 Once we have gotten this edge, we will now use it later on in calculations, but now we move on to what is called as the wet bulb temperature. So, this is opposed to what is normally called as a dry bulb temperature. So, the dry bulb temperature is nothing but the ambient temperature and this whole concept of a bulb comes in because the regular thermometers have a bulb at the bottom where mercury is stored and if you just take the temperature as it is, it is the whole thermometer is dry and that is why it is just called the dry bulb temperature. And one method of getting the wet bulb temperature or the so called wet bulb temperature is just to put a wet cloth or a wet wick around the thermometer. So, basically you have this thermometer here and you will tie a cloth here, this is wet. So, in general you are saying that the bulb is wet and really it is the temperature seen by the bulb is what the thermometer will display. Now, you may say if I just you know put a wet cloth there when the temperature be different, not really if there is an equilibrium and a steady state, then the temperature of the cloth will not be really different from what is the ambient temperature. But what we do is we have a draft of air flying over this or you can gently spin this thermometer and this is what is normally done people just spin this thermometer. So, roughly there is some kind of flow of air which is going over this thermometer and what is assumed to happen and this is something that you have seen often. This is again I will just go to the T S diagram so that again there is straight forward as to what is going on. That means, this is our P V 9, this is the L V R, this is the dew point temperature, this is P sat at T and this is P sat at T. So, you come like this, you come to dew point temperature, you come like this, you get to saturation pressure at the same temperature. Now, let us say that and this is some phenomenon that all of you would have seen in dry climate is that you actually start putting moisture into the room and you use something which is called cooler and what the cooler does is that it has water and it just sprays water vapor into the air and what happens really is that the water vapor evaporates and the air is dry and hence it can absorb moisture and the energy required for evaporation comes from the air itself and the temperature drops down that is because the air has lost energy in trying to evaporate the air and this is the principle that is used in a regular cooler and it is used in hot and dry climate where you can actually put in water and the climate is dry, it will have the air will absorb moisture and as it loses energy to evaporate the air sorry to evaporate the moisture it will the room will start cooling down. Obviously, this would not work when the climate is moist or it is very heavily humid and this is because the moist air has very less capacity to absorb moisture, but let us see it from the point of view of what the wet bulb temperature is and what is really happening is that as let us say that the air is flowing over the thermometer let me again go back here. So, the air is flowing over this thermometer and it has a particular temperature and it is the dry bulb temperature because that is the temperature that would have been measured by the thermometer, it has a particular value of omega which corresponds to p v which corresponds to particular p v and of course corresponding to all of this I can always calculate the R H that is because for the dry bulb temperature I know what is the saturation directly from the steam table I know what is p v I just take the ratio I will get the R H. So, basically the state of moist air is defined and as long as the R H is very less it is dry it can absorb moisture what is actually happening is that once this air starts blowing over this thermometer it will start absorbing moisture from this wet cloth here or the wet wick and that is because it can absorb water vapor it has the capacity to absorb and initially so this water which is on the cloth is really in just saturated liquid at the temperature. So, we need to evaporate it to get it into the air and the energy for evaporation has to come from somewhere and energy will come from both the air as well as the cloth I mean some energy is picked from both places what this means is that if the energy is lost from the air then the temperature of air drops down if the energy is lost from the wick then the temperature of the wick drops down and hence both temperatures drop down. So, if I look at this diagram here as I told you there are various pressure lines that I can keep on drawing higher and higher pressure and finally this is the saturation pressure. So, now when the moist air absorbs water or water vapor obviously PV is going to increase that is because now you have put in more water vapor than originally there was. So, if you were here you can move to this next line here. So, you have moved to a higher pressure line these are higher and higher pressures as you go like this. So, you move to a higher pressure line, but at the same time because you have lost energy your temperature is dropping. So, you will go like this rather than horizontally and you would not move like this along this because it is not the same pressure line you have moved to a higher pressure line as well as your temperature has dropped. Now, let us say that you put in more water vapor you will move still like this you put in more water vapor you will still move like this until you reach here. So, now you have reached the state where you can no longer put water vapor into the air and that is because you have reached such a temperature and such an omega that you have reached full saturation at that temperature. So, this is some temperature that you have reached which is in between these two points which is the dry bulb and the dew point temperature and you have moved to a higher vapor pressure line than the existing vapor pressure line, but you have not moved to the saturation pressure at the T that is because you have reached to a saturation pressure which is lower than the dry bulb temperature. So, you have not reached this pressure line you have reached the lower pressure line here this corresponds to P sat at some lower temperature than d B T, but definitely higher than dew point temperature. So, this is the point you have reached at this point and you no longer you can put in a moisture into the air and it has become saturated at a particular temperature and you reach finally steady state. So, now what happens is once steady state is reached what normally people assume after this I reach here the air here is let us say T 2 where T 2 is just this one this temperature is T 2. So, I have reached T 2 and I have reached an omega 2 where omega 2 is saturation omega at T 2 and P v is P v saturated at T 2. So, this is what we have reached and what is assumed is that further the temperature cannot drop for the moist air and as it is coming here it has T 1 or this d B T and any more and what happens is now once the air has passed over this this temperature also has reached the wick temperature also has reached T 2 and as fresh air come the temperature of the wick cannot drop any further because that is the equilibrium T at which the vapor is sorry the air is going to leave when it is passes over the sorry over the thermometer and what we say is that entirely the energy required to evaporate water vapor is coming from the air itself. So, anything any air which is coming here water vapor is going to dry sorry water is going to evaporate from this wick and join into this moist air, but the energy for evaporation of this entire water vapor is going to come from this air itself and no longer the temperature of the wick is going to drop. So, the wick has reached some kind of a steady state temperature and the air is gaining moisture or it is evaporating moisture from the wick purely using its own energy its temperature is supposed to drop down to T 2 which is the steady state temperature and the wick is showing a lower temperature than T 1 it is supposed to be an equilibrium temperature with T 2 and it is supposed to be T 2. So, the wick finally shows this temperature T 2 and this temperature T 2 is what is called as the wet bulb temperature corresponding to this P v and T. Now, of course you realize that if I had started at a higher T, but with the same on the same P v line if I started at higher T I may reach at some different W B T or at the same T if I started at a higher pressure line here I will reach some other W B T. So, for a particular T and a particular P v there will be a particular W B T that I will reach. So, this is T 2 is what is called as the wet bulb temperature or W B T. So, one thing that you must realize is that this is not something which is where you can exactly say what is completely happening to the state of the air. This is the steady state situation. So, in the steady state situation definitely the thermometer temperature is not dropping. So, that has in fact what temperature you are measuring actually is only the thermometer temperature it is not the temperature of the air which is leaving. So, we are only making an assumption here that the temperature of the air which is leaving is actually T 2. So, the air may not really have reached T 2 in the steady state you would reach a particular temperature and that is what you are measuring and that is what is called as the wet bulb temperature. And you realize that you know as the air is passing you know there is no way to know after the air has passed over the thermometer what its state is really, but we will assume that it has reached a saturated state and this is the temperature. So, this is in contrast to something it is called as adiabatic wet bulb temperature. So, what is the adiabatic wet bulb temperature? So, we can think of an adiabatic situation here where air is entering at a particular T that is the d B T and omega. So, there will be one temperature. So, if I keep here water at a particular T star, there is one temperature where this T star can be where if I keep the water at T star this air will go out at T star and omega is equal to omega star is equal to saturation omega at T star and entirely adiabatic. So, that means no energy is obtained from outside entirely the energy is captured. So, if I just add up the enthalpy here and here that will give me the enthalpy of the outgoing moist air and this is an entirely thermodynamic process. So, here we are saying that there will be a particular T star if I keep the water at that or the saturated liquid at that T star then I will get adiabatically the moist air should reach the same T star and omega should reach the saturation omega at that T star. So, this is what is called as the adiabatic wet bulb temperature. So, this is of course, a situation which we can imagine that this is what can happen adiabatically. But if you look at this situation here sorry where this thermometer was what we really measured was only the temperature of the wet bulb. There is no real guarantee that we achieved the same temperature T at for the moist air which exited and this is a totally empirical situation. There is no thought about what the mass of the water vapor is how much enthalpy is being balanced how much energy is picked from the surrounding. We are just saying that in steady state the thermometer will reach a particular temperature and you know we have assumed some kind of equilibrium and assume that the leaving moist air is at T 2 and at saturated condition at T 2. And it turns out that if I can give enough energy from the air and the water vapor diffuses fast enough. So, that whatever from wherever you had picked up the energy from the amount of air that you had picked up the energy if the water vapor can diffuse fast and occupy that same amount that is the same situation here. So, what is happening here is that air is entering here and we are assuming that water vapor is you know getting into this and this has you know mixed with this moist air and the entire portion here is leaving with T star and omega star. This is a condition that we have you know made specifically using a particular control volume here and this is a totally thermodynamic situation where I can just do an enthalpy balance. I cannot do an enthalpy balance there at the thermometer that is because I do not know where the H is being picked from, but if you can pick up things fast enough from the wick and the same amount of moisture is distributed in the amount of air from where the energy was picked up then there is some guarantee that the temperature that you reach for the moist air is the same as the adiabatic weather. This is what really happens for the moist air condition that we have it is pretty close by the wet bulb temperature that we measure using the wet bulb method is more or less the same as what we get if we assume an adiabatic situation like this and you will see that the calculations are nearly the same, but irrespective of this in most cases people will not really use the adiabatic method to get the wet bulb temperature they will use some kind of an empirical relation. So, there are empirical relations that will relate wet bulb temperature and T and P V. So, T and P V is what the entering moist air was there is a particular W B T corresponding to this T and P V and we need to find it out and for the method that we use because it is not completely an adiabatic situation we will use only empirical relations and one of the standard empirical relation is what is called as the carrier equation. So, you recognize the name from carrier air conditioners. So, this is the person who whose name this equation is attached and I will just write down the carrier equation for you T dash T minus T dash 1.8 you will notice that in this equation there is often this 1.8 and 32 coming because this equation carrier was an American and all equations are written in Fahrenheit term T is temperature in degree Celsius. So, this T actually is D B T, T dash is W B T and P V dash is saturation T V at T dash. So, what we get is that if I get the W B T. So, I use one thermometer I get the dry bulb temperature. Now, if I use this wet bulb method I will get the wet bulb temperature. So, I know T and I know T dash I know what is the pressure right now and if I subtract from it this P V dash which is the saturation vapor pressure at T dash. So, I use this theme table and get the P V dash or the saturation pressure is the temperature that I have measured so at the W B T. So, and this is also the same saturation pressure. So, if I put plug it in here then I will get the saturation vapor pressure that right now I have. So, it is the quantity that normally I could not measure so easily. So, specific humidity and P V are not something that we can measure very easily. What we can definitely measure very easily are the barometric pressure and the dry bulb temperature which is very easy you just put a thermometer in air whatever you get is a dry bulb temperature. So, normally if I want the state of air then I require this third quantity to get my P V or omega I cannot measure P V or omega. So, either I measure the wet bulb temperature or I measure the dew point temperature and what is exactly happening is that again let me draw this T S diagram so that things are clear. So, we are here we have moved along if we move along this line we get the dew point temperature. So, what we know for sure is this temperature here this is the D B T and I know the total pressure, but I do not know what this pressure is. One thing that I can do is take a vessel and start putting cold water in it. So, if I put let us say cold water which is lower than T I should just see if water is condensing outside the vessel. If not what you do is you put in ice cubes into this vessel and measure its temperature. And you see if water condenses outside this vessel if it does not you add more ice cubes and you continue this process still you see some condensation outside the vessel. So, you realize that at this point you have started condensing water vapor from the outside air and this is what is corresponding to the dew point temperature, but this is slightly tricky it can, but you can do it you can get the dew point temperature in this fashion. So, if I know the dew point temperature I immediately know what is P V because it is just P V is just the saturation pressure at the dew point temperature. So, if I know P V I get omega straight forward and then I can do all my calculation. So, the whole idea is to somehow get omega because that is what is to be used in all air conditioning calculation and if I want to know omega I need P V and that is why we need that. So, I can use the dew point temperature to get my omega or I can get use the wet bulb temperature. So, the wet bulb temperature is somewhere here and this is P dash V this is P dash or the wet bulb temperature. So, if I know what is the wet bulb temperature I can go to the steam tables and get this P dash V. So, if I go to the previous equation here I have measured P the dry bulb temperature. So, this is the dry bulb temperature I have measured the wet bulb temperature using the wet bulb technique that is P dash and P dash V is just my saturation pressure at P dash if I just plug it in I will get my P V. So, this is the other method here to get my P V here. So, this P V is being related to this P V and that is what that carrier equation is doing just an empirical relationship between P V and P V dash using D B T and W B T and that is what we do and get our P V. Once we get our P V omega is known and we can do all our calculations and this is how we get to our property. So, finally, if we want to know either we should know P that is P total P. So, this is P total this is dry bulb temperature and we should know dew point temperature or we should know P T and wet bulb temperature either of this way this will give me P V that is because P V is just P sat at dew point temperature this will also give me P V because I can use the carrier equation to get P V and once P V is known omega is known H is known my state of moist air is known and I can just go ahead and do all my calculations and this is what is done normally. Of course, you realize that in certain situations let us say you know P V and you do not know what P is P dash is then you know there is for there for a particular T dash there is a particular P V dash and you may have to do trial and error. So, for example, I know T and I know P V you will have to do trial and error to get your T dash. Now, in this equation specifically because we have written in terms such that we have to substitute temperature in terms of Celsius. So, this is in Celsius this is in Celsius P can be in any consistent unit. So, either you can use for all of these pressures Pascal's or you can use bar or you can use millimeters of mercury, but use consistent units as long as these units are the same you will get P V in the same units as P or P dash because that is how this equation is written out. So, P should be in some consistent unit. So, once we have done this so this is what we require is what we have said. So, now we will get to the psychrometric chart and see what this is all about. So, the psychrometric chart if you need to draw it you will have to assume an ambient pressure because the chart is made for a particular pressure and the regular charts that you have are made for an ambient pressure of one atmosphere and in all textbooks you will see this chart available. You will realize that if the ambient pressure changes you will have to remake this chart. So, it is not a wise idea to use this chart everywhere unless you are at the same place and that is why this emphasis on using the steam table because to do all the calculations that we needed to do the steam tables were enough apart from the ideal gas equation all that we really required is the steam table. So, it is not a good habit let us say in the thermo course to use the psychrometric chart so often, but the students must be told about the psychrometric chart. So, in a later course if they do refrigeration and air conditioning this is where it is used heavily and it is much faster to do the calculations once you have a psychrometric chart. So, we just see what the psychrometric chart is and really there are many forms of psychrometric chart. The most standard one uses the dry bulb temperature on the x axis and the omega or the specific humidity on the y axis and it is drawn such that the y axis is drawn on the right it is it is just a standard connect you could have drawn it the other way around without much problem and this normally is in degree Celsius I mean this is in this part of the world it will be in degree Celsius if you go to the USA you will see things are drawn in degrees Fahrenheit and omega would normally be given as grams water vapor upon kg dry air. So, not kg to kg basis because I said the water vapor is very small in quantity and it is better to express it in terms of grams of water vapor per kilogram of dry air. So, the first thing that we can think of here is what should we now plot on this. So, we have put the dry bulb temperature and the wet bulb temperature. So, the normal rain I mean for countries that are here is to plot the dry bulb temperature from 0 degrees centigrade to around 50 degrees. So, we will assume that our real harsh deserts are around 50 degrees and we are rarely going below the freezing point and this is what is roughly plotted. So, what we can do first is plot what is called as the saturation line. So, what is the saturation line? So, you realize from any of these previous graphs that we had that if I have a particular temperature I will have for the first time for that temperature a saturation line or saturation pressure line going through it and there is a saturation omega corresponding to that temperature. So, though the temperature is here, this is 3 v and this is p sat for one particular temperature here corresponding to this temperature this is p sat and this is omega sat for that particular temperature. So, if I choose a particular temperature I can get p v sat for that temperature using the steam table. If I get p v sat I can calculate omega is just 0.622 I mean as I said it is better if students stick to the original formula of mass of water vapor upon mass of dry air, but now I will just write the final formula p v sat upon p dry air and this is omega sat. So, p dry air of course is depending on p minus p v sat and you realize that this is where the barometric pressure is coming in and p if p changes your omega sat will change because p v sat for a particular temperature is the same. I just take the steam table I open it I get the saturation pressure at a particular temperature, but the omega sat will differ based on the ambient pressure that is because p dry air will change is the ambient pressure changes and so if I change the ambient pressure my denominator will change and my omega sat will change. So, it does not mean that if I have a p v sat I will have a corresponding omega sat the omega sat will depend on p v sat as well as the ambient pressure. So, let us assume that we are having the ambient pressure as 1 atmosphere. So, this is what is the standard quantity at mean sea level. So, if I choose a particular temperature I will get an omega sat. So, let us say this is 25 degrees I will get an omega here. So, this is omega sat and this is for this temperature. Obviously, at a lower temperature my saturation pressure would be lower which means omega sat also would be lower I would be somewhere here and at a same lower temperature somewhere here. If I go to higher temperature my saturation vapor pressure is higher I will reach higher omega saturation values and hence I will just draw a line through those points like this. So, this is the line omega sat and obviously you realize that at a particular dry bulb temperature I cannot have an omega which is higher than this line because it is beyond my saturation pressure for that line I can no longer hold water and this is also what is called as the 100 percent relative humidity line which is pretty obvious that if I go here this point is p v sat and this is also the saturation vapor pressure. So, at this point if I take the ratio of p v to p v sat it is 100 percent and what I get is 100 percent relative humidity whenever my omega is saturated omega. So, if I go here this line I can also label as r h 100. So, this is what I do so we drew what was called the 100 percent relative humidity curve and all we needed was just use the steam table get the p sat at a particular temperature and get the omega sat plot put the point and then choose another temperature get omega sat choose another temperature get omega sat and so on and then just draw curve through all those points and that is what is called the saturation line and it is also the 100 percent omega line. What next? So, next what you can draw is relative humidity line for other relative humidity. So, for example, I need 90 percent relative humidity. So, you realize it is very straight forward if I know what is p v sat then relative humidity is just p v upon p v sat because this is what our definition was. So, I choose a particular temperature which means I know p v sat and let us say I want the 90 degrees relative humidity line that means this is already 0.9. That means my p v is just 0.9 times p v sat. So, if I use this I will get a particular omega because now I will not plot omega sat I will just draw omega at 0.9 which means here I will put 0.9 times p v sat. So, if I get put that I will get omega for 0.9 r h. Now what I will do is I will just vary my temperature every time I will get p v sat I know this is 0.9 I will get p v I will put here and get an omega and obviously you realize that let us say I am at 25 degrees then 0.9 would be somewhere here I will get an omega which is lower than omega sat. Similarly, I will get other points here and I can draw a curve through all those points and this would be a 90 percent humidity line. Now, I can change the r h to 0.8, 0.7 and people would normally draw for 10 percent, 20 percent, 30 percent. So, they will draw many here 0 percent r h is the same as 0 specific humidity because the vapor pressure is 0 it is completely dry. So, this line is actually of course the 0 r h line or it is also the 0 omega line, but all these curves will look like this. You will start flattening out here till I reach to 0 r. So, you will have r h decreasing. So, 100 percent 90, 80 so on till you reach 0 here. So, you can draw various r h lines typically you will get for you know 100, 90, 80, 70 and so on till 0. So, these are the relative humidity lines. So, what next we can have lines for constant specific volume. So, again you must realize that as with all quantities specific volume is also defined on a per kg basis for dry air. So, if I have one kg of dry air it will have omega kg's of water vapor, but this is very straight forward if I just put p v is equal to m r t where this is a r is for dry air m is 1 kg then volume is just r t upon p dry air and this is r dry air. And it is the same volume in which omega kg of water vapor also exists, but this is the volume that you are looking for. So, you realize that if I want to draw specific volume lines then if I know the temperature r is known so all I need is p d a and p d a is just p minus p v. So, if I choose a particular p I will get p minus p v is equal to r t by v. So, if I choose a particular specific volume so this is v is fixed. So, just like I fixed 100 percent r h I will say I will fix my specific volume and I will vary my temperature. Now, if I vary my temperature you will see that this quantity has to vary p is the same so p v will keep on varying. So, for every t for a fixed v for every t I will get some p v and once p v is known omega is known. So, once that is done you will get specific or constant specific volume line. So, all you have to do is choose a particular value of a specific volume put it here get your p v if you know your p v you will get your omega. And for that same specific volume here let me not draw the other r h line p minus r t by v and omega by v. So, omega is just 0.622 p v upon p minus p v and I just substitute this p minus r t by v is this one and p minus p v is just r t by v. So, if I just go here get omega 0.622 by r t is what we get. So, you will see that in general if I change the temperature my omega should vary as roughly by 1 by t it should be some kind of a hyperbolic curve, but it turns out that in this section is nearly straight lines and I will just see curve like this for constant volume. So, if I fix the volume as I change the temperature I will get constant. So, I will just plot the omega and I will get curve like this. So, this is specific volume curve and then we can draw specific enthalpy curve what we have is h as we wrote the final expression c p a t plus omega times c p vapor t plus 2 5 0 1. So, if I fix my h it is pretty obvious that if I fix an h all I have to do is vary t. So, if I vary t then h minus c p a t is just omega c p v t plus 2 5 0 1 and omega is just h minus c p a t upon p minus c p a t p v t plus 2 5 0 1. If you fix your h as you vary t you will get a particular value of omega. So, choose a value of h go on varying t you will get different values of omega draw a line and that would be your constant h line. So, you get different values of omega just draw a line through those points you will get a constant enthalpy line and again that will be a curve which will be this landing to the right and then you can draw constant w b t line. So, something that you must realize is that if I have this curve like this this is t this is omega. If I reach here corresponding to this omega whenever I touch this this is my dew point line or this is my dew point temperature here, but at the temperature t if I reach dew or if I am already at dew point it is the same as w b t that is because if I draw my t s curve here and we have drawn it often. If you are here this is the dew point, but if you are already here if you are already at this saturated condition. So, this is your temperature. So, this is your 100 percent saturation line if the temperature is the same as the dew point temperature. If I put a wet wick it cannot go any lower and you are actually at the wet bulb temperature too. So, this line at this point your temperature is the same as your wet bulb temperature is the same as your dew point temperature and what you can do is again you know get your constant wet bulb temperature line. So, either people what they do is normally they will use either the adiabatic wet bulb temperature equation to get the constant wet bulb temperature line or you see this carrier equation here that we had. So, if I have my temperature I will let us say start at this point where I am at 100 percent r h. So, if I have that 100 percent r h line I know if I fix my wet bulb temperature all you have to do is then use the carrier equation because you have fixed your wet bulb temperature this p dash is fixed p v dash is fixed and p is your ambient pressure which is anyway fixed all you do is vary your temperature you will get different values of p v once you get p v omega is very straight forward you will get the omega. So, choose a fixed wet bulb temperature change the change the dry bulb temperature obviously you can go only to higher dry bulb temperature because your dry bulb temperature cannot be lower than your wet bulb temperature choose values of temperature which are higher than the wet bulb temperature. So, in effect you will move you will move this is the wet bulb temperature corresponding to the dry bulb temperature and as I move here I will get different values of omega as I keep on changing my p I will get different values of p v which are lower and lower and I will get different values of omega and hence I will keep on moving like this. So, this is how I will get different or constant wet bulb temperature. So, these are the different lines which can be drawn and used on a psychrometric chart. So, in general the psychrometric chart will have if I know t and omega I can immediately know the constant wet bulb temperature line which is passing through it I can know the constant h line which is passing through it and if I know the omega. So, for example, if I am here so I know my t I know my omega I should find out which h line is passing through it I know the h I should find out which w b t line is passing through it I will get my wet bulb temperature. So, I will get the enthalpy and wet bulb temperature if I want to know the dew point or I do is that the same omega I continue till I hit the current or rather the saturation line and see what temperature is corresponding to it that would be my dew point temperature. So, if I know a point here I immediately know all quantities immediately and that is what is normally done using the psychrometric chart, but please remember this chart was drawn assuming the total pressure of one atmosphere. If I change the total pressure the lines will change because everywhere when calculating omega the total pressure was involved. So, I will get a different chart. So, if you are teaching a basic thermo course let the students know the chart exists, but let the calculations be done using the steam table. In a regular refrigeration air conditioning course you know where all calculations are being done for some ambient conditions they can use the standard psychrometric chart and see it is very straight forward you know t and omega you get h and actually h is very important or if you know t and d p t you will immediately get the omega. So, for example, if I tell you t is here. So, I know that the point is somewhere on this line if I tell you d p t is something. So, I go to dub this is the d p t the dew point temperature will be less than the temperature the current dribble temperature this is my dew point temperature I go straight upon the dew point temperature till I touch the saturation line I know this is the omega and then I just move straight horizontally till I touch the temperature line and this would be the point that I am existing at and the moment I get t and omega all your other quantities for calculations are right there you can get your enthalpy you can get wet bulb I mean you do not read the wet bulb later on for calculation, but you know all these quantities that you require. So, this is in general what you would require if you similarly if I know the temperature and the wet bulb temperature. So, I just know that the temperature is somewhere here I find which wet bulb temperature cuts through this I know the point immediately and once I know the omega I can do all my other calculation. So, this is how you would use a normal psychrometric chart. So, once I have this all I do know is calculations for simple mixing. So, let us say you have you know one stream coming here m 1. So, if I know this is the net mass you know that 1 plus 1 kg of dry air corresponds to omega kg of water vapor which means it is 1 plus omega kg of moist air. So, when people say there is a stream of moist air coming of at m 1 kg per second either they must tell you it is m 1 kg of moist air per second or m 1 kg of dry air per second. If they claim it is m 1 kg of dry air kg dry air per second then you immediately know that along with this flow you have omega times m 1 dot kg of water vapor per second because per kg there is omega. So, if there are m 1 kg then it is just omega into m 1. But if they claim that there is m 1 kg of moist air then you know that 1 kg of moist air corresponds to 1 plus omega kg of moist air. So, if I want 1 kg of moist air it corresponds to moist air corresponds to 1 upon 1 plus omega kg of dry air. So, if it is given to you that m 1 kg of moist air is coming then the amount of dry air is just m 1 dot or m 1 dot sorry I should say m 1 dot upon 1 plus omega this is kg is dry air per second and this m 1 dot upon 1 plus omega into omega is your kg is water vapor per second. So, if you get the kg is for water for dry air you immediately know how much water vapor is there because you just have to multiply by omega. So, this is how much water vapor is there. So, if I know how many kg is dry air are there how many kg is or you know if I know and if I know omega then getting h is very straight forward sorry I know h because if I know c p t plus omega c p vapor t plus 2 5 0 minus omega h. So, my net h is just m 1 dry air into h. So, this is where you should remember that h was expressed in terms of per kg dry air. So, all my calculations are on basis of per kg dry air. So, I just find out how many kgs of dry air there are and just multiplied by h because this is expressed in a per kg dry air basis. So, this please remember this I just find out the number of kgs of dry air and multiplied by h that will give me my h 1. So, if I say two streams are mixing and forming a third stream here m 3 m 1 m 2. So, let me say that this is m 1 dot kgs of dry air. So, if moist air was given I have already found out let us say that there are m 1 dot kgs of dry air. Similarly, there are m 2 dot kgs of dry air they will give me m 3 dot kgs of dry air. Now, obviously you it is very simple balance will tell you that if this many kgs of dry air are coming here this many kgs of dry air are coming here then this better be equal to just the addition of these two. So, that is what is going to happen. What about the water vapor? You realize that the water vapor coming here it just m 1 dot into omega 1 where omega 1 is the area for this omega 2 into omega into m dot 2. So, this if I add this this is the net moisture going here. So, what should be omega 3? It should be such that m dot 3 into omega 3 should give me the net moisture. So, it is very straight forward then and just because everything is expressed in per kg of dry air that m dot 3 omega 3 is the total amount of moisture or water vapor in this leaving stream that is just going to be the net incoming moisture because nothing we are assuming nothing is disappearing. So, this is it this is as far as the straight forward as the balance. Now, if I say you know what is the enthalpy again it is expressed in terms of per kg of dry air you realize that m 1 dot h is your enthalpy for stream 1 and similarly enthalpy for stream 2 is m dot h sorry this is h 2 this is h 1 and if no external heat is added or something is removed then if it is an adiabatic situation then in an open system 2 streams mixing and the third going out if this entire system is adiabatic then here h 3 would be just the same as h 1 plus h 2. But what is h 3 it is just m dot 3 dry air times h 3 that means very straight forward m dot 3 h 3 is just m dot 1 h 1 plus m dot 2 h 2. So, it comes out as straight forward addition equations just because we have expressed everything in terms of you know dry air. Now, of course you realize you know these are situations where nothing condensed out or you did not add external heat. So, you can imagine what will happen. So, for example, if I go to this previous situation I can you know remove heat from this and condensed matter out in which case the incoming moisture is m 1 omega 1 plus m 2 omega 2 let us say I know per unit time how much moisture is going out and let us say that is x. So, I have condensed out x kg. So, m 1 omega 1 was the moisture in stream 1 I added m 2 omega 2 this is moisture in stream 2 this is the net moisture if I subtract x from it this is all per kg per second basis then I should just get omega 3 m 3 omega 3 because this is the net moisture in the outgoing stream. So, again it is very straight forward because everything has been expressed in terms of per kilogram dry air basis I just get amount of water coming in subtract what has been lost due to condensation I should get the water going out and that should be just be equal to m 3 omega 3 because the dry air is not going to condense out it is just going to get out as dry air part. So, just omega 3 can be expressed as per kg of dry air how much moisture is there and what we are doing is this much moisture came in this much condensed out. So, the remaining is going out with the dry air. So, omega 3 should be if I just multiply omega 3 into m 3 I should get the total moisture going out because that is what it is and I will get the value of omega 3. So, I can calculate omega 3 similarly here I may have removed some heat because of I put a cooling coil and condensing out or I may have just increased the temperature by adding heat. So, then I can in the open system I can put a Q term either plus or minus. So, this will have such that h 3 will be h 1 plus h 2 either plus or minus Q will give me whatever. So, even in this case if something has condensed out this should automatically be taken care of here that I should have a net enthalpy balance let us say there is a stream going out of condensed water. So, this is x kg is going out. So, if I have a net energy balance here there is an m 3 going out there is a Q coming in and there is another thing. So, I will add incoming enthalpy here h 1 and h 2. So, much energy either may be let us say getting out and there is a third stream here this is x into h of this stream. So, I will have incoming enthalpy this and I will subtract this part here I should get my outgoing. So, this straight forward open system analysis what is coming in figure out what you added or subtracted and that should give you what is going out and you will get the net enthalpy of the stream going out. So, it is just going to be m 3 into you know small h 3 and you can find out what is the specific enthalpy of that and once you get this specific enthalpy and omega. So, in general you will end up with always x 3 and omega 3 whenever you do this calculation you would not know the temperature. But you can you know that h 3 will be just c p a t 3 plus omega 3 into c p v t 3 plus 2 phi 0 1. So, using those two equations I would have gotten omega 3 and h 3. So, I know this quantity and I know this quantity and of course, these are all fixed constants here 2 phi 0 1. The only unknown is this t 3. So, when I put h 3 and omega 3 I can get the value of t 3. So, the outlet stream conditions are known I will get t 3 and I will get omega 3 that is good enough. If I know omega 3 and t 3 I can get dew point temperature, I can get wet bulb temperature, I can get everything because net total pressure is anyway known. If the total pressure is known and if t 3 is known I just require one more quantity like omega 3 and I will get everything that I want that is the existing pressure the dew point temperature the wet bulb temperature and hence all calculations can be done very easily. So, of course, you realize even for doing this calculation I do not require the psychometric charge I can just do with the steam tables and in fact, in the afternoon all such calculations will be done entirely using the steam table and we would not resort to the psychometric charge and we will actually never touch it in this course and that will be kept purely for if you are doing the refrigeration course and you can use the psychometric charge. So, I hope you know in general at the end of this you could figure out that every time I use the t s diagram and this is something that you must often draw when you are trying to understand this subject because you realize immediately what is this p v and what is d p t because d p t is just the t sat at your p v using p v why should I get omega in fact, remember the basic definition of omega it is just m vapor upon m dry air and then I use the ideal gas law to express it in terms of pressures and this 0.622 which are the molecular weight. So, then you should know what is relative humidity you should know what is the wet bulb temperature you should know the enthalpy how to calculate the enthalpy and finally, you should know about the psychometric charge and you should know simple mixing of moist air stream. So, these are a few quantities that you need to know and all our problems in the afternoon for psychometry will be based on these quantities and we will stick to this. So, overall I hope you have got reasonable idea of psychometry as far as how it should be taught in some kind of regular thermodynamic force entirely based on steam table do not resort to any psychometric charge and you realize that this t s diagram keeps coming and there are only few definitions which are just based on ratios of mass of vapor to mass of dry air or pressure of vapor to pressure at saturation and all the quantities are just you know simple definitions and all you really require is the t s diagram and the steam table. So, if this is good enough I think I can stop here now. 1 0 4 0. How does wet bulb temperature differ from thermodynamic wet bulb temperature? So, you can see very well that the wet bulb temperature as defined using a wet wick is just an experimental process and you are not really assured that the air which passes after passing over the thermometer is actually fully saturated at the WBT. All you are really assured is that the wet cloth around the thermometer is at the wet bulb temperature. So, this is an empirical wet bulb temperature. So, now the thermodynamic wet bulb temperature is very very clear that there is a certain set of gas which is coming in I know its entire properties and there is one particular so that there is a pool of water over which it is passing. Now, if you can imagine that the pool temperature is the same as your wet cloth that is the equivalence first, but at the end when the vapor leaves we are claiming there that no Q came from anywhere outside and what happened was whatever evaporated went into the air and the air has now reached a particular temperature which is exactly equal to the temperature of the pool of water and it is saturated at that temperature. So, that is the thermodynamic wet bulb temperature, but in the actual wet bulb temperature process that we carry out there is no such guarantee that that temperature has reached the temperature of the thermometer and apart from that there is no guarantee that it is saturated. It is just that we believe it is because we do not know where all the energy has come from. Now, if the entire energy has come from the air and the whatever has left is at the temperature of the wick as well as it is saturated then completely the two wet bulb temperatures become the same, but since there is no guarantee wet bulb temperature thermodynamically the wet the thermodynamic wet bulb temperature is some process that we can very well define in terms of only the thermodynamic quantities. Whereas, if you want to define the wet bulb temperature for the wet bulb process we have to define it in terms of heat transfer coefficients and mass transfer coefficients. So, that is where the difference is. O to U, 1032, do you have any questions? I would like to know the phenomena of breeze, the land and fine breeze with respect to the thermodynamic point of view. So, I mean it is just dependent on what the temperature of the land is during the day and how much time the water takes to heat up and how much time the land takes to heat up and hence it just a phenomena which is dependent on the temperature difference between the two. So, somewhere where the temperature is higher the density is lower and just there is a flow from the high pressure region to a low pressure region. So, I can only answer so much I mean that is as far as you know it is a fluid flow phenomena based entirely on pressure difference. So, that is all I can answer at this point. 1182. When I want to condense the cloud of vapor then if I will maintain I will bring the temperature to the saturation level then at a time it will get condensed. But I do not want to condense at a time I want to condense that cloud of vapor particle by particle. So, what will be the probable what will be the process which has to follow to condense the cloud particle by particle. What I can answer regarding this is that normally if you have a huge quantity of vapor to just get it down from a particular temperature to a lower temperature all at once is going to be difficult. For example, even if you start cooling it at some point it will start getting cooled and then only everything will slowly start getting cooled. Now, if really all at once they get you know it gets cooled at a time then you have a very heavy shower something like a cloud burst. But in reality this is not what happens and you usually have small seeds or you know dust particles which slowly start accumulating some moisture here and there. And once they start becoming heavier they start moving down and accumulate more moisture on them and that is how you normally get these rain droplets. And hence it is very necessary that you know you somehow seed these clouds so that you can start some kind of a nucleation process out there where the moisture will condense on to the seed and they will go. Otherwise if you just try to condense it in one go then you can you know get into this cloud burst. But you know that is something I do not think we can easily achieve but we can definitely try to achieve this seeding and that is what normally people do when they do cloud seeding that is they put lot of seeds they ensure that some condensation occurs and as the condense nucleus start falling down they accumulate more vapor and hence you get rain. I assume this is what you are asking. Actually if I want one particle nano part nano size particle of the water vapor then in that case which conditions I have to maintain? I will assume that if you really want this you will have to focus your condensation only at one particular point only if you can achieve that you can do it. So I mean how do you physically do it? I am not very sure but at some one particular point you will have to suddenly start cooling so if you can achieve that yes I mean I do not think it is going to be easy at all. Thank you.