 okay so heading right down comparison of graph in both isothermal and adiabatic so we know in isothermal process the pv graph is what according to the relation of pressure and volume we have in isothermal process the pv graph is this is isothermal process so for isothermal process the graph is this pv is equals to constant if you try to find out the slope of this graph will differentiate this with respect to v will get minus of k any constant k 1 by v square where constant is k we have over here minus k v square if I substitute this k as pv then it becomes minus p by v isn't it so slope in isothermal process dp by dv is minus p by tell me any doubt once again I should not write this slope this is isothermal dp by dv itself means slope okay you don't get it tell me if you have a y in x axis then what is the slope of this curve if you draw any curve here x is y and x we have what is the slope you'll write here do we write dy by dx is the slope right you know this guys respond yes you know this so instead of y we have p here instead of x we have v here so what is the slope for this graph the slope for this graph is dp by dv so this is what we need to find out if the graph is in between any under any two parameter like suppose entropy and temperature then the slope will be ds by dt anything dy by dx you have to take correct slope for this curve is dp by dv dp by dv we need to find out so we had that relation of pressure and volume we differentiate pressure with respect to volume and we get this tell me any doubt here no yeah this is one thing for isothermal process now if you see the graph of adiabatic process say since it is also the same kind of relation we have so the graph of adiabatic and isothermal process very much similar it's very difficult to differentiate the graph between the two right I am assuming this as adiabatic correct so the graph is like this but the curve is steeper over here right because of v to the power gamma here the steeper curve will have over here but nature is looked like very much same right so we have the condition of adiabatic is p v to the power gamma is equals to constant now I want you to tell me the slope of this graph dp by dv for adiabatic tell me gamma into p by v yes so we'll write this as suppose a constant is k so k times minus gamma divided by v to the power gamma plus one isn't it the first step is this now again k we can substitute as p v to the power gamma so minus gamma into p v to the power gamma is equals to v to the power gamma into v we can write because plus one we have over here correct so this v gamma v gamma will get cancelled so we'll get one sec so we'll get gamma minus gamma into p by v if you remember this p by v is the slope of minus p by v is the slope of adi is the slope of isothermal process right so relation of these two slope is what dp by dv at for adiabatic process is equals to gamma times dp by dv of of isothermal process isn't it since gamma value is more than one so we can say the slope of adiabatic graph is more than to that of isothermal graph yes that's why you see the graph of adiabatic is steeper the slope is more over here very important relation this is one more point here we have like in the previous one you write down the note over here here the note you write down isothermal graph never intersects intersects each other isothermal graph never intersects each other then what do you mean by this means if you draw the graph isothermal graph at different different temperature the graph will be parallel to this like this you'll get the parallel graph it won't intersect each other that is what the meaning of this clear if the graph is intersecting it means both the graph is not for isothermal okay listen to me carefully here i said what if the graph is intersecting it means both the graph is not for isothermal we can have one isothermal one adiabatic we can have both adiabatic but we cannot have both as isothermal clear yes keep that in mind okay so i'm just removing this it is not required just for your understanding i said i'm coming to that mother just wait for some more time i will come to that okay see i'll take up your doubt mother here only see work then comparison if you do in isothermal and adiabatic curve in which process it is more isothermal or adiabatic work then if we are considering expansion if we are considering expansion expansion work done in expansion of adiabatic and isothermal process yes yes so if you have expansion by two different processes isothermal and adiabatic in which process we have more expansion sorry more work done tell me no you see negative when we say more work done we are talking about magnitude because sign is just a notation like whether it is work done by the system or on the system but the magnitude of work then we need to compare okay so that you can understand once you understand the graph of the two curve the comparison of the graph of the two curve so mother first we understand the comparison of graph then automatically you will understand in which process we have more work done answer is isothermal if it is expansion right how we'll see this just a second see i'm considering here the case of expansion the case of expansion i'm considering okay and we have two possibility here expansion is taking place in such a way that final pressure is same final pressure is that is pf pf is same okay so see this the graph if i draw i am drawing here two graphs okay concentrate guys otherwise you will have the you know confusion so a to b we are trying to move a to b we are trying to move by two different processes one pressure one process is this just a second and another one is this i've come to this point only because we have assumed the final pressure is same so this is the final pressure we have this is pf final pressure because the axis is pressure this is volume so this is the case of expansion we have okay two processes we have now we need to identify which is isothermal which is adiabatic like i said the two graph is intersecting so both cannot be isothermal correct which one is isothermal which one is adiabatic okay so look at this see what happens final pressure is same but if you look at the final volume in the two processes here the final volume is this and here the final volume is this or i'll write on v1 and v2 v1 and v2 correct so in this process the final volume that is v1 is less than v2 we have pressure is constant only right pressure is constant means what we have constant pressure correct and if it is adiabatic any one of the process in adiabatic process what happens work is done at the cost of internal energy so expansion we have worked in by the system internal energy decreases so final temperature should decrease final temperature decreases means final volume should also decrease are you getting my point listen to me about i'm saying i am considering i don't know which one is adiabatic so what happens in adiabatic process you see in adiabatic process worked in by the system we have because this is a case of expansion so worked in by the system worked in by the system system does work at the cost of its internal energy so internal energy decreases see this adiabatic expansion means wd worked done by the system since this adiabatic system is doing work so internal energy will decrease delta u is negative internal energy decreases means temperature decreases the final temperature in adiabatic process will decrease more and when temperature decreases means the volume also decreases vf also decreases final volume in case of adiabatic process so we can say in case of adiabatic process the final volume is lesser right so here we have the lesser volume it means this graph is the adiabatic graph we have because the final volume is less corresponding to this graph and this graph is isothermal in that oh by slope also you can tell by slope also we can you can tell by slope method it is easier to understand but this kind of understanding you also have okay because they can ask you this question also right final volume is look at the second condition what is the second condition the first one i took final pressure is same now i'm assuming if final volume vf is same this is the second condition here so the graph goes like this both are expansion so that the final volume is same you see this is the final volume vf this is pressure this is volume case of expansion which graph is adiabatic okay again you can draw a line here the final pressure is more over here p1 and p2 so like the discussion that we had similarly you can understand this and in this also you will get the graphs this one this graph is adiabatic and this graph is isothermal here no it's not no it's not don't go by the drawing over here okay this one is more steeper i guess no it goes like this it is stands like this logically also i can tell you see in adiabatic process what happens final volume is same again internal energy decreases u decreases in adiabatic process why because we have expansion u decreases means t decreases final t final t decreases means vf also decreases right so for adiabatic process pressure final pressure will be lesser so p2 is this corresponding to this graph this graph is adiabatic this graph is ideal now you see what we can generalize here see for both whether it is volume same or pressure same if the case is of expansion then the lower graph is always adiabatic this is one thing that we can generalize you can write down these things in your own words okay case of expansion whether the final volume is same or final pressure is same the lower graph is adiabatic graph is the adiabatic curve here correct this is one point you can generalize another point is what you see this isothermal process we have pv to the power gamma constant sorry pv constant right constant and adiabatic we have pv to the power gamma constant so here the power of v is one and here it is more than one it means if the gamma value increases the graph will shift down okay one say if it is one point something it comes down so if the gamma value increases or you can say the power of v volume increases the graph will shift downward it will come down these two points right okay you see this we have work done in adiabatic and work done in isothermal both the cases of expansion we have let me draw the graph here whatever condition you have final pressure same final volume same whatever it suppose final volume same we have so the graph is this okay so this is the process we have this is the process we have the lower graph is the adiabatic graph just now we discussed so area under the curve because this pv graph we have so area under this curve is the work done in what process tell me in adiabatic cross because the graph is adiabatic so work done is this in adiabatic process but when you talk about the work done in isothermal process we have this much work done right and again what we have here we have this much extra work this is the extra work done we have right that's why we say in expansion work done in adiabatic process is lesser than to that of isothermal yes both stated portion if you you both stated portion if you add that is the work done in isothermal process because this graph is isothermal graph this graph is adiabatic graph area in isothermal graph is more hence work done is more we'll see contraction also once again second we see compression first case we have same final pressure final volume same pressure and volume this is pressure and volume okay final pressure same means the graph goes till this point suppose this is the final pressure we have compression right final pressure this is the graph we have so in this we have opposite the graph which is down the graph which is down is isothermal and the one which is up is adiabatic logic I have told you with that logic you can understand this if final volume is same if final volume is same for example you see this bf we have compression you know this is decreasing in this also we have the same thing the above the graph which is here is adiabatic and this one is isothermal clear so this kind of comparison of graph you must understand and we have seen when there is the case of expansion then as the value of gamma increases the graph will shift down right it will move down on the basis of this one question they have asked in J what is that question I'll show you what they have done they have given a graph like this pressure volume graph obviously like this they have given the graph okay these are the process of expansion and three gases were given three gases were given helium oxygen and SO3 which graph represents which gas one two and three this was a question no they haven't given process they did not mention yes no nothing is mentioned apart from this see I tell you wait okay right see I said what whenever the graph intersects it can never be isothermal first thing correct it can never be isothermal so the graphs are adiabatic here since they are intersecting at a point it is the adiabatic graph adiabatic graph correct I have also told you one thing as the value of no it's not it's not I have also told you as the value of gamma increases the graph will shift downward correct so for this graph we must have maximum value of gamma yes or no tell me and for this graph we must have minimum minimum is out of the three minimum gamma correct so which gas will have maximum value of gamma that depends upon their atomicity more atomic gas gamma value is 1.66 diatomic gamma value is 1.40 and this one is 1.33 so obviously the graph one is for helium the graph two is for O2 and the graph three is for SO3 because you see this graph and this graph right it is for isothermal so PV to the power one constant it is adiabatic PV to the power gamma means gamma constant so gamma is more than one so if the value of gamma I have done it other way yes yes yes by my mistakes by mistake I have done this yeah right right so what we'll do since you see the value of this gamma is increasing and the graph is shifting downward correct so this would be what this would be Ulta this is three this is two and this is one logic you understood yes tell me okay what is the statement you have written just revisit your statement is it fine according to this it goes as the value of gamma increases the graph will shift downward let's let's discuss some problems on this some questions on whatever topic we have covered we'll see some questions so we have this one have we done this question done tell me the answer okay two moles of an ideal gas and there goes isothermal reversible expansion this to this enthalpy change what is the enthalpy change isothermal process delta H is what delta H is zero we have constant temperature so option C now one more next question you see one mole of a mono atomic gas expands adiabatically at initial temperature T against a constant external pressure one atmosphere one liter to three liter okay so two things we have here first of all number of moles is given one more constant external pressure one to three so what is the work done in this process minus one into three minus one that is the work done okay we need to find out final temperature and we can also write this as Cv delta T work done so what is delta T delta T is Tf minus T the final temperature we need to find out is equals to minus two divided by Cv what is the value of Cv because the gas is mono atomic to Cv value we know for the gas Tf is equals to T minus two divided by the value of Cv is mono atomic five by Cp by Cv right so five three by two R so it is three by two into R that would be T minus two divided by 1.5 R value is 0.0821 this K stands for Kelvin that is it option C is correct right so two work done just we have equated P external delta V Cv delta T because it's adiabatic process clear understood question number 16 and 17 then 16th one what is the answer see a mother without his delta H is zero in case of isothermal process this equation that we have that PDV that we use when we have a pressure volume relation correct oh once again let me just discuss one doubt over here just a second okay this question the previous question I'm just going back once ideal gas undergoes isothermal reversible expansion right isothermal reversible expansion we have enthalpy change delta H you see we have constant temperature and reversible expansion means what exchange of heat is not there the process is extremely slow exchange of heat is not there right temperature is constant right there's no change in internal energy delta u is zero right and it is a process we have it is we have a gaseous molecule and expansion is taking place you are mixing this with this equation which we generally use when we have or this thing delta Ngr T when we have a chemical reaction given so you just consider we have a system in which the gases present two moles of gas and it is expanding without changing its temperature correct so heat content is what heat content of the system is what if it is expanding which is the case we have here so obviously it is possible when it takes heat and release the equal amount of heat so system is at the same heat system is the same temperature so the energy involved with the gaseous molecule which is over there that also won't change and hence delta H is zero over here right if it is a case of chemical reaction where a and b reacts and gives some other compounds then we can think of this relation because of the internal reaction also there will be some phase change there will be some change in the molecular property because of that delta H changes over there but when we have the same gas there is no chemical reaction it's simply expanding right so in that case the heat content of the system is same that won't change and hence delta H is here yeah question number 16 how many of you have done 16 you are getting the 42 degree okay simple 16 I'll show you question number 16 what we need to do you see two cylinders a and b fit in the piston contains equal amount of ideal gas the piston a is free to move while that of b is held fixed the same amount of heat is given to the gas in each cylinder the rising temperature in gas a is this rising temperature of gas b okay now two things are there you see for a it is free to move and for b it is held fixed right free to move means we have constant pressure here fixed means we have constant volume right free to move means what whatever external pressure we have it is low enough so that it will expand freely against that pressure only so free to move means we have constant pressure correct and the system the piston is fixed so we have constant volume right so at constant pressure the heat exchange is delta H is equals to ncp delta t at constant pressure this is the heat and this is equals to the heat at constant volume cv delta t that is delta u according to the question we have this relation then we how many of you understood this equal amount we have is it clear yeah so so n will get cancelled only both side gas a the rising temperature gas a is this so cp into 30 is equals to cv value for which gas it is a and b pistons diatomic gas so diatomic gas what is the value of cp cp value is 5 by 2 r cv value is 7 by 2 r into delta t this delta t only we need to find out so 5 by 2 r into 30 is equals to 7 by 2 r into delta t if you solve this then we'll get here what oh i've written it ulta i guess yeah yeah correct correct yeah yeah correct this is 7 this is 5 as i written b this side correct right so it is 7 it is 5 so it will get cancelled and delta t is equals to 42 kelvin we get clear so this was the catch in the question free to movements constant pressure health fix constant volume and then there's nothing in the question question number 17 what is the answer expansion in three different ways we have first is to isobaric right b1 to b2 this is the final volume pressure and b so obviously which one has the highest work highest area it will be mentioned you see which one you're talking about 17th one right see if it is free expansion no it will be clearly mentioned and in case of free expansion as a 16th one you're talking about in case of free expansion work done will be zero since 16th one why you need that is it 16 or 17th as a free to move free to move we are not talking about work done over there free to move means see free to move you can also consider one thing that the external pressure is extremely low it is not zero if it is free expansion it will be clearly mentioned that it is free expansion if it is not mentioned then you don't have to consider that free to move means pressure is extremely low it will expand freely correct 17th one tell me the answer work done in case of isothermal processes more how see here this is the graph no so this one is isobaric the top one is isobaric this is isothermal and this is adiabatic correct so in case of adiabatic it is least w adiabatic is least because minimum area then we have w isothermal and then we have w isobaric whatever w1 w2 w3 is given you can relate with this clear any doubt in 17th one guys 17th one any doubt all of you okay 18th you also solve quickly work done when a gas at p1 v1 changes to p2 v2 adiabatically remains same irrespective of the nature of gas why we can say that b because cv will increase now w is equals to cv delta t no w is equals to cv delta t correct adiabatic process so if atomicity is more cv value is more if you compare cv value for monatomic is 5 by 2 r for diatomic is 7 by 2 r and for polyatomic it is 4 r isn't it right and w is equals to cv delta t hence atomicity increases cv value increases c value increases so work done increases fine guys we'll take a break now we'll resume at 635 and we'll see the another concept in this the first part of this chapter is done we'll see the next part of this chapter okay take a break