 So, just while we are going for psychrometry it is basically the properties of moist air that we are studying and what we realize is that air anywhere is not completely dry it has moisture in it and we do require certain amount of moisture to ensure that you know our skin is proper otherwise the skin rise off and probably all of you know comfort conditions require around 50 percent R H or relative humidity. But, we will now during the course of this lecture try to understand these properties of moist air and to begin we will just draw the T S diagram for water. So, this is the standard T S diagram that everyone knows this is the critical point and we have various constant pressure lines and this region here is the vapor region. So, water obviously as it exists in the atmosphere is in the vapor region and we can say its state is superheated steam at the particular pressure it is at. So, the vapor pressure of water is not one atmosphere it is very very less and it is in a superheated format and in this format here water vapor can be thought of as an ideal gas it is very low pressure reasonably high temperature compared to its boiling point and along with air it forms a good ideal gas mixture air reasonably at one atmosphere can be considered as an ideal gas and these two together can be thought of as a mixture of two ideal gases. And we will apply the ideal gas equation P V is equal to M R T for both dry air and water vapor. So, both of these together constitute moist air and moist air is made up of dry air as well as water vapor and we can think that both of these are ideal gas gases and we can apply the ideal gas equation to both of these. Now, R of course will be different for air and I will call it R dry air and R will be different for water vapor and we will call it R water vapor. So, R for dry air would be just universal gas constant upon molecular weight of dry air, molecular weight of dry air can be assumed to be close to 29 whereas R for water vapor will be R u upon and molecular weight of water vapor or water can be roughly assumed to be 18 it is made up of H 2 O that is 2 H and 1 oxygen. So, this is how we will apply the ideal gas equation to both of these. Now, there are certain properties of moist air that everyone is supposed to know of and these are what are called as specific humidity, view point, relative humidity and then we will have wet bulb temperature, enthalpy and finally, we will draw the psychrometric charge. So, this is what we will follow. So, each of these topics will be discussed from the point of view of water vapor being an ideal gas inside air and you may have seen something called a psychrometric charge which we would not use at all till we come to the last topic. In fact, all our calculations will be done entirely using steam tables and you would be required to use your steam tables continuously and even then when there is a quiz on this topic, we will expect that you will be using only the steam tables for calculations and it is a good habit to know this thoroughly on how to use the steam tables. In fact, I would emphasize that we would tell all our students not to use the psychrometric charge initially because the psychrometric charge is usually made for one atmospheric pressure as the ambient and if the pressure changes then you need a different psychrometric charge which is made at that pressure and normally we would not have so many psychrometric charge, but if you know the barometric pressure as well as if you have the steam tables in your hand, you can do all your calculations without a problem and hence all our calculations will be based entirely on the steam tables. So, let us just start with specific humidity. So, we will see that all calculations are normally based on a per kg basis and this is purely for convenience because it helps us to do our calculations very easily and we will come to how we use this. So, let us start with specific humidity. Specific humidity is nothing but the amount of water vapor per kilogram of dry air or let us say you take a particular volume, you find out how much dry air is there in it and you find out how much water vapor is there in it. Divide the mass of water vapor by the mass of dry air and so you get the amount of water vapor per kilogram of dry air. So, it is on a kg to kg basis. Of course, we will realize that the water vapor is so less, so just talk about kg to kg basis is probably not very good and a lot of times people will express this in grams of water vapor per kilogram of dry air and this is a very common unit that people would normally use, but we will believe as if we are first you know carrying out all our calculations on a kilogram to kilogram basis and then we will go we can always convert it into a gram to kilogram basis and this is purely how the definition is and you will realize that it is better if students you know stick to this definition, it is the original definition for what specific humidity means and now you will use the ideal gas law and see that you come up with some expression which people always try to remember, but there is no need to remember this. So, I will just use p v is equal to m r t or rather m is equal to p v by r t. So, we are taking one particular volume of gas and we will assume that the temperature everywhere is the same and it is what is called as the dry bulb temperature. So, t is equal to same for dry air and water vapor, it is what is called as the dry bulb temperature and same volume is what we consider. So, mass of dry air is the same volume will be just v by t the constant into pressure of dry air upon r of dry air which will be v by t times pressure of dry air times r u by m. So, this is what we would get and if I go ahead pressure of water vapor r of water vapor is just r universal constant upon. So, I will have m is equal to p water vapor upon r water vapor into v by t and this is for water vapor. So, I have now two things m water vapor upon m dry gas dry air is just v by t p water vapor upon r water vapor v by t p dry air. So, this is what I am going to have upon r dry air or we will have in this case p water vapor upon p dry air to r dry air upon r water vapor which would be p water vapor upon p dry air r u by m dry air v by m water vapor and I will just get m water vapor. So, this is what we would get. So, we have taken a constant volume of air moist air at a particular temperature and we are finding out how many kilograms of water vapor are present for 1 kilogram of dry air. So, all we do is in that volume we figure out how much water vapor is there and divided by how much dry air is there in that volume and we just apply the ideal gas law. We just say p v is equal to m r t express m as p v by r t you realize that v and t are constants p is for individual gases and these are thought of as ideal gases. So, p total that is the p barometric pressure is just p water vapor plus p dry air. So, this is just the partial pressures adding up as per Dalton's law for ideal gases and it is believed as if the two are separate ideal gases and they each have their own individual partial pressures and this is all that we are focusing on. And the moment we take the mass ratios we realize that we just have to take mass of water vapor is p v by r t for water vapor and mass of dry air is p v by r t for dry air. And all we get is the pressure ratios and the molecular weight ratios and roughly you will see that this is 18 upon 29 p water vapor upon p dry air. And this I have put roughly because 18 and 29 are just approximately approximations the mass of water vapor is actually 18.01 something and dry air is actually 28.9 something, but roughly once we put these values we should get 0.622 pressure of water vapor pressure of dry air. So, in effect what we have done is that we have taken the basic definition of mass of water vapor upon mass of dry air which is what you must remember just put in the ideal gas law by substituting mass as p v by r t and get an expression in terms of molecular weights and pressure ratios and molecular weights are fixed for water vapor and air. So, we just take the ratio it is 0.622 and we just say it is p v by p d a. So, we give this specific humidity a symbol is 0.622 p water vapor upon p dry air and we can write it as p water vapor upon p total minus p water vapor. This is because p dry air is p total minus p water vapor. So, this is the expression we get for specific humidity, but do not forget omega is just purely m water vapor upon m dry air and we used ideal gas law to get this and people just often try to remember this expression on the top, but it is preferable they remember the original definition and know that you just have to use the ideal gas law and this is something that probably must be emphasized many times rather than trying to remember a formula like 0.622 p water vapor upon p p minus. So, what we will do right now is from now onwards instead of p water vapor I will be using the symbol p v and for p total I will just be using p and for p dry air I will just be using p a. So, slightly shorter version so that we can move faster. So, this is in effect what we will be trying to do. So, we have finished the first definition for what the specific humidity should be and I think I have emphasized enough that we must ensure that the students remember only the primary definition and then the use of the first sorry the use of the ideal gas law. So, now let us go to dew point temperature. So, again it is best to draw the T S diagram and explain to students where water vapor is lying. So, there is a pressure line here this is let us say your current temperature. So, T ambient also called as dry bulk temperature. So, this is where we are at a particular temperature and this is where steam is on this partial vapor pressure line here. So, if this is where we are you realize that we can start cooling if we start cooling then the partial vapor pressure of water vapor remains the same and we move along a constant pressure line along this or as you go lower and lower in temperature until we reach a point that we touch the vapor dome and this is where we are just going to start forming some amount of water that is liquid water. So, because here this is completely dry saturated steam and we were at superheated state and we started cooling it down at constant pressure and we moved along this line till we just reach dry saturated point. After this if we start cooling or we start removing heat from this it will start condensing out and it will just go along a constant temperature line here and this point where at a particular vapor pressure it starts condensing this is what is called as the dew point temperature and you realize that the dew point temperature is just the saturation temperature at the particular vapor pressure. So, all you have to do is actually take your steam tables figure out for a particular pressure what is the saturation temperature and you know your dew point temperature. So, that is as fast as you can do it. So, just look at your steam tables if you know your PV you know your dew point temperature or in a reverse fashion if someone tells you what the dew point temperature is then all you have to do is look at that temperature in the steam tables. So, in the temperature table part of it and look at what the saturation pressure is. So, whatever the saturation pressure is that is going to be PV. So, if DPT is given look P sat for DPT that will be PV. Obviously, if your temperature right now is the same as the dew point temperature then PV is P sat otherwise you will realize that at that temperature here if I go here again let me draw the T S diagram. So, you are here this is your temperature at which you are this is your dew point temperature if your temperature is. So, this is P sat at DPT this is the same as this PV because it is the same pressure line. So, if your temperature existing temperature T is here then your existing temperature is the same as the dew point temperature and sometimes you realize that at night when the temperature dips it reaches the dew point temperature and you see dew start forming then that is because the temperature has dropped down along this line of constant pressure and you have reached the dew point temperature. Now, of course you see that at this temperature I could have tried to fill in water and I can still do it and move like this that is because there are many pressure lines here and you realize that there is one pressure line here and which just goes up like this and you realize this point is nothing but P sat at the temperature as a ambient temperature or dry bulb temperature. So, we have two things now we have T sat at dry bulb temperature and we have T sat at PV. So, T sat at PV is the same as T sat at PV. So, PV is nothing but the dew point temperature DPT and P sat at a particular temperature is the pressure or the partial vapor pressure that we can reach by continuously putting in more and more water vapor into the moist air system. So, as long as your dry bulb temperature is much above the dew point temperature you can go on filling water vapor into the system your humidity goes on increasing that is because we will be moving along this line now the temperature is the same, but we are adding more and more water vapor to the system that means we go on passing lines of higher and higher PV here. So, each time we go to a higher PV line our specific humidity increases and then we put in more water vapor we move to a higher PV line our specific humidity increases and so on till we reach here. So, this is when you can no longer put water vapor in because now it will start condensing out and this is the maximum water vapor you can put in at that particular temperature. Of course, if you reach a higher temperature you can put in more, but here you will reach this and this is what would be called as the saturation point for that or the saturation pressure for that temperature. And so you realize that that is this P sat at your dry bulb temperature and corresponding to this I will have what is we can call as omega sat let me just call it as omega s that would be m sat. So, we will call it m sat upon m dry air and you will realize that this would be just 0.622 PV sat upon P dry air or this would be just 0.622 PV sat upon P minus P. So, this is omega s. So, we can define something called as the degree of saturation and this would be just omega upon omega s and this is just the ratio of what your omega is right now with a current PV. So, this depends on PV and this is a function of PV sat both at existing temperature. So, basically PV of course, will be the current PV, but PV sat will depend on the existing temperature. So, this is what is called as the degree of saturation. So, finally, we have again let me keep on drawing this diagram so that people do not forget it. This is one line we are here this is the temperature we are existing we are here. I can move like this along constant pressure line till I reach a temperature here this is called d P T this is d B T and this is P sat at d B T and this is T sat at PV. So, if I move along the constant pressure line and cool my moisture system I will reach the dew point or I will move along the constant temperature line and go on adding more and more moisture. So, that I move to higher and higher PV values till I reach P sat I will reach something called as omega sat or the specific humidity at full saturation and then I can define a degree of saturation where my omega is here I take the ratio of this omega to whatever omega I will get here if I had reached saturation. Obviously, if we have put in as much moisture as possible and reached P sat and if this is the current state of moist air then the dew point temperature is the same as the dry bulb temperature because you cannot cool any longer once you have reached maximum saturation the moment you start cooling you are already condensing. So, if you are fully saturated then your dew point temperature is the same as the dry bulb temperature it cannot be lower else your dew point temperature is always going to be less than the dry bulb temperature and at the limit it will be the same as the dry bulb temperature. So, this is up to what we have for specific humidity dew point temperature and degree of saturation. So, the next topic that we cover is what is called as relative humidity and again it is best to stick to the definition it is just mass of water vapor to what you can have at saturation. So, it is the ratio of masses of vapor existing to what you can put maximum when you have reached your saturation condition. So, again you can just use p v is equal to m r t and now both of these equations we are going to use only for vapor because both the numerator and denominator are only for vapor. So, r is the same. So, m is equal to p v by r t. So, at the same temperature whatever saturation we can reach that is m v sat. So, t is the same r is the same because we are talking only of water vapor right now. So, it is the r for water vapor and we are talking of a particular volume. So, we realize that if we take this ratio all these other three terms are constants and the ratios of m v upon m v sat is just p v upon p v sat. So, again I have used the regular definition for what relative humidity is it is the mass of water vapor right now to the mass of water vapor that you can put when you have reached the saturation condition. Obviously, m v sat is going to be much higher than m v and this is what we get and if I just use the ideal gas law you will realize that the ratios of masses is nothing but the ratios of the partial vapor pressures. So, this is what we get and this is called relative humidity and it is usually expressed as a percentage. So, what we do is r h is equal to p v upon p v sat multiplied by 100 else the ratio would have been a number less than 1 the moment you multiplied by 100 now it is like a percentage and we will get back to the T s diagram and see what we are trying to do here again I will draw the T s diagram. So, we are here as we said in the superheated state this is your dry bulb temperature this is your dew point temperature and this is p sat this is the p sat line this is the p sat line at T. So, this is your temperature here and this is your saturation pressure at that temperature of course, here if you start heating you will go higher, but this is your saturation pressure at this temperature and this is what you can reach maximum as you start putting in more and more water vapor and this is your current p v line and all we are doing is taking a ratio of this pressure to this pressure. So, r h is just a ratio of p v to p v sat and then of course, we are multiplying it by 100 just to express it in terms of percentages and that is what we are trying to do else you realize that this is what the ratio is the degree of saturation was just omega upon omega sat. So, you realize that omega is calculated with this p v and omega sat is with this p v and r h is just the ratios of p v, whereas omega sat involves p p also. So, for example, I will just write r h is p v by p sat and degree of saturation this we have already figured out. So, this p v and this p sat are the same here and obviously, these two are related and we can express the degree of saturation in terms of the r h if we want, but it is very common especially when weather reports are given to talk mostly about the dry bulb temperature and the relative humidity. So, you must always notice that the moist air conditions are always given in terms of temperature and relative humidity very rarely do people talk in terms of degree of saturation and of course, when people are who are dealing with psychrometry and air conditioning processes you will realize that they will consider omega very often because omega is extremely useful to do all the calculations and relative humidity just tells you how far we are away from saturation. So, that is something that people know that when relative humidity is close to 100 it feels extremely sticky and you the air is full of moisture whereas, when relative humidity is very less it means that we are very far away from saturation and the air is very dry and you can feel the dry air. So, it gives to the common people something that they can relate to as to how dry the air is, but for all calculation purposes whenever we are talking of air conditioning etcetera. We will realize that specific humidity is the quantity we will often look at because we are always trying to get a balance between how much water vapor is existing in the current moist air system and that is very useful for our calculations else these are the two quantities which are normally given apart from P that is the total pressure. So, once we have covered this. So, now we can go to the enthalpy of moist air and again just for convenience you will notice that even for the moist air system the enthalpy is defined on a per kg basis of dry air and this is again for convenience. So, we take 1 kg of dry air this implies that there are omega k g's of moisture this is because omega is just mass of vapor upon mass of dry air. So, per kg of dry air there are omega k g's of moisture available and we write the enthalpy in terms of per kg of dry air. So, let me get back here if I want to define enthalpy we will normally have to have some standard as to or some reference point as to where we will put our enthalpy 0 and most air conditioning and the refrigerator systems as far as when they are dealing with moist air they will say that let us put the reference enthalpy for dry air as 0 when the temperature is 0 degree centigrade this is for dry air. So, if we assume that we are living in a place where the temperature is always going to be higher than 0 degree centigrade then h assuming that C p is constant throughout the temperature range we are talking about h would be just T minus T reference and T reference is just 0 degrees. So, just for ease it we will just write it as C p T where it is assumed that T rep is equal to 0. So, we are assigning an absolute value or a number assigning a number based on h is equal to 0 at T is equal to 0. This is how we are assigning a number for dry air. So, once we get this so you if you remember you know for air C p would be just roughly around 1.005 kilo joules roughly and this is something you can use using your ideal gas law and mass of water vapor you get your R for air and then you get your C p and C v for air. So, this is for air now if I go for moisture what we say is that reference h is equal to 0 when water is in saturated liquid state. So, this is what we say is h is equal to 0. So, and this is how most steam tables would be made. Obviously, you realize that when steam tables are made it is actually at 0.01 degrees that this is normally put as 0 and what we have is that if we. So, again let me draw the state of water vapor we are here at the dry per temperature. Now, one thing which is very easy is something what you can do is because I know the temperature and the partial vapor pressure all I need to do is go to the steam tables and get h here read it from the superheated section this is the easiest thing that you can do. Now, what else we can do is that you know as we said that moisture or you know I would say water vapor behaves as an ideal gas and one of the things that we will see h will be nearly a function of only temperature and not pressure and we will see that if you look up your steam tables you will realize that this is true and the way to do it is just simple you I will just draw the T S diagram again that I keep drawing now again and again you take this. So, this is where we are at a particular dry bulb temperature. So, method one is just look up enthalpy using superheated tables directly look up this enthalpy second is at the same temperature here I will claim that the enthalpy here is the same as the enthalpy here it is a function only of temperature you realize that this pressure line is different, but we are talking about really low pressures and the fact that water vapor behaves as an ideal gas and we will say that this enthalpy is nearly the same as this enthalpy and this is something that we will try out often and you one exercise that you should do before we get to our afternoon classes is that you just take up some vapor pressure which is you know common in moisture get the enthalpy from the superheated tables get the enthalpy for saturated dry saturated vapor at the same temperature here. So, this is a different vapor pressure line. So, get H sat vapor at T and something which is otherwise done often is we say that we were 0 here sorry this is a particular pressure line. So, we can move along the pressure line for 0 to 0 degrees really the pressure line for 0 degrees does not exist because we are it is below the triple line and you can actually move along the triple line which is at 0.01 degrees it does not matter 0.01 is pretty small compared to 0. So, I will just for the sake of argument say that we are moving along the 0 degrees line here. So, now we have many many I will this is my 0 degree line or rather the triple line this is my P V line here. So, this is T this is S. So, I am actually on this line here and this is the point we are at. So, we said method one was read this out of the steam table method two was get this and I say method three is you can get this from the steam tables or what people do often is they say start from 0 here this is our reference point anyway. So, we know it is 0 enthalpy is 0. So, if I move along this this is now a standard number it is 2 5 0 1 because we have fixed the temperature and pressure. So, this H F G is fixed. So, if I go from here to here H G would be just 2 5 0 1 kilo joule per kg. So, this is what we will get here and if I start moving here I will say this is a vapor and this difference here of enthalpy delta H it just C P vapor into delta T. So, C P vapor into delta T is equal to delta T is C P D minus 0 that is because this is the 0 degree line. So, what we are doing is basically going for convenience. So, the most accurate way would have just been method one which is look at the steam tables and find out your enthalpy, but we are suggesting other methods that is you go to saturated temperature sorry saturated condition at that temperature and find out H again you will require the steam tables, but we are suggesting a simpler way where you do not have to go to the steam tables. You just say that we had decided that enthalpy was 0 at and this is how the steam tables will operate that you have enthalpy reference enthalpy 0 at liquid conditions at 0 and you just move along till you have reached saturated vapor conditions. You know that you have changed the fixed number and 2 5 0 1 is what you get and from there on if I increase the temperature I will increase my enthalpy as C P delta T as any other gas and this C P value is roughly 1.88 kilo joule per kg Kelvin and because we have chosen 0.8 kilo joule per kg Kelvin 0 degrees this is just T. Again we just write it as T here and finally you see that we have come up with a third method which is to get the enthalpy which is move along this line and take C P delta T here and since delta T is just T minus 0 we just take it as T and you can choose method 1, you can choose method 2, you can choose method 3. Method 1 is obviously the most accurate. In method 1 what actually is happening is that we have gone from 0 degrees to this temperature corresponding to the saturation temperature of T v as a liquid. So what we have done is we have gone as C P liquid times T minus 0 to go till this temperature then we have added h f g at this pressure and then we have taken C P delta T here that is how we get this point really and this is the most accurate way to go ahead. But we have chosen seen two other method and you can check that either of these three will give you values which are very very close to each other and just for simplification people will often use only this method 3 because you do not require to get to the steam table. But in general if you stick to one consistent method there is no problem because finally we will be dealing in delta h s and if you choose one method then the errors more or less any small error that is there in getting the enthalpy using method 3 it just is the same in all the in all calculations and it just cancels off. So either you use method 1 consistently which means you always use the steam tables or you use method 3 and this is something which is done very often. So in many calculations people will just use method 3 but just for convincing yourself you must look at the steam tables and figure out these three using these three methods what the h is and you will realize that you know so these are we are on three different pressure lines here you will realize that this is the actual pressure line this is p sat at t of course this is not really 0 degree 0.01 degrees. So this is the p triple really okay is the triple point pressure and you are moving along that and you realize that you know these are three methods and you would see that it is the same irrespective of whatever you have is hardly differing by a small number after the decimal point. So we will just prefer to use method 3. So once we have decided what to do for dry air okay and water vapor okay so enthalpy or specific enthalpy is just c p air into t this is the dry air part plus omega into c p vapor times t plus 2 phi 0 1 okay so this is the water vapor enthalpy okay. So we have taken 1 kg of dry air figured out that there are omega kg's of water vapor in it the dry air part has this enthalpy per kg and the moisture has this much enthalpy okay you have multiplied it by omega and you realize this is not a specific enthalpy really for the moisture because this is not per kilogram of the moisture in fact this whole enthalpy here is actually for 1 plus omega kilograms of moisture okay so this is actually for 1 kilogram of dry air and 1 plus omega kilogram of moisture but we will stick to writing the symbol as if it is for specific enthalpy but remember it is enthalpy per kilogram of dry air and this is done purely for convenience because you will see later all our calculations become extremely easy if you do everything in per kilogram of dry air basis and that is why we stick to this convention but overall you have gotten this formula okay what you really have is actually h dry air plus h water vapor okay which is h dry air I should not say h water vapor it should be omega times h water vapor okay and this sorry let me write in this is equal to C P T for dry air plus omega times P P T so this is what we have done