 Now let us look at the effect of humid air. Now for this we have to go back to our class 11th and 12th chemistry in school. Some students hate this subject of chemistry. I have one of them when I was in school but we have to use it. So just recall some definitions about humidity. So what is humidity? It is an indication of how much water vapor is there in the ambient air. Interestingly, there are several definitions of humidity. So we will revisit them very briefly. So there is something called as absolute humidity, also called as the volumetric humidity. There you look at the mass of the water vapor upon the volume of the moist air. Moist air means air which has got water vapor in it. So that is absolute humidity. How much mass of water vapor you have per volume? You also have something called as a specific humidity or mass humidity. This is mass upon mass. So mass of water vapor upon mass of the moist air. Then you also have what is called as a humidity ratio or a mixing ratio which is the ratio of mass of water vapor upon mass of dry air. So now you remove the mass of the water vapor, remaining thing is mass of dry air. So that ratio is called as humidity ratio and most important for us is what is called as the RH or the relative humidity which is mass of the water vapor divided by mass of the saturation water vapor. So does somebody remember from your school chemistry what is meant by saturation water vapor? After that what happens? It will condense into water or ice or sleet or you know hail whatever, appropriate to the operating conditions. How much water vapor can air hold without condensing? That is called as the relative humidity. We express that as a percentage. Now question is how do you measure it? So this is something I want to leave it to you for Moodle. So go down on Moodle page, tell us how the relative humidity is measured in real life. There are many ways you will remember. I remember hot and wet, bulb, thermometer, then there is a hygrometer. Just to revive my memory in your old school days, on Moodle page I want but please do not copy paste from some source and put it, apply your own mind, make it in a slightly interesting fashion, perhaps put a photograph of some instrument, give some numbers about RH values of various places say Mumbai, how it varies, so some information about humidity because this is going to affect. So now let us look at some other physical concepts, concepts about saturation. So this is what we have already seen, saturation is a condition in which any additional water vapour will not remain water vapour, it will condense into liquid. So there is one confusion which many people have. Many people feel that this water vapour, these molecules of water will actually go inside the molecules of the gas and it is not true, there is no mixing. You cannot break Avogadro's law, you cannot have intermolecular forces cannot be broken by some other particle unless you apply huge amount of energy. So the water vapour is just like any other gas, just like air is a mixture of nitrogen, oxygen, there is also water vapour, take it as a gas. So this water vapour is a gas which is there in the air like any other gas, it does not actually mix. Now dew point is the temperature of the ambient air, if you cool the ambient air up to dew point then saturation vapour pressure occurs and this will start condensing. So when you operate any vehicle or an airship, if you operate at a temperature lower than dew point, the air will actually shed all its water vapour in the form of dew. So at or below dew point, the relative humidity is 100 percent and above the dew point it will be 80 percent, 90 percent, etcetera, etcetera, etcetera. So there is an alternative way in which we can estimate R H. Now you cannot go around and calculating, you cannot go around with the thermometer and checking the humidity at every point of time. Yes, you need that number but there is an alternative way of measuring this and for that we again revisit our school chemistry and we look at two laws, the ideal gas law P V is equal to RT and we look at the Dalton's law of partial pressures. So there is something called as the actual vapour pressure, we call it as small e, subscript e. This is the partial pressure of the water vapour in the atmosphere. You take a small amount, let us say unit volume of moist air. It consists of a mixture of many, many gases, homogeneous mixture of many, many gases, one of the gases water vapour and you know that mixture of gases in a container will exert their own pressures, we call it as partial pressure. So the partial pressure of the water vapour in air is called as the actual vapour pressure. So this is basically, now PS is the ambient pressure. Please note I am not using PA because PA can be confused as pressure of the air and you might get mixed up saying air and water vapour that is why we use S. So subscript S will be used for something like a atmospheric condition instead of A. So the pressure of the atmosphere is PS. It consists of many, many gases. So every other gas other than water vapour we would call it as dry air. All the nitrogen, oxygen, there is also traces of helium in the ambient air and so many other gases, all of it are clubbed as dry air. And the partial pressure of that is called as PDA, dry air, DA for dry air. And the partial pressure of water vapour is PWV. Now why are we doing all this? We are doing all this because we want to use pressure volume relationship to figure out a numerical way to calculate the humidity. And water vapour will stay as water vapour as long as we have temperature above dew point. So we need to also look at the concepts of relative humidity in that way. So therefore PS will be P of DA, dry air partial pressure plus E. I hope this is clear. Although it may seem little bit involved right now but very soon we will use this to converge. Now let us look at a concept called as ES, ES is the saturation vapour pressure. This is what occurs atmosphere in nature. There is some saturation vapour pressure, it is a partial not paper but pressure of hydrogen at saturation. This is a mistake, I will correct this mistake. It is a partial pressure of hydrogen of water vapour at saturation. Beyond that it will become fluid. So what happens in this case is very interesting. The physical phenomena is extremely interesting at this particular condition. The vapour phase in is equivalent with liquid phase. So both of them are happening simultaneously. Anything below that. So we know that the R H is going to be 100% when the T ambient is equal to dew point. Now how do you calculate the saturation vapour pressure? It will change based on the temperature of the ambient air. So for that there is an Arden-Buck equation which relates the ambient air temperature in centigrade because we mostly measure in centigrade with directly it gives you the saturation vapour pressure. So it is a slightly involved equation that is 6.1, 6.1.2 into exponential of this 18.678 minus temperature in C upon 234, etc., etc., the units of this are Pascal's. Now one can simplify this without much loss in accuracy and make it just like this. So it is a simple formula now. So 18.5 C upon 257 plus C this is a raise to exponential times 6.1.2 in Pascal's. So obviously when the value of C is 0 that means when the temperature of the ambient air is 0 ES will be 611.2 e power 0 is 1. So you can calculate the value of ES simply by noting down the ambient air temperature. Now I was a bit curious when I was making these transparencies on how much error do we actually get in these two. So what I did is I actually plotted this graph. So the dark line is the approximate value and the points are the exact value. You can see there is hardly any difference. So we can safely use the simple formula without much loss in accuracy. So on the y-axis we have the saturation vapour pressure either you can call it as SVP or you can call it as ES, E subscript S. On the x-axis we have and if you look at the ambient condition around 15 degrees centigrade you have a saturation vapour of around 1700 also. So at 1700 Pascal's ambient pressure that will be the value. So now let us revisit two basic gas laws and I must tell you when I made this slide I went back to my own old memories about the schools. So Dalton gave us a law of partial pressures. Does anybody remember it? I could not recall it when I was making these slides. Yes. One by one. Yes, please tell me what is the Dalton's law of partial pressure pressure? Correct some of the partial pressures. So if you have gas 1 and gas 2 at pressure P1 and P2. But same volume. So now you mix them it will become 2 times volume because there will be 2 volumes mixed. But if you have it you will find that the pressure of a mixture of gases is equal to the sum of the pressure that the gas would exert separately if each occupied the same volume as the mixture. So water vapour, nitrogen, oxygen they will not all have the same pressure. Depending on their partial contributions there will be partial pressures. There is also another interesting law called as the Amagat's law. This is for partial volumes. Does somebody remember this law? Yes. This is not something that we really read. So Amagat's law is a kind of a corollary to the Dalton's law of pressures. What Amagat's law says is that the volume of a mixture of gases is equal to the sum of the volume they would occupy when they are under the same pressure as the mixture. So what we will do is we will use a combination of these 2 laws to try and get a numerical expression for calculating the effect of relative humidity or RH. So we look at vapour pressure and RH. So what we do is, so consider 2 kinds of situations. One is a situation in which the air is saturated with water vapour. So it cannot take any more, any more water vapour it will condense into water and same temperature. So gas law is PV equal to MRT. So for unsaturated air, E into V will be, now here I have not put ENV, I have just put V as the volume. So because E is basically P pressure, so the actual vapour pressure and actual partial masses, mass of the water vapour and mass of the dry air. Now just take a ratio, you will get E by ES is equal to MVW by MS. By definition, 100 into MVW mass of the volume of the, mass of the water vapour upon mass of the dry air that is defined as the saturation, as the vapour pressure, sorry as the relative humidity RS. So therefore E which is the vapour pressure of unsaturated air is equal to humidity as a percentage into the saturation vapour pressure. Now this is very nice because ES is a number that you can calculate using that Arden-Buck's formula for a given ambient temperature. So the RHS is completely known, RH is given by the atmospheric conditions, RH is an input and E is the pressure that you require. Now what do we do with this E? We are not dealing with the vapours, we are dealing with the combined mixture.