 So, we are going to understand next the pressure due to liquid, how liquid exerts pressure? Right on the heading pressure due to liquids. See, when you talk about the three different states of matter, solid, liquid and gas, the gaseous particle exerts pressure, exerts pressure due to collision. And that we have already discussed when the two viscous particles moving, they collides and the force per unit area that we have there is called the pressure, right? So, if the gaseous particles exerts pressure because of collision, they collides, correct? If you talk about solid, the solid particles exerts pressure due to its mass, right? Suppose you have a table here and on this table, if you place a block of certain mass like this, okay? This is suppose 5 kaseous viscous 2 kg mass we have here. So, the weight component of this mass of 5 plus 2 7 kg here that is mg. This force that is acting on the block like in downward direction which is there on the table, right? So, this force per unit area on this table is the pressure on the table by the block that is 5 plus 2 7 kg block, right? So, this exerts pressure because of its mass, correct? We can also add some block over here, the pressure will be more because it has more mass. So, solid exerts pressure due to its mass. When you talk about liquids, it exerts pressure due to its height or depth also we can say whatever. Have you seen this formula? I want you to respond all of you. Have you seen this formula before? P is equals to H rho g, I will write down this just a second, P is equals to rho gH. Have you seen this formula? Correct? What is this rho gH means? Rho is the density of the liquid, H is the height and g is the gravitational input. How do we get this formula? You know that? The derivation of it? Okay, fine. Quickly we will go through it. See what happens as the height of the liquid increases. Suppose you are at this position and this side you have liquids, correct? So, at this point, you know, you will have certain pressure because of this column. It is not the water that is below you. We have nothing to do with this. The water which is above you, whatever the height of this water column we have, this height will exert pressure, correct? So here we will have more height, right? Then the pressure will be more. If you go up, the pressure will decrease. Go up, the pressure will decrease. The pressure will decrease, correct? So as you go deeper into the sea, the height of the water column above you increases and hence pressure also increases, right? That's how you see when you go, you know, deeper like 50, 60 feet if you go, randomly I am taking some number, right? Not very sure with it. But after a certain depth, you know, the divers, they starts bleeding from the nose because the pressure is continuously increasing on his body, right? That's why that, I know, it's very, it's, it becomes very difficult to, you know, go beyond a certain point into the sea or river or whatever it is because gradually the height of the liquid column is increasing and hence the pressure on you is also increasing. That's why it becomes difficult, okay? So liquid column exerts height because of its pressure, okay? So based on this formula, we are going to use this formula only. How do we get this formula quickly? We'll see this and what kind of problems you are going to get, get that we'll discuss, correct? So now you see. So we are going to, you know, discuss a device that is barometer which we use to measure pressure right down into this, right down. It is an instrument which is used to measure, it is an instrument which is used to measure pressure of liquids used to measure pressure of liquids, in barometer the mercury, the liquid which is used is mercury. The liquid which is used is mercury. why we use mercury because it is non sticky plus it has very high density volume is less so occupy less volume right so why we use mercury because it's non sticky the volume is less because of its high density right now now you see this suppose we have an arrangement we have a you know beaker like this this is filled with mercury for example this is filled with mercury and if you place a tube like this with open end downward place a tube like this then what happens this mercury column will rise in the tube and it goes to a certain height suppose this height I am assuming edge it goes to a certain height and it depends upon the atmospheric pressure okay we'll discuss why and how but obviously when the open end you will put it down then the mercury column will rise in the cube and we have this arrangement here now could you tell me the relation of pressure at point P and it's the same level and q this is p and q p and q are at the same level the pressure at p and q is what same pressure okay so we can write at the same level because the depth is same height is same the pressure at p and q would be equal and same right so because of liquid the pressure varies only when the depth of the liquid is different it is same for these two points hence the pressure here would be same first point could you tell me this point is suppose I'm assuming A exactly at the surface of this liquid A and here the point is B I'm assuming the pressure at A and B will also be same right what is the pressure at A since it is open so P at A is nothing but the atmospheric pressure okay it means it is the pressure at B also now this liquid column Hg column will rise in this tube and will go to a certain height because we know as the height increases its pressure increases so height of this column if you consider at this point when this pressure of this column equals to the atmospheric pressure that is the pressure at B then it won't you know go further the rise the rise in the height will not be there once the pressure of this liquid column equals to the pressure at B isn't it right yes correct understood so can I write this the pressure due to liquid column due to Hg column I'll write down in the tube equals to the pressure at B which is nothing but the atmospheric pressure now you see this part I am drawing it separately here because we need to balance it the force we must be equal so this the liquid column will have here suppose we are assuming this this is the Hg column we have exactly this part I have taken over here assume this so obviously this will have certain mass so its mass component is mg downward direction right and this pressure will exert in upward direction P atmospheric that is the pressure at B into the area of cross section this is the force in upward direction right this B will exerts pressure P atmospheric into the area of cross section becomes a force in upward direction and weight component is in downward direction no doubt in this at equilibrium what we can write we can write this force in upward direction equals to the force in downward direction okay m is the mass j is the expression due to gravity so P atmospheric into A mass of the liquid obviously we can take so density into volume this is for Hg into G any doubt here further what we can write that atmospheric pressure P atm into area of cross section equals to rho density into volume would be what again area into height of the liquid column this is for the liquid which is Hg here we have into the gravitational acceleration and then this A and A will get cancelled and the atmospheric pressure atmospheric pressure is equals to we have rho g h where this height is the height of liquid column and this rho is the density of liquid sorry mercury anybody has any doubt in this clear now for any liquid of height h and density rho we can give the pressure as rho g h for any liquid so generally rho g h now since we know that atmospheric pressure so we can find out the height of the mercury column what height of the mercury column exerts pressure which is equals to the atmospheric pressure so when you substitute all the value here right you will get the height of the mercury column h of hg is equals to 76 centimeter means if you take 76 centimeter of mercury column it will exerts a pressure of which is equals to the atmospheric pressure that's why we say that atmospheric pressure is equals to 76 centimeter of hg or 760 mm of hg okay like that means 76 centimeter of height of liquid hg is one atmospheric pressure any doubt in this yes all of you you can type in clr quickly guys so what we have concluded pressure due to liquid of height h is equals to rho g h sometimes what happens if you look at this arrangement here we have a column and suppose we are having a liquid here in this beaker and there is an again tube with open and down like this so obviously this liquid level will rise in the tube this is it and we'll have some gas over here some gases some gas here in this tube is trapped okay this gas here it trapped so this point is a this point is b right so we have p a is equals to pb is equals to p atmospheric right p atmospheric and if you write down the relation of pressure so pb is equals to what on this pb on this point this liquid will exert pressure and the gas will also exert pressure so pb is equals to pressure of the liquid whatever liquid we have plus the pressure of the gas this is the relation we can write if any gas is trapped so if they ask you to find out the pressure of the gas in this case right pb is the atmospheric pressure p liquid you know because the height and other things will be given and then you can find out the pressure of the gas the basically you need to understand that how to write down the pressure a relation here pb is here above it we have liquid so this pressure will be in downward direction this gas will also exert pressure in downward direction and b is in upward direction so pb is equals to p liquid plus p gas did you understand this now based on this only you see a few questions this is open and up open and down and again open and up so the question here is we have 15 centimeter of liquid column here hg 15 centimeter of hg we have and here some gases are trapped okay you need to find out the pressure of gas density of mercury low of hg is 13.6 gram per ml in this we have 10 centimeter of mercury 10 centimeter and here are some gases are trapped you need to again find out the pressure of gas here okay here also we have some liquid trapped we don't know about this liquid but the density of this liquid is given the height is h and the density of this liquid is given rho is equals to 6.8 gram per ml what you said here we have gas free to find out the pressure of the gas try all three yeah done gives you place it in a centimeter of hg you don't have to place in Pascal you also won't get such options okay what happened guys okay so I'll do this first one let's see see here what happens we have a pressure here this liquid column and this and we have atmospheric pressure in downward direction correct so atmospheric pressure is this PATM what is the direction of this liquid column is it upward or downward upward or downward liquid column are you there because of this liquid column the pressure is in downward direction or upward direction I've already told you yeah I have already told you that the height the pressure because of liquid is the liquid which is above right so this liquid column 15 centimeter of it will exert pressure in downward direction and the pressure of gas is in upward direction right so if you balance this what you can write PATM in downward direction pressure of hg in downward direction equals to the pressure of gas in upward direction any problem in this tell me any doubt any problem please go ahead you just need to know the direction of the pressure here what is the direction of gaseous pressure what is the direction of liquid column what is the direction of atmospheric pressure so atmospheric pressure is always in downward direction I am also sitting here at most atmospheric pressure on me right it is very downward direction so if you have a liquid column here the atmosphere will also exert pressure in downward direction right because it is there in upward above only so it will exert pressure in downward direction pressure of atmosphere is in downward direction liquid column we know it exerts pressure because of its height so this height we have so it exerts pressure on this gas see actually what happens when this liquid column is trapped right suppose liquid column will have here like this if you can see me this is a liquid column we have and it will be here when this pressure and this pressure is equal are you getting it correct obviously this also contributes into the downward pressure the liquid column also contributes but suppose I when I say the liquid column is trapped here like this in between somewhere like it is trapped here so when it will be trapped when this pressure total downward pressure is equal to total upward pressure right so gas is pushing the liquid column in upward direction atmospheric pressure is pushing the liquid column in downward direction liquid column also exerting pressure on the gaseous species or the gas which is present here so total pressure in this direction equals to the total pressure in this direction and then only will have the equilibrium are you getting it now yes tell me guys first yes or no if you understood fine otherwise let me know I can explain you 10 times all these things okay I have no problem but you have to know speak up all of you understood I am not doing anything I am just balancing the force when you to when you balance the force total force yes correct so force the cross sectional area will get cancelled Shradha you balance the force only the cross sectional area is same you see in that that expression all that you have calculated the area gets cancelled right so you balance the force pressure into area this is the force because of atmosphere right this into a it is a force because of the liquid column pressure gas into a it is a force because of the gaseous column so cross sectional area will get cancelled and hence we are left with a pressure clear Shradha understood this so you will get this now everything you know we know the atmospheric pressure atmospheric pressure is 76 centimeter of hg we know this and plus 15 centimeter of hg is also present plus 15 centimeter the pressure of hg is what because we have only 15 centimeter of hg so we have 76 centimeter of what plus 15 centimeter this so total pressure is this equals to the pressure of gas so pressure of gas equals to 91 centimeter of hg tell me is it clear yes now one more thing you try to understand very carefully okay see I have just added this p atm and p hg 76 plus 50 91 okay why because this column is mercury right and we know the atmospheric pressure is 76 centimeter of mercury only so since the atmospheric pressure is defined with respect to mercury so whatever height of mercury column you have here you can directly add with 76 but if you have any other liquid here then you cannot add this in that case you have to think again in that case you have to think again that if this is the height of the liquid given this liquid will exert some pressure the what should be the height of the mercury column which exerts the same pressure as this liquid is going right so in case of another liquid which is a case number three we'll discuss this how to do but first you try this one the second one yes low hg in that case you need to take yes arjit fine which one you are talking about Shradha no no see Shradha it depends you cannot add here p hg and pressure of the gas you cannot do that because the direct see if the liquid if this liquid and the gas if both exerts pressure in upward direction then you can add the two but here the liquid column is exerting pressure in downward direction gaseous gas exerts pressure in upward direction so both are in the opposite direction you cannot add p hg and p gas here that's what I'm telling you you have to balance the force first then you'll get the relation of pressure which are the liquid one yes for that you need to find out hro g and then you have to find out the height of the you know hg column which exerts the same pressure fine this one I'll see first then I'll go to the third one see here the liquid column liquid column exerts pressure in which direction downward direction obviously right this p of hg in downward direction pressure of gas is also in downward direction but the atmospheric pressure is in upward direction because the atmospheric pressure will hold this liquid column here right so we'll write down the relation here p atmospheric one second we have p atmospheric equals to p hg plus p of gas so p of gas equals to 76 minus 10 66 centimeter of hg in the last one you see it is given density 6.8 obviously this liquid height column is not mercury so here if you look at the pressure the pressure of atmosphere is in downward p atm pressure of this liquid we don't know what liquid is it is in downward and pressure of gas it is in upward direction so we'll write down the pressure of gas equals to the pressure of atmospheric plus the pressure of liquid now this liquid column is given its densities 6.8 so pressure of liquid is what is equals to rho g h okay and remember one thing always that p atm is 76 centimeter of hg but since this liquid is not hg so if you directly add this 10 cent this whatever the height we have if we add this here this will be wrong because this liquid is not hg so we cannot add height of this liquid with the height of mercury column here so this we are not going to do here now what we need to do next then see we have this height of liquid this will this height of liquid will exert some pressure which pressure is this okay now we'll find out that what should be the height of the mercury column right which exerts the same pressure as this height of this liquid does exerts correct so what we have done we have taken this pressure of this liquid and we equate this with certain height of mercury this is the pressure of mercury we have so with this two relation you see we'll find out what height of the mercury column is required so that the mercury column exerts the same pressure as this liquid column exerts so that would be the rho of liquid into the height of liquid divided by the rho of hg this is what the formula we use in order to find out the height of the mercury column which exerts the same pressure as h height of this liquid exerts did you understand this can you doubt in this so first of all we'll find out this height of mercury column and then this height will add over here so for this this formula you can memorize it is useful for all the questions okay in general you can memorize this formula h of hg is 6.8 the density of that liquid given 10 centimeter height and it is 13.6 so obviously it is coming out to be 5 centimeter of hg this means what that 10 centimeter of this liquid 10 centimeter of this liquid and 5 centimeter of hg will exert the same pressure correct so here we'll simply add 5 centimeter so answer is 91 centimeter of hg any doubt in this tell me look at this again and let me know if you have any doubt just you need to balance the pressure total pressure in downward direction equals to the total pressure in upward direction balance the two you will get the unknowns copy this down yes done it's given in the question is it not given oh wait let me check that's the height of the liquid I haven't given you I guess okay wait let me check this just a second or it is not I have not written over here fine my bad guys this height of the liquid is given 10 centimeter okay that's why I have taken this whatever height you just have to substitute and find out this my bad okay this height is given right down here this edge is given over here it is 10 centimeter okay got it understood let's see this question another one you can like this you can have multiple liquids like more than two three four liquids can be given like you see this question concept is exactly same you have this to you and we have any three liquids we have we do not know l1 l2 l3 and here we have gas this height h1 of the first liquid is given it is 80 centimeter h2 is given it is 20 centimeter h3 is given 50 centimeter row of this first liquid is density is 3.4 row of this is 6.8 row of the third one is 27.2 gram per ml is the unit you need to find out the pressure of this gas yeah that's correct yeah this end is open this is open end right arshith correct no that's not right 461 is wrong 156 is wrong 226 is wrong yeah kenshukh that's right 130 is wrong yeah redhu that's right correct rohan srohan ritu kenshukh arshith you got the right answer you must be doing some calculation mistake lucita have a check your calculation once see what we need to do again corresponding to this height okay what should be the height of the mercury column which exerts the same pressure so with that formula we can directly find out okay so for the first liquid h of hg should be 80 into 3.4 divided by 13.6 this is 20 centimeter I guess similarly for the second liquid the corresponding height of the mercury column would be 6.8 density 20 centimeter is the height divided by 13.6 this we are getting 10 centimeter of it h of hg for the third liquid is 50 into 27.2 divided by 13.6 equals to 100 centimeter of it okay and all these liquid will exerts pressure in downward rate means what instead of these three liquid we can place hg column of height 20 plus 10 plus 100 that is 130 centimeter means this height of the three liquid is equivalent to 130 centimeter of hg so this 130 centimeter of hg the pressure is in downward direction pressure of gas is in upward atmospheric pressure in downward direction so what we can write we can write p atmospheric plus p of hg equals to p of gas so 76 plus 130 is equals to p of gas so pressure of gas equals to pressure of gas equals to 206 centimeter of hg tell me is it clear pressure of gas see Shrata you try it's logical you can understand see you have gas correct here you have gas and there is some liquid column here so obviously this liquid column has natural tendency to come down if you remove this gas this liquid column will come down completely right so you have this liquid column which has tendency to come down and this gas will exerts pressure in upward direction this gas only won't let the liquid column to come down right hence this this gas will hold the liquid like this so it will exert pressure in upward direction and liquid has means to come down hence the pressure of gas is in upward direction now you see all of you have got the answer fine so this kind of very basic questions you will get to find out the pressure of the liquid so I guess all of you have understood this properly okay how to do this kind of questions okay so this formula that we have done here this formula you must remember because in the exam when you get the question they won't give you simply mercury liquid over there okay this one this formula you must keep in mind any this is see you have made a mistake over here height of Hg is this any liquid if it is not mercury of a certain height okay corresponding to this height what should be the height of the mercury column which exerts the same pressure so H of Hg rho into H of that liquid divided by rho of mercury this is the formula we have and this is what we have used here so anyway so this is done I know for this chapter we are done all these things okay I hope you understood this properly okay fine so this chapter is over we'll take a break now and after the break we'll start hydrogen okay hydrogen and its compounds theoretical theoretical chapter we'll do it quickly okay you have to read ncrt throughout for this okay but take a break now we'll resume the class at 645 okay we'll start with hydrogen correct yes take a break 645 we'll resume