 The gaseous system you see first of all we have to understand there are measurable properties into this and measurable properties are what? mass, volume, pressure, like take moons also right? mass, volume, pressure and temperature all these four measurable properties we have for any system okay volume there are unit conversion very important here pressure unit is what? atmospheric, faster also you can barely use faster what atmospheric is this what? 760? m m h t and 1 energy is equal to what? 1 torque so 760 torque its value in Newton per meter is 1.013 into 10 to the power 5 Newton per meter is equal with some time we assume as 1 atmospheric is equal to 10 to the power 5 Newton per meter is equal this conversion is important okay especially this 8 m to m m h t and then Newton per meter is equal okay so 1 energy is equal to 1 torque and 1 8 m is equal to 1.3 which we sometimes we assume as simply 10 to the power 5 Newton per meter is equal to okay temperature unit in this chapter we always take in Kelvin always in Kelvin whenever you are using PV is equal to nRT, temperature you have to assume in Kelvin correct there are various gaseous law we have okay see first volume unit you know ML 1 liter what is the relation of this with meter cube? 10 to the power 3 meter cube when you convert this into centimeter then 10 to the power 6 centimeter cube and 1 centimeter cube is equal to 10 to the power minus 3 and this will be about 10 to the power 3 centimeter cube which is 10 to the power 3 ml right 1 centimeter cube for cubic centimeter is 1 ml okay all these conversion you must know liter meter cube meter cube centimeter cube and ml one ml is equal to 1 centimeter cube next write down gas loss write down these are the laws these are the laws which shows the relation properties at the time keeping the other property visible properties first one is what? Boils law what is Boils law? keeping the temperature temperature and the amount of the gas which is nothing but mass you can say or mole right mass or moles both are related right so for a given amount of gas at a constant temperature or fixed temperature the pressure is inversely proportional to volume this is the point statement I am not giving you you can understand this easily for a given amount of gas at a fixed temperature the pressure is inversely proportional to volume temperature and amount of the gas and number of moles of volume is extremely constant see if I draw the graph here pressure and 1 by v what is the graph again? straight line passing through or any suppose this is T1 temperature this is the T2 temperature this is the T3 3 different temperature the graph is this right if I remove this proportionality sign what we get P is equals to K into 1 by v right where K is what? K is the constant proportionality constant and this K is the function of what? function of LV in this graph if I ask you what is the relation of T1, T2 and T3 can you tell me which one is maximum, which one is minimum T1, T2 and T3 T1, T2, T3 what is the relation? T3, T3, T3, T3 T1 is maximum we are getting this during T1 is maximum see how do we understand this what do you do you just draw a line parallel to x axis or y axis any one of these two you can do right you can draw a line parallel to x axis or y axis I am drawing along parallel to y axis no so this is what see along this line 1 by v is constant and this point gives you a pressure here which is suppose according to T3 it is P3 as this value is T2 and this value is what? P1 increases 1 by v is constant here so P1 increases T also increases 1 by v is constant and then what we can say temperature is here since K increases function of temperature so P increases, K increases so P maximum, so K maximum T1 is maximum it is P1 by v is constant understood this so you can do like this also I am drawing the same graph this is pressure and this is 1 by v suppose I am drawing a line parallel to x axis this pressure is constant right for this line and this gives you 1 by v1 this gives you 1 by v2 and this gives you 1 by 1 by v3 1 by v1 is minimum it means v1 is v1 is maximum v1 is maximum one thing also you can write here K is the function of temperature and it is directly proportional to that K is directly proportional to that another way how you can do this you can just find out the slope of this graph see here which line has maximum slope this is the T1 T1 is this and T1 is this right the slope for T1 is maximum and slope K is nothing but the slope of this line so when K is maximum when the slope difference is maximum so K is maximum for T1 it is directly proportional so T1 is also maximum and T3 is minimum this kind of question is very important for competitive exam but in competitive exam they ask this question they will give you 2-3 graphs at different temperature they ask you what is the relation of these temperatures understood this first point is P and 1 by V graph will be a straight line passing through origin the slope of this line will be K which is the function of temperature as slope increases temperature increases correct what if we give P versus how we do that that is the maximum area P and V you are saying P and V you are drawing this the second this is the one graph we have here the second graph is this suppose pressure and volume axis we are taking this is pressure and this is volume this P V is equal to constant this graph will be P V is equal to constant the graph will be like this hyperbolic graph X, Y is equal to constant this graph will be at one temperature suppose this is T1 this is T2 and this is T3 how do we compare this T1, T2, T3 the same thing we draw a straight line to either X axis or Y axis suppose this line I am drawing P is constant for this line this gives you what V1 this gives you and this one is V2 as temperature increases volume also increases V3 is maximum hence T3 will be maximum then T2 actually taking the T3 we are actually taking the reference of this P V is equal to Nr this reference we are taking however we did not discuss this equation but we are taking the reference of that equation unless what is the nature of this graph pressure because P V is constant this is the graph for this graph even if you write here V also the graph will be same because P V is constant solve this question turn in answer to this question we have two container connected with in pipe of negligible volume here the pressure is 5 atmospheric the volume is 10 litre here the volume is 15 pressure you need to find out there is this top graph here but the pressure in just continue T this is A that this has negligible volume there will be the pressure over there similarly you see this question we have a tube so if you the stop part is open yes because if it is closed then there are two isolations yes when you open this then only you will have P1 is equal to 2 atmospheric P1 is 10 litre from this the gas is leaking out after some time the volume is found to be 5 litre what is the pressure here minus pressure T i and V a the gas is leaking out after some time the volume is found to be 5 litre what is the pressure in the same level why should the pressure what that doesn't make any sense yeah the pressure is the gas is lost all the pressure exactly yeah what is the what is the what is the what is the what is the pressure it is 1 but this we cannot use because the gas is leaking out the mass is not constant so we can just say that we can say if we are to the atmospheric pressure we can say that but we cannot use this while it is not here we can also we cannot what I want if it is open we can say it is equal to the atmospheric pressure that we can say T i and V a is equal to T 2 V 2 since the mass is not constant the statement you see 2 variables 2 properties are constant the amount and the temperature here the pressure and volume is here but the amount is not constant because it is continuously going into that constant so we cannot use T 1 V 1 is equal to T 2 understood this ok one more question calculate the percentage change calculate the percentage change in pressure calculate the percentage change in pressure if the percentage change in volume is 25% percentage change in volume is 25% at a given temperature and amount of the gas 25% what is the amount 25% 25% 20% 20% what is the percentage 20% say V 2 is 1.4 1.4 so V 1 is 1.4 V 2 is 3.4 V 2 is 3.4 V 2 is 3.4 V 1 is what? 100 and V 1 is also 100 because volume is 25 and it is given in that question percentage change in volume is 25% ok you see percentage change in volume is what? 25% now the percentage change is what? it can increase also and decrease also that is not mentioned in the question 25% how we need to answer right so it is saying that percentage change is 25% we do not know whether the volume is increasing or decreasing both means we have to consider in case of when volume increases volume increases when V 2 is equals to what we can write 125% that will be 125 ok then we can use P 1 V 1 is equals to P 2 V 2 so P 1 V 1 is 100 into 100 divided by V 2 is 125 is equals to when you solve this what we can P 2 is equals to 80 so percentage decrease in pressure is what? decrease in pressure is 180 ohms is 20% this is close answer percentage decrease in pressure is 20% second one if the volume decreases volume decreases then the V 2 is equals to what? 75 again we will use this P 2 is equals to 100 into 100 divided by 75 that will be what? 400 by 3 right 400 by 3 is 133 0.33 so the pressure percentage is what? 33. when you get this kind of question there will be option A 20% option B 33.3% option C will be option D will be none so answer will be both right they will mention you percentage decrease is 20% percentage increase is 33% and then option C will be both A and B the point is if they haven't mentioned you whether the volume is increasing or decreasing you have to consider the both conditions I will ask you