidity is also adjusted that is something that you do not see, but you feel the humidity level is also adjusted so that you are comfortable. So, merely setting the temperature does not ensure comfort. For example, in India, you may always want to set the temperature to be say 22 degree Celsius. But dry air at 22 degree Celsius actually makes people generally very uncomfortable, the air is simply too dry. For example, like the air in an aircraft, so if you go on long distance flights, then the dry air can actually cause redness of the eyes or some nose bleeds for some people and so on. So, dry air at low temperature is also is not very good. Now, at the same time, if the humidity level is high, that is also not very comfortable, although temperature may be okay, but high humidity level is also not good because you feel sticky. Again, there is a sense of discomfort. So, for optimal feeling, you should set the temperature and the humidity at optimal levels. So, not just temperature, but both temperature and humidity must be optimal. So, psychrometry essentially deals with that. So, essentially, it looks at the state of moist air, which means air with water vapor in it and also the content of moist air. So, if the air is too dry, then we may want to add more water vapor to the air to make it more comfortable. If the air is too humid, we may want to remove some water vapor again to make the environment more comfortable. So, comfort depends on both temperature as well as humidity and that is what we are going to study in this module. How temperature, state of the air and content or in other words, temperature and humidity of air can be controlled in these sorts of applications. So, if you go to big buildings, the temperature and humidity are automatically controlled by the central air conditioning system. Automobiles also nowadays have very sophisticated systems where you can set the temperature and everything is regulated. So, you have a very good sense of comfort. So, we will see how this effect is achieved. In other words, how do we control the temperature and the moisture content in the air? Or this quantity is measured so that appropriate control actions can be initiated. So, we will look at both these aspects in this module. In addition to HVAC, psychrometry is also of importance in drying and also in cooling towers used in thermal power plants. We will look at these applications, but by and large, it is used in HVAC. So, the next question that arises is what is moist air? What do you mean by moist air or humid air? Because when you say moist air or humid air, in colloquial terms, this sort of gives an impression that the air is too moist or too humid. But that is not the correct impression that one should have. So, if you take the air in this room or air in the room that you are in, the air contains primarily as O2 and N2. In addition, it also contains water vapor. There is some amount of water vapor in the air and that is colloquially referred to as humidity. So, humid air does not mean there is a lot of water vapor in the air or moist air does not mean there is a lot of water vapor in the air. Moist air or humid air refers to the fact that we have air, just dry air plus some amount of water vapor. The amount of water vapor, again, is what we are actually going to quantify and try to control in practical applications. So, let us take say air at a temperature of 25 degree Celsius and 1 atmosphere pressure. So, it contains a certain amount of water vapor at the same temperature, but depending on the amount of water, it is at its own partial pressure PV. So, let us look at the state of the water vapor and a PV, a TV diagram like this. So, you can see that the water vapor is at a temperature of 25 degree Celsius and at some partial pressure. Note that it lies on the superheated side or in other words, the water vapor is superheated because the partial pressure is so low because the amount of water vapor that is in the air is very, very small. But still important for psychrometric applications, but it is generally very small, which means that the partial pressure is very small, which means that at a temperature of 25 degree Celsius for such a low partial pressure, the water vapor exists as a superheated vapor or in the superheated state. Now, as we increase the amount of water vapor in the air, its partial pressure increases and so you can see that this is the isobar corresponding to the partial pressure of the water vapor. So, this is the isobar corresponding to the partial pressure of the water vapor and as we increase the amount of water, the pressure increases. So, the isobar moves in this direction and as we decrease the amount of water vapor in the air, the isobar corresponding to the partial pressure moves in this direction. So, the water vapor in the room is superheated on account of the fact that its partial pressure is quite small. Once again, the word superheated in normal connotation usually implies high temperature and you say something is superheated immediately you have steam that comes into mind and you know temperature is very high, but that need not be the case. So, here we have air at room temperature the water vapor is also at room temperature 25 degree Celsius, but because its partial pressure is so low that it exists in the superheated state and it is important to keep that in mind. Now, typical psychrometric applications experience more or less constant pressure around one atmosphere or maybe slightly higher than that and the range of temperature that we are looking at is usually between 0 degree Celsius and about 60 degree Celsius. So, for these conditions, for these conditions, so 60 degree Celsius the isotherm corresponding to 60 degree Celsius is here and the isotherm corresponding to 0 degree Celsius is here. So, this is the range of temperatures that we are looking at and for this range of temperatures usually the water vapor exists as a superheated vapor and we may essentially assume the water vapor to be an ideal gas. As shown here, notice that this illustration was actually discussed in the previous course when we talked about properties of pure substances particularly steam and R134A. So, roughly this shaded area denotes the region in which the vapor obeys the ideal gas equation of state to within 10 percent. So, for the range of temperatures that we encounter in psychrometric applications, the water vapor may safely be assumed to be an ideal gas which obeys PV equal to MRT where V is the volume or P times specific volume equal to RT. And we will assume that in this course and that is a very safe engineering assumption to make there is no need to use the tables the departure from the tables is very small. So, we can essentially use that and we will use that. So, these are the two important points that the water vapor in the room is superheated on account of its partial pressure being very small and the water vapor is superheated and we will assume it to be an ideal gas which obeys PV equal to RT. So, moist air itself may be treated as a mixture of two ideal gases. Once we say that we are going to treat the water vapor as an ideal gas, we may take the moist air to be a mixture of two ideal gases dry air which is usually denoted with a subscript A and water vapor denoted with a subscript V. So, the air in this room is taken to be a mixture of two ideal gases dry air itself and water vapor. Note that dry air itself is a mixture of two ideal gases O2 and N2, but we need not worry about that because the composition does not change. So, we treat that as a single component gas namely dry air. So, the air in this room is comprised of dry air and water vapor and this enormously simplifies the thermodynamic analysis of psychrometric applications. Again bear in mind that we have already discussed or rather it is a mixture of ideal gases, calculation of properties, ideal gas equation of states, mixture of molecular weight all these concepts have been discussed in great detail in the previous course. So, the no new concepts are being introduced here. The only special thing is that moist air is a mixture of just two ideal gases. Again bear in mind that this course deals with applications of concepts that were taught in the previous course. So, this is an application of mixture of ideal gases and first law both non-flow process as well as steady flow process and so on. So, we are just applying the concept of a mixture of ideal gases to a very interesting practical mechanical engineering application or mechanical engineering applications namely HVAC, drying, cooling tower and so on. So, for the mixture we may write P equal to nRT over V where n is the number of moles of the mixture. For the dry air we may write its own equation of state dry air PA equal to number of moles of dry air times RT over V. Notice that we are using the Dalton's model. So, all the components occupy the same volume and are at the same temperature only their pressures are different. And for the water vapor again we may write because we are assuming it to be an ideal gas we may write PV equal to nV RT over V. And since we have only two components we may write the total pressure of mixture is nothing but the sum of the partial pressures of its components. So, PA plus PV and the total number of moles is also the sum of the number of moles of the individual species. And by definition the partial pressure is nothing but mole fraction times the mixture pressure and so that is we can use that for both PV and PA. So, if you are not familiar with this I suggest that you look at the video in the first course which deals with mixture of ideal gases and then revise these concepts before you proceed. So, the first new term that we are going to introduce I am sorry introduce in psychrometry is the humidity ratio. The humidity ratio denoted omega is defined as the ratio of the mass of the water vapor to mass of dry air in a given sample. So, MV over MA is defined as the humidity ratio. What is that? In psychrometry it is always important to write kg vapor over kg dry air because otherwise this quantity is dimensionless because both numerator and denominator have units of mass. But it sometimes gets lost in the development if you do not use this what happens is you know you sort of do not realize that you are talking about MV or masses of different substances in the numerator and denominator. So, it is always a good practice to denote this as MV over MA kg vapor per kg dry air. Now, we can write this since by definition molecular weight is mass divided by number of moles we may write MV as Nv times MV and similarly for the dry air. And if I divide the numerator and denominator by N in this case for instance if I if I do this. So, I divide the numerator and denominator by N then Nv over N may be written as Yv and NA over N may be written as YA is nothing but the mole fraction. And since there are only two components in the mixture the sum of all mole fractions as we learnt in the previous course sum of all mole fractions should sum up to 1 in this case there are only two components of YA plus Yv equal to 1 and I can replace YA in the denominator with 1 minus Yv. And I can also write replace Yv with the partial pressure like this. And remember we have we have said that the mixture pressure is a sum of the partial pressures and this is we may use the mole fraction to define partial pressure like this. So, which means I can write omega in this form also. Now, if I substitute the value for molecular weight of water vapor 18 and for air 28.97 we get this to be omega equal to 0.622 times Pv over P minus Pv kg vapor per kg dry air. So, this is an expression that we will use quite extensively. This is a humidity ratio. Another term that is used in the context of synchronometry and HVAC application is relative humidity denoted by the Greek letter phi. Now, from practical experience you may probably have noticed the following. Let us say that we have a certain amount of water vapor in the air in this room. And we keep adding more and more water vapor and beyond a certain point you see that it is no longer possible to add any more water vapor there the air appears to be saturated. Now, saturated is used colloquially here, but there is actually a much more specific connotation for saturated. I will explain that in a minute, but the air appears to be quote unquote saturated. You cannot add any more water vapor to the air in the room. So, if you try to add any more water vapor it simply condenses back to liquid water it does not stay in the vapor form or superheated form. So, that means that there is a maximum to the amount of water vapor that this air can hold at this temperature. We have not changed the temperature of the air in the room. So, the temperature remains constant. We try to add more and more water which means that the partial pressure of the water vapor increases and the partial pressure of air decreases, but the mixture pressure remains the same. So, we keep adding more and more water vapor and it appears that there is a maximum amount of water vapor that we can add at the given temperature. So, relative humidity is defined as the ratio of the mole fraction of the water vapor in the given sample to the maximum mole fraction of water vapor that can be present at the same temperature. So, the air at this temperature can only hold so much of water. So, there is a maximum amount of water vapor that the air can hold at this temperature. So, the ratio of Y v over Y v saturated and that pressure and temperature is called relative humidity. So, Y v we may write in terms of the mixture pressure like this and as I said the mixture pressure remains the same. So, when the mixture appears to be saturated the mole fraction of water vapor is a different value it is likely to be higher because we have added more water vapor. So, Y v sat times P is the partial pressure of water vapor at that state. So, the ratio comes out to be P v over P sat of T. Remember once the water vapor amount of water vapor reaches its maximum value then what we can say is we say air is saturated what we actually mean by that is that the partial pressure of water vapor is equal to the saturation pressure corresponding to the temperature. So, although the word saturated is used colloquially it happens to be correct even in an engineering sense. So, when the maximum amount of water is present in the air we say the air is saturated what is precisely meant by that is that the partial pressure of water vapor the amount of water vapor is such that the partial pressure of water vapor is equal to the saturation pressure of water corresponding to that temperature the mixture temperature. So, that is called relative humidity. So, relative humidity 100 percent implies that the air is fully saturated any value less than that we can say the air is not saturated there is room for adding more water. So, if it is too humid so we say the relative humidity is high then you feel sticky. So, 80 percent 90 percent 100 percent you feel sticky if the relative humidity is 20 or 30 percent and the temperature is also in a reasonable range then we feel comfortable. So, relative humidity measures not only the amount of water vapor present, but also the amount that can be present in relation to the temperature. So, it brings in both the effect the amount fraction of amount of water vapor and the temperature. Whereas, the humidity ratio talks only about the amount of water vapor not the temperature of the mixture. So, relative humidity is a very important term that is used in psychrometric applications and also if you listen to weather forecast and say temperature predicted tomorrow is let us say 26 degree Celsius relative humidity 50 percent. So, this is what is meant by relative humidity. Now, let us look at this in this chart let me just clear some of these lines here. So, let us say we have water vapor at 25 degree Celsius and certain partial pressure. Let us say that the partial pressure is less than the maximum value and now if I add water more water vapor to this air while keeping the temperature constant the state of the water vapor moves like this because as I add water it is the partial pressure increases and the state the partial pressure keeps moving like this. So, we keep moving along the isotherm into different isobars because we are keeping the temperature constant we are moving along the isotherm and we can move along the isotherm until we reach this point. What is that this state lies on the saturated vapor line. So, this is the saturated vapor line. So, this state lies on the saturated vapor line we cannot add any more water beyond this point we do the water will condense right back into a liquid. So, this corresponds to phi equal to 100 percent that is a saturated state. So, the partial pressure corresponding to the given state which is P v divided by this pressure which is nothing but the saturation pressure corresponding to 25 degree Celsius. Notice that this is the saturation pressure corresponding to 25 degree Celsius that is called the relative humidity corresponding to this state. So, relative humidity corresponding to this state is P v over P sat of 25 degree Celsius. Another term that is used in connection with the psychrometry is the so called dew point temperature. The dew point temperature is defined simply as the saturation temperature corresponding to the partial pressure of the water vapor. So, we have moist here at let us say 25 degree Celsius and there is a certain amount of water vapor that is partial pressure is P v. So, the saturation temperature corresponding to P v is called the dew point temperature. Now, let us try to look at this physically. So, let us say that we take this moist here which is at 25 degree Celsius and without adding or removing any water let us say that we cool the mixture which means that the partial pressure of the water vapor remains constant. So, we are as opposed to constant temperature process that we looked at in connection with the relative humidity. Now, we are looking at a constant pressure P v constant mixture pressure also constant. So, we are looking at a constant pressure process for the water vapor. So, as I cool this, I am going to reach a certain temperature at which point I reach the saturated vapor line. So, let us take a look at this this line. So, here I start from this state, I start from this state and then at constant pressure I move along this isobar like this until I reach this state point. So, once I reach this state point again it is on the saturated vapor line and if I lower it any further water will begin to condense. So, this temperature the corresponding temperature here this temperature is called the dew point temperature and that is nothing but the saturation temperature corresponding to P v. This is why you see dew or dew drops on grass and leaves in the early in the morning. So, the air contains a certain amount of water vapor in the evening there is no more evaporation. So, that is the maximum amount of vapor that you are going to see. So, as the temperature begins to drop during the night the amount of water vapor remains the same. The temperature begins to drop and then if it drops close to the dew point temperature during the night you will start to see dew drops on leaves and other surfaces. If the amount of water laid in the evening is sufficiently high and the temperature drops sufficiently low during the night then you will definitely see dew early in the morning. So, let us some of some of the things that we have already said as moist air is heated at constant pressure it becomes drier. So, you can see this here. So, as we heat moist air at constant pressure that means you are moving along in this direction. Let me just change the color here. So, if I heat moist air at constant pressure then I am moving along this isobar like this. So, as I keep moving up you can see that it becomes drier because it is distant. So, let us say heat it up to this point it becomes drier because the saturation state corresponding to this lies over here this corresponds to phi equal to 100. So, this is phi equal to 100 for this state. So, as I move up here you can see that here this state is closer to the saturated vapor line here it is far away from the saturated vapor line. So, as I heat air moist air at constant pressure the air becomes drier. As I cool moist air at constant pressure the state gets closer and closer to the saturated vapor line. So, the air becomes more and more humid. The interesting point about this is that I have not added or removed any water vapor. The amount of water vapor remains the same because I am heating at constant pressure. However, the relative humidity changes as I heat it it becomes drier and as I cool it it becomes more humid without any change in the amount of water vapor. So, that is very important. So, relative humidity involves both the amount of water vapor as well as the saturation the amount of water maximum amount that can be present. So, relative humidity brings in both not only the amount of water vapor but the temperature also. So, relative humidity actually brings out the fact that perception of humidity in a colloquial sense depends both on the amount of water vapor as well as the temperature. So, that brings in the effect together. The most important thing is here in this experiment the amount of water vapor remains the same. So, what practical HVAC systems try to do is to heat and cool and humidify and dehumidify air to achieve an ideal combination of temperature and humidity for maximum comfort of the occupants. So, heat the air if required cool the air if required humidify by adding water dehumidify by cooling the air so that the water vapor condenses out. Humidification is done by adding steam to the air dehumidification is done by cooling the air so that the water vapor condenses out. So, this is what HVAC systems do but in order to do this you need to know what the temperature is and also what the amount of water vapor in the air is that is also. So, both these quantities have to be measured and monitored continuously so that the room can be groom or dwelling or automobile can be maintained the interior can be maintained at a comfortable temperature and humidity level and that is what we are going to see next how that is done is what we are going to see next.