 Okay. Hello everyone. Who are all there? Hi Puppy. How are you? Yeah Puppy. We'll discuss some questions. We'll discuss some past year JEE question and again, since this is a revision class, so a little bit of concept also we'll discuss. Okay. So basically we are trying to cover the whole chapter today in 3R. Okay. So every single thing we'll not discuss in this session. But again, whatever session or the section are important in this chapter for JEE point of view and few questions based on those concept we'll see. Okay. So yeah. So basically, since it is already end of September, we have then October, November, December, January, you have JEE main exam, correct? And we are almost about to finish the syllabus. Okay. In coming few days. Okay. So after that, yeah. So after that, we have to revise the whole thing of 11th and 12th chapter in by the end of November. Okay. So this is just, you know, we are starting this thing from today. Okay. So hello everyone. Hello. So since you have finished this particular chapter in 11th class. Okay. So I know you must have the idea of this, the basic idea you already have. Okay. So you can text me because I'll go a bit fast. Since we have to finish this chapter today itself. Okay. So you can text me wherever you will have problem or difficulty. Okay. So initially we'll start with all those basic things, the terms that we use in this chapter. Okay. And then we'll go a bit faster. Right. So first of all, you see thermodynamics in this chapter will deal with flow of heat. Right. How the heat dynamics means what dynamics means motion thermo means heat. Right. So basically in this chapter will deal with flow of heat. Right. How the heat flows and work done internal energy and all those things we'll discuss in this chapter. Okay. Dynamics means motion. Correct. So before going into this particular chapter, first of all, we have to understand certain terms into it. And those terms are the first term I'm straight forward I'm going into the chapter that is system and second one we have that is surroundings. Okay. System is anything which is under consideration. Okay. And you don't have to write. See, I will usually like when I take classes, I usually, you know, dictate all those theories, all those theories and concepts so that you can make your notes properly. Okay. So in this class, I am not going to dictate all those things because again, we don't have that much time. Okay. So I'll just write down every possible thing here and I'll, you know, say every possible thing. Whatever you feel important, you just write it down on your notes. Okay. Or you feel like, okay, this point you have to keep in mind or suppose you forgot those points, so you can write those points. Okay. So system and surrounding system is what system is anything which is under consideration. Right. System is anything which is under consideration. Suppose if I take one pen or marker or notebook or anything and we are talking about that particular pain, anything, you know, you know, if the pain is at this height or that height or in terms of energy if you're talking or anything suppose you're talking about about any object. Right. So that object at that point of time becomes system for us. Right. And every other thing is surroundings. Right. Suppose in the classroom and talking about the whiteboard. Okay. So this whiteboard is the system and every other thing in the class is surroundings. Right. So system plus surroundings gives you universe. Okay. So universe are made up of system and surrounding. Okay. So in this chapter, we mainly deals with system. Okay. See, one more thing you can understand here, which is very basic. You must know. But then also I'll tell you one more time this thing that whatever change you do in the system. Okay. Whatever change you do in the system, if you work on the system or system is doing work, then there will be change in the energy of the system. Either the energy of the system will increase or it will decrease. Correct. With respect to that change, the change in surrounding is negligible. Okay. What is the meaning of this? You try to understand. Suppose the system is releasing some energy. Right. Suppose the system is at suppose, suppose the system is at suppose 300 Kelvin. Right. And suppose it does some work and its temperature decreases of the system to 300 to 250 Kelvin or 290 Kelvin. Suppose. Right. So this is the change in temperature of the system we have. What happens, whatever the energy or heat this system releases that energies that heat is obviously taken by the surroundings. Right. Yeah. So whatever heat releases by the system and its temperature decreases to 290 Kelvin. This 10 Kelvin, which is the difference in temperature. It is given to the surroundings. Right. So if I ask you what is the decrease in temperature of the system, the system is 10 Kelvin. Right. And this 10 Kelvin of or whatever the heat releases in this process that is taken up by the surrounding. The surrounding is very large. Right. So suppose you have a pen. Right. You are in the classroom and you have a pen. Right. If this pen releases some energy, so this energy goes into the entire classroom. Right. So since the size of surrounding is like, you know, is comparatively big in comparison to the size of the system that you have. That's why the change in surrounding. Change means what in terms of energy or whatever you say. Right. The change in system with respect to that, the change in surrounding is always negligible. Okay. This, this idea also helps you sometime in solving that question. The very, no, the basic example of this you can understand. If you have in the classroom or wherever you are in the computer lab or wherever it is. Right. If you switch on the AC, the temperature of the lab decreases. Right. Whatever temperature you like, no, fix over there. According to that, that will be the temperature of the entire classroom or lab. Right. But the heat of the classroom is going outside. Right. Going into the surroundings. Right. So within the classroom, you will have less temperature. Right. But outside the classroom, the temperature, the change in temperature is not that much. Okay. You will not feel any decrease in temperature in the surroundings when you come out of the classroom. Right. So this is a very basic example we have that change in system we can observe easily. But with respect to that, if you try to observe the change in surroundings, it is negligible. Okay. Always. Right. So this one thing you must keep in mind. Now you see, since we are talking about system, right. So system are mainly classified into three categories. And you know all these things. So I won't take much time on this. But why I'm discussing this because on this, you may have multiple choice question in J exam. Okay. That's why I'm discussing this. So definition. I hope you all know. If not, then you can tell me. I'll tell you what is the definition we have. And the system we have three types that is isolated system, open system and closed system. I hope you know the definition of all these three types of system. Correct. What is isolated system? Isolated system is what? There is no exchange of mass and energy. Right. Suppose if I take a system like this, if this system is isolated, right. So neither exchange of mass or not exchange of energy is possible in this. Okay. So energy and mass exchange with surrounding is not possible in this. If the system is isolated, right. So there's no exchange of energy and mass we have in this. Right. So what we can write in isolated system, the energy is constant. And the mass of the system is also constant. Okay. Similarly, what is an open system? Open system is this. Now, since it is open, so exchange of energy and mass both possible. Right. System is open. So exchange of energy and mass both possible. So in this, the energy is not constant. And mass is also not constant. Nothing is constant into this. Okay. Yeah. What is closed system? Close system is what exchange of only energy is possible. There is no exchange of mass, energy possible, energy exchange is possible, but mass exchange is not possible. So what happens in this mass is constant, but energy is not constant. This is what the definition we have. Correct. Now, you see on the basis of this definition, you may have multiple choice question that they have asked already in very like previous exam. Okay. 90s. Okay. I'll give you five, six, four, five statement. Okay. I'll just rub this off. I'll give you four, five statement. And this is the true, false statement. Right. Just you have to give me the answer whether it is true or false. Right. Like this, they can give you four option in multiple choice question. Okay. So you have to be very clear with the concept. See, let me tell you one thing in this chapter. This chapter, I have seen many times most of the students, they attempt question from this chapter. But most of the students I have seen, they have ended up with the wrong response with the negative mass. Because in this chapter, you may have numerical question also. You may have conceptual question also theoretical question. Okay. So you have to be very clear with the concept. Right. So first of all, you see the first statement that I am giving you is a closed statement always has constant volume. What I said a closed system. Let me write down the statement first all those four, five statements. Then you give me the answer. Okay. And you also write it down. This one you also write it down. Okay. A closed system always have constant volume. The first statement is this. Second one, neither heat nor matter is exchanged. The system must be isolated. Isolated system system will be a closed system. Next one, an adiabatic container and adiabatic container container fitted with rigid adiabatic adiabatic piston example of closed system will be an example of closed system. Okay. Now you tell me the true which of one of these statements are true or false. One more if I give you a closed system must be system must be isolated system. A closed system must be an isolated system. Okay. Okay. Think on all these statement once and give me the answer true and false. Pratik is saying second one is true. Shweta one and two are true. Shweta is saying one and two are true. Shruti five is false. What about other Shruti? Kushal true true false true false. Three is true because being a closed system is a prerequisite to be an isolated system. Three isolated system will be a closed system. Sanjana is five is false. True true true false false. I think how will third one be false? What about the fourth one? What about the fourth one adiabatic container fitted with rigid adiabatic piston will be an example of closed system. Now you see the first question we have a closed system always have constant volume. A closed system always has constant volume. You see this statement this statement is false. Why? Because you see if the system is piston cylinder system we are taking and this piston is movable piston we have. You see the system is closed but since the piston is movable it can go up and come down also so the volume is not constant. So the first one is false. The second one neither heat nor matter is exchanged then the system must be isolated. Is it true or false? Neither heat nor matter is exchanged then the system must be isolated. This is also false. You know why? Because we can do the work on to this. See the isolated system means there is no exchange of heat or energy or matter. But the exchange of energy takes place in the form of work also. We can exchange energy when we do work also on the system. If you are doing work on the system or if the system is doing work in that form also the exchange of energy is possible. Since there is no exchange of heat or matter but because of work done the exchange of energy is possible into this. That's why the second statement is also false. Isolated system will be a closed system. This one is true. Isolated system will be a closed system. System if it is isolated it must be closed. Now the fourth one is true. Fourth one you see an adiabatic container fitted with rigid adiabatic piston will be an example of closed system. Is it a closed system? It is an isolated system. So this statement is also false. Since it is closed the piston is rigid. So we cannot move this piston up and down. Piston is rigid. It is adiabatic also. This system is also adiabatic. So since it is adiabatic no exchange of energy possible into this. So this is the definition of what isolated system. That's why this statement is false. If it is isolated it should be closed. See isolated means what? No exchange of energy. What I told you here? System is closed. But if the piston is movable then exchange of energy possible. Isolated system see this is the one of the condition we have. See the closed system we have two types of closed system. One is what? When the piston is rigid constant volume closed system. And when the piston is movable where the volume is not constant. So when we are saying that isolated system will be a closed system it is correct. But when you are saying adiabatic container fitted with a rigid adiabatic expansion. Here you see. We are talking about a closed system here. Try to understand this. System is closed. Means the piston may be fixed, may be movable. Both conditions are satisfied here. But with fixed piston this statement is false. But if you consider movable piston then this is true. Since it is only mentioned about the closed system so we will take it as true. Because for isolated the system must be closed. Now if here you see in the next statement an adiabatic container fitted with rigid adiabatic expansion. A rigid adiabatic piston will be an example of closed system. So this will be a closed system. But the thing here is what? That the piston is movable. If it is movable then the energy exchange is possible. Then it will definitely be a closed system. If you see the definition of isolated system you will get this as a definition of isolated system. So if I write here isolated system then this statement will be correct. Now the last one you see a closed system must be an isolated system. This is also closed system with movable piston. It is not an isolated system. So like this on the basis of this open system and closed system you can have this kind of question in the exam. Multiple choice also or single choice also. You can have this kind of question. So you must keep this particular thing in mind. Now you see this is the one type of question that forms in the exam. Another one is what? That is related with thermodynamic property. But before that we will see one small thing here since we are dealing with this various terms that we have. State variable. State variables are those term actually we have which depends on state only. Example you see. Example we have temperature. We have pressure. We have volume. All these are state variable. It depends on only the state of the system. Suppose here the temperature is 300 Kelvin and here the temperature is 100 Kelvin we have. So no matter how do we come to this point, whether this path or this path or this path but whenever you are at this point the temperature must be 100 Kelvin. Whenever you are at this point the temperature must be 300 Kelvin. So all these are state variable. It depends on the state of the system, at what state the system is. Now the important thing here and this thing that we are going to discuss here that is thermodynamic property. On this they have asked question in JEE exam that I will give you after the discussion of this particular topic. Thermodynamic properties. Thermodynamic properties you see. Thermodynamic properties are of two types basically. And those properties are what? Extensive property and intensive property. Extensive and intensive. What is extensive property anyone? Extensive property depends upon the amount of substance. So extensive properties are what? It depends upon the amount of substance or upon mass or mass. Whatever amount you are taking it depends on that. Extensive means independent. Intensive independent. Independent of mass. On the basis of this one question they have asked previously that question I will give you but there are some examples we have for extensive property that you write on first and you must keep this in mind. You will definitely have this question. Whatever exam you write, whether you write JEE, whether you write BITSAT, whether you write Karnataka CET or NEAT also. So you will definitely have one question on this it is possible. You see it depends upon mass. So whatever this heat capacity, suppose if I write down the mass itself it is an extensive property. Volume also depends on mass. If you take one ml of water that will have a different value of mass. 100 ml of water will definitely have different mass. So mass, volume, moles. All these energy terms in short I will write down internal energy, enthalpy, entropy, internal energy. Heat capacity. Heat capacity. All these are mass dependent term. That is why if you try to recall since you have done this chapter earlier when we do thermochemistry and whenever we define enthalpy of formation. There always we use the term one mole. It is the energy required to form one mole of substance. What is the enthalpy of combustion? It is the enthalpy of neutralization. It is the energy required or releases or required when one mole of acid get neutralized by the base. So we always defines the amount that we are taking. Since all these terms are extensive properties depends upon the mass. So these are the example of extensive property we have. Intensive property you see all terms which are all concentration term are intensive property, all concentration term. Like in example, molarity, molality, all those are intensive property. Concentration does not depend on mass. Concentration term are intensive property. Density is also intensive property. Density you see density will write mass by volume. But this is actually intensive property because when you suppose water you have whether you take one glass of water or one bucket of water the density of water will not change. So density is always an intensive property. If you change the mass in proportion to that only volume also changes so that N by V ratio will be maintained. We can understand this mathematically also suppose we have a container and the mass of this container is suppose 2M and the volume is 2V. Initially the density is what? M by V, mass by volume, 2M by 2V, 2 will get cancelled. Now when you divide this vessel into two equal half then the mass of this part will be M, volume will be V mass of this part will be M, volume will be V so whatever the density of this part D is equal to again mass by volume M by V. You see whether you take 2M mass the density is M by V or you take M mass the density is again M by V. Since mass and volume both are extensive property the ratio of 2 extensive property gives you intensive property that also you can write down. So when you take the ratio of 2 extensive property you will get an intensive property but also you can keep in mind. So concentration term, density we have temperature, pressure, temperature, pressure mole fraction, mole fraction, molar enthalpy, molar enthalpy molar entropy, molar entropy refractive index, refractive index you can write down specific heat, specific heat, viscosity, viscosity surface tension, surface tension dielectric constant, electric constant, pH or EMF of the cell. All these are intensive properties pH and EMF of the cell. Now you see on the basis of this one question that they have asked in previous year and that question is you see the question is identify the intensive quantities from the following. J e 1993, intensive quantity you have to find out enthalpy, volume, temperature and refractive index enthalpy, volume, temperature and refractive index. So this was actually the multiple question multiple correct answer we have. So first option they have given what? Enthalpy. You have to find out intensive property. Enthalpy they have given first option then they have given temperature then they have given volume and then they have given refractive index. So you see enthalpy is what? Enthalpy is the extensive property, not possible. Temperature is an intensive property. Volume is also an extensive property. Refractive index is an intensive property. So answer will be B and D in this. Which one of these are intensive property? Enthalpy, temperature, volume, refractive index. Temperature and refractive index are the intensive property. Now you see there are various, I am assuming that you already know this first law of thermodynamics and all that we are not going to discuss. So only few things we will discuss about that that I will tell you first and then we will continue with this. So first of all we will discuss work. So we will discuss work first and then we will go into this. There are a few, what do I say, conversion in this we have important. So work you see, whenever we say work generally in thermodynamics, we are talking about pressure volume work done. Pressure volume work done. There is a convention, sign convention we have into this. And that is work done by the system. Work done by the system is always negative. Work done on the system is always positive. Whenever system does work, then expansion takes place. These few things you must remember. When we do work on the system then compression takes place, volume decreases. Now whatever the process we have, you must have got various expression of work done in various different processes. But the only formula of or the basic formula of work done we have and that will be W is equals to minus P external into dv, where this volume can change from vi to vf, initial to final volume. This is the only formula of work done we have. Now whatever process we are taking, according to that we will apply the condition and we will get the formula of work done. You must have done in physics that the work done by the system is positive and work done on the system is negative. Yes or no? Tell me this one. In physics you must have done work done by the system is positive and work done on the system is negative. Yes, but in chemistry it is opposite. Work done by the system is negative and work done on the system is positive. Because you see in physics generally we take external pressure. Suppose you have a piston cylinder system like this. In physics generally we take this pressure, external pressure. But in chemistry we will take pressure, the pressure of gas, internal pressure that we have. This is the pressure of gas and this is the external pressure. Suppose it is just a convention. Suppose you are taking pressure in this direction positive. So obviously the pressure in this direction is what? Negative. Negative and that's why we have written minus P external into dv here. Minus P external means what? P gas is equals to minus of P external. So this one thing you don't get confused with. In chemistry we always take work done by the system is negative and work done on the system is positive. Now can you tell me, this is very important. Can you tell me what is the unit of work done we get from this formula? What is the unit of work done? See from this the unit of work done that you get that will be what? The unit of pressure and the unit of volume. And that will be what? From this formula, whenever you calculate from this formula, you always get unit of work done in ATM litre. Pressure is ATM, volume is litre. No rethink, that's what I am telling you. No. Because you see we have pressure and volume. So we always get from the formula we get Pascal meter cube. Fine, we will get ATM litre in terms of Pascal also you can say. So this is the unit we have. But in the option you will not get this ATM litre. You will get unit in terms of joule. So ATM litre this conversion you must keep in mind. One ATM litre you have to convert in joule then you have to equate this with 101325 joule. Or if the pressure is in bar then one bar per litre is equals to 100 joule you have to substitute. So this you must keep in mind this conversion here. Usually whatever value you get here suppose you are getting 100 ATM litre. So they will give you 100 joule also in the option. In Hari we generally take we got 100 so it will be 100 joule. So don't make mistake over here. Unit curve and conversion is also important. Now if 102 condition we will take here. If we have closed and rigid system. Close rigid container suppose if we have. What do you mean by closed and rigid container? Means it's DV is 0 there is no change in volume because the piston is rigid now. When DV is 0 then work done will be what? Work done will be 0. So in this case work done will be 0 or if we have P external 0 then also work done will be 0. Now you see the next term that we have that is internal energy. Okay you tell me one thing that's one thing I wanted to ask you. Change in internal energy du is equals to and CV dt is one of the formula we have yes or no. When can we use this formula? When we use this formula du is equals to and CV dt. Constant volume. Okay I know that you all give me this answer only. Where is Purvik what is the answer Purvik? Vaishnavi, Shweta what is that? Oh you have given volume is constant. Prateek, Khushal, Vaishnavi what is the answer? Okay so you see all of you are saying constant volume but this is not true. Okay this formula we can use for all process. For all process whether the volume is constant or not. Okay we can use everywhere this formula. Why you try to understand this. Okay so internal energy you see internal energy basically we will start with the basic thing from this. Okay internal energy I don't know Purvik what are you saying. Anyways we will discuss this. See internal energy is what? It is the summation of or the sum of all kind of energy right. Kinetic energy, potential energy and chemical energy also. And chemical energy also. Means whatever different different kind of energy whatever energy you have everything you add for the system you will get the internal energy of the system right. Chemical energy means what? It is the energy which involves in bond making, bond breaking energy involves in the nucleus also everything comes into this. Okay kinetic energy is what? Kinetic energy is nothing but the because of the motion of the particles right. And motion can be translational, rotational and linear. Translational, rotational and what we have the next one vibrational also right. All these three kind of motion includes kinetic energy. Potential energy is what? It is because of the position right because of the position of the molecules of the system. All these kind of energy if you you know add then you will get internal energy of the system. Practically if you see it is very difficult to calculate all these energy and add those to get the absolute value of internal energy right. That's why we do not ever calculate absolute value of internal energy but we actually calculate the change in internal energy del u. We always calculate del u the change in internal energy at one position and another position. We never calculate the value of u. You also must have observed if not then you can go through some of the question. They never ask you what is the value of internal energy? They never ask you this question. They always ask you what is the change in internal energy? Because the absolute value to calculate the absolute value is very difficult. This is the one thing. The next thing is what? We all know that the kinetic energy is what? The kinetic energy is the function of temperature right. Potential energy is the function of volume. Why volume? Because you see the system molecules if the volume is suppose large right then the system molecule will be away from each other. The distance between the molecule will be more when the volume is very high but if the same amount of gas you put into a small volume then the distance between the two molecule will decrease. When the distance will decrease its potential energy will also change. Correct? That's why we say the kinetic energy is the function of what? Sorry potential energy is the function of volume and we neglect this chemical energy. Because the change in chemical energy is very minimal always. So we generally neglect this chemical energy. Now we have two different variables and we can write down the internal energy is equals to the function of temperature and volume. Now if you know this Euler's formula we can write down the change in internal energy du is equals to dou u by dou t at constant volume into dt plus dou u by dou v at constant temperature into dv. This formula you know have we done this formula? This we call it as Euler's theorem. Euler's formula you can apply whenever the one variable depends on more than one variable like this. You see u depends on tv and suppose if I write down like this suppose if you see y is a function of suppose p q r and what we can write the change in y is equals to dou y by dou p keeping this q and r constant into dp plus the another term plus the another term like this we write. So anyways it is not that important. This we call it as Euler's formula or Euler's theorem. Euler's theorem. Euler's formula or Euler's theorem. So anyways you let it be this is not at all required but let me tell you one thing here. Now one thing if you remember that the heat content you must have done this derivation from here that I am doing just now. Heat content constant volume is equals to q which is nothing but u we have and at constant pressure q is equals to h that is enthalpy. Internal energy is the heat content at constant volume and enthalpy is the heat content at constant pressure. So I did not give you this thing initially because it comes from the heat capacity and what is the heat capacity? I will just tell you here only. This term you just let it be will come to this again. Heat capacity is what it is defined by the heat required to change in temperature by 1 degree Celsius. Heat capacity is what? Heat capacity is C. Suppose if I write dq is the amount of heat required to change the temperature by dt. Heat capacity is what? It is the amount of heat required to change the temperature by 1 degree Celsius. Amount of heat required I am repeating this again and again if you do not have this write it down. Heat capacity is what? It is the amount of heat required to change the temperature by 1 degree Celsius. So C if I write down dq is the amount of heat required to change the temperature by dt. So for 1 degree Celsius change in temperature the heat required is what? dq by dt and which is nothing but C we have according to the definition. Now when I take constant volume, it is the heat content at constant volume. At constant volume what we can write this dq is equal to du and at constant pressure this dq is nothing but dh. We will come to this dh part later on. But this is what at constant volume dq is equal to du. So if I substitute here you see this is the heat capacity at constant volume if I write. So Cv is the heat capacity at constant volume and this dq becomes du here. So du by dt for 1 mole we are talking about Cv is equal to du by dt and then what we say that this du is equal to du is equal to Cv dt and for n moles we will write nCv dt. Yes or no? I think I guess you have done like this only this derivation. Correct yeah you see if you do the derivation like this by the definition of heat capacity you always get this only and you will say okay we can use this formula whenever the volume is constant but that is not true this formula we use for all process. Now we are just taking the reference of this thing over here. Now you see du by dt is what Cv? So for n number of moles for n number of moles this formula becomes du is equals to du by dt is Cv that we can write for n number of moles nCv dt plus du by du by du v at constant temperature into dv. This is the actual formula of change in internal energy for all process whatever process we have for all process you can use this okay whether the volume is constant or not. Correct now you see one thing if you see this term here u internal energy right this is what internal energy right this is internal energy du is the internal energy right I will just make some space here you understand try to understand this term du by dv du is the internal energy right and energy we can always write pressure into volume try to understand the unit of it okay so you wrote dq as du because at constant volume q is equals to u so you should not be at constant volume no actually you see this du by dt right in this expression we are coming from here right we are coming from here right so du by dt here do we apply any condition here from this to this step do we apply any condition we did not apply any condition over here just du by dt at constant volume we write cv this is the simple definition of heat capacity at constant volume it is a definition of heat capacity at constant volume we haven't applied this any condition over here the definition of heat capacity that's why I was like paying attention over there that definition of heat capacity heat capacity is the temperature heat required to change the temperature at 1 by 1 degree Celsius at constant volume right the heat content is nothing but the internal energy of the system it is the another definition of internal energy right at constant volume the heat content of the system is nothing but the another internal energy of the system it is for all process q is not equal to u if it is for all process q is not equal to u yeah if it is for all process q is not equal to u no actually see again this from this to this term we are writing down it is just a definition of internal energy okay that's what I'm telling you one way to define internal energy is this all kind of energy you add internal energy is also the heat content of a system at constant volume right so this from this to this you are coming getting over here it is by the definition of internal energy right which is the heat content of the system at constant volume right so simply that definition of u we are taking over here we are not applying any condition we are not keeping the see whenever you have internal energy u correct you will have some value of this okay whether the volume is constant or not right so when but when you take the volume constant and you try to find out the internal energy of the system then also you get the same value that's why we are having this definition also right so when the volume is constant then the heat capacity is defining by this c v and this is equals to du by dt at constant volume for one mole right that is the definition of heat capacity at constant volume right and that definition we are just using over here to write down one expression that is it we are not applying constant suppose if you take constant volume here right constant volume if you take then this term automatically becomes zero if you take constant volume but that is not we are taking over here we are just substituting the expression here that is it okay now one thing you see doh u by doh v by v we can write u is an energy right and pressure volume p into v is also an energy so this we can substitute here and this volume volume will get cancelled will get the unit of pressure over here correct so since this is the internal energy so we call it as internal pressure try to keep this no the term in mind doh u by doh v is what doh u by doh v has the unit of pressure and we call it as internal pressure okay now for ideal gas now the general formula is this which is applicable for all process now in this we are taking the condition and the first condition is what for ideal gas because 99% of the situation we are dealing with ideal gas right and we know in ideal gas there is no intermolecular attraction gases molecules are not attracting right there is no intermolecular force right so since there is no intermolecular force of attraction there is no internal pressure a will be zero a is the correction factor of pressure there we have in gaseous state a will be zero and that's why the internal pressure which is doh u by doh v is zero and when this is zero you substitute this here you will get the formula which is doh u is equal to du is equal to ncv dt so for ideal gas the formula of change in internal energy will get is ncv dt for ideal gas and that's why we use this formula directly but for real gas if they have given they must give you at constant temperature the relation of internal energy and volume that you have to find out this by the given condition and then you have to add these two you will get the change in internal energy then I hope you understand this see we got this formula of change in internal energy is equal to this this is the du is equal to correct purvi correct purvi this is actually for ideal gas right the actual formula of change in internal energy is this will get from euler's formula wait wait wait I am telling you let it be actual formula of change in internal energy is this right now in this if you take the unit of this u is the energy so energy we can write pressure into volume because that is a work done work done is nothing but energy and volume volume gets cancelled will get pressure means du by dv doh u by doh v is nothing but the pressure unit we have since u is the internal energy we are calling it as internal pressure ok now in case of ideal gas there is no internal pressure right in case of ideal gas there is no internal pressure because of ideal gas molecules we do not have any interaction into this if you remember gas is the state right since we do not have any interaction so a value which is the pressure correction factor will be 0 in this case and when a is 0 the internal pressure is 0 and when the internal pressure is 0 doh u by doh v is 0 when you substitute this doh u by doh v is 0 over here you will get du is equals to ncv dt right so du can be ncv dt in two cases when we have ideal gas or when we have constant volume constant volume means what the vessel is rigid ok if you have a rigid container close a rigid container if you have then only the change in volume is 0 which gives you du is equals to ncv dt understood yes or no hello we will see some questions on to this after some time ok one more thing we have to discuss here so like the bottom line of all this story is what du is equals to ncv dt you can apply whether volume is constant or not we don't have to do anything with volume thing over here for ideal gas for rigid container we can always apply du is equals to ncv dt whether the volume is constant or not ok now you see another thing here so for one mole one mole we have just now we have done that du by dt is equals to cv right now if you are talking about enthalpy right so heat capacity write down this thing heat capacity constant pressure is cp right and cp we can define as at constant pressure we can also write or write down like this enthalpy is the is the heat content of the system at constant pressure constant pressure ok so dq is equals to dh when the pressure is constant ok and again heat capacity is what it is amount of heat required to change the temperature by one degree Celsius suppose dq is the dt is the change in temperature we have when we have supplied dq amount of heat into it one degree rise in temperature the heat required is dq by dt if it is constant pressure so this will write dq by dt is equals to cp and we know at constant pressure dq is nothing but dh we have so cp we can write down dh by dt now we can also write down one more relation here that is dh is equals to du plus pdv ok at constant pressure see what we can write h is equals to u plus pv is the mathematical definition of enthalpy we have right h is equals to u plus pv or if I suppose if I write down q here right from first law of thermodynamics right so at constant pressure if I write down dq is equals to what we can write du plus constant pressure we have so pressure outside dv we write and we know at constant pressure dq is nothing but dh so we will get this expression right now if I divide both sides by dt so what we get dh by dt is equals to du by dt plus pdv by dt so dh by dt is nothing but cp du by dt is nothing but cv plus r pdv by dt is nothing but r we have gas constant right so we will get the formula cp minus cv is equals to r this is the derivation of this we have which is important for board exam also cp minus cv is equals to r one more thing we have here the ratio of cp by cv cp by cv is equals to gamma right and if you combine these two we will get cv is equals to r divided by gamma minus one cp is equals to gamma r by gamma minus one this is the formula of cp and cv we have in terms of gamma you know we have a formula in case of chemical reaction and that is again important if chemical reaction is given then we write down del h is equals to del u in terms of p del v we will write delta ng rt ok where this delta ng delta ng is the number of moles or in short if I write down moles of product a product we always take which are in gaseous state minus moles of reactant this also must be in gaseous state ok now one thing you see from this expression it is important ok from this expression if delta ng is less than zero which means what this is nothing but the work done we have this part is nothing but the work done because you see work done is what like I said the formula of work done is always minus of integral pdv always the formula is this we have where we have v initial and v final since we are talking about enthalpy on the left hand side and we know it is the heat content of the system at constant pressure yeah yeah see Shweta what happens whenever we are talking about one thing you must all of you must understand properly whenever this reaction this formula is always true for chemical reaction if chemical reaction is given or suppose if chemical reaction is not given they will give you like this what is the change in enthalpy we have when the combustion of methane takes place ok so we know methane combustion takes place it forms CO2 NH2 where CO2 is in gaseous form like this you will have the information of chemical reaction the first thing is that this reaction or this formula we can always use when chemical reaction is given or you know right now any chemical reaction if it is not mentioned it always takes place at constant pressure and constant temperature process right any chemical reaction if it is not mentioned it always takes place at constant pressure and constant temperature so obviously this T is constant over here right understood Shweta ok now you see work done is this so since the pressure is constant so we can take this pressure outside and when we solve this we will get what vf minus vi right f what we can write final volume can we write this as number of final number of moles for gas into RT final number of moles for gas into g stands for gas here minus the initial number of moles for gaseous particle into RT p will not be there p I have taken into this side and minus sign will be there as it is p v f is this p vi is this correct now p v f is this so what we can write here you see we can easily take this RT outside so minus of RT in bracket we have final number of moles for gas for gas minus final number of moles for final number initial number of moles of gaseous reactor this we write it as delta n g RT and that's why the work done is this minus of delta n g RT ok now coming back to this point and that is what we have substituted this thing over here and the formula becomes this the initial formula is what del h is equals to del u plus p delta v p delta v is nothing but delta n g RT now you see if delta n g is less than 0 means what work done is work done is positive and work done is positive means what work done on the system work done positive means what work done on the system on the system work done means what compression takes place all these data you can easily retrieve from this ok now when delta n g is greater than 0 it means if this is positive means work done is what work done is negative work done negative means what work done by the system by the system by the system means what expansion so whenever negative work we have it means expansion takes place right so if you have some example of reaction if I write down you see this if I write down the first reaction 302 gas gives you 203 gas what is delta n g for this reaction is less than what is the value delta n g or if I write down CaCO3 solid converts into CaO solid plus CaO2 gas delta n g one more if I write down N2 gas plus 3H2 gas gives you 2NH3 gas delta n g you see for this one delta n g is what gaseous product minus gaseous reactant minus 1 it is negative gaseous product is 1 there is no reactant right so minus 0 it is 1 here we have 2 minus 3 plus 1 is equals to minus 2 ok so like this we can find out delta n g and we will get the idea of what idea of whether expansion takes place or compression takes place ok whether expansion or compression takes place ok so the next we have to understand is various process ok and this one is again the most important thing in this chapter what are the different types of process we have what are the different types of process yes various thermodynamic process isochodic isothermal adiabatic ok so basically we know all these process like most of you have this idea isothermal temperature constant isobaric temperature constant isochoric isochoric volume constant then we have adiabatic no heat exchange right so del q is equals to 0 next one what we have cyclic process then we have reversible and seventh one we have irreversible process cyclic process in cyclic process del u is equals to 0 always even whatever the state function we have all change in 0 because in cyclic process we know the initial and final state are same right from where you start you comes finally at that position only right so this is the cyclic process we have suppose right we start from this point a when to be and then c and then d and finally at a right we can have cyclic also right like this also we can have the process okay so this is the cyclic process initial and final state are same and I hope you know all this isothermal isobaric isochoric and also I'm not discussing these things right one thing is important for this cyclic process you write down that one okay see whenever you have this kind of cyclic process right with this arrow you will understand that whether it is going into clockwise manner or anti-clockwise manner okay so one thing you must keep in mind so how is enthalpy 0 in cyclic see enthalpy is what enthalpy is the state function right so it depends on initial and final state of the process suppose you are going from here to here enthalpy has nothing to do with what path you have chosen from going like when you go from one state to another state it only depends on the initial position and the final position that is it right so you see at this point suppose you are starting and finally you are coming over here only right so enthalpy changes what initially the enthalpy we have at this point and final enthalpy is what at this point only when final enthalpy is same that's why it is 0 correct so enthalpy change whatever state function we have if you write entropy also usually right but there are many condition in case of entropy that's why we do not write here but usually as we talk about only state function then entropy change will also be 0 there is no mixing of gases and all then whatever state function we will have the change in state function will be 0 now cyclic process you see if the process because if the process is given like here you see it is clockwise right so when clockwise process is there then what we assume that work done work is always done by the system clockwise is work done by the system which is always negative the assumption we have and T clockwise if it is given it is work done on the system work done on the system right so this gives you positive this you must keep in mind okay now if I give you one question here right and if you see this diagram on this this is pressure and this is volume pressure is in suppose ATM and volume is in leader okay now we are starting from this point A B C and D and we are going like this at this point the pressure is suppose 10 atmospheric and at this point the pressure is 5 atmospheric the volume here is suppose 4 and here is suppose we have 8 liter you have to find out work done in this process A to B, B to C, C to D, D to A tell me the answer I will give you one minute you just solve this and tell me the answer okay so all of you are getting minus 20 right see there are two methods to solve this right there are two methods to solve this one okay first one you see for A to B if the process is going from A to B what is the work done for this W A B if I write that will be minus P del V right minus P delta V now since I have taken minus P delta V so just you have to write whatever pressure we have initially I will not solve this thus I will tell you this 10 into final volume minus initial volume 8 minus 4 final volume is 8 minus 4 work done for B to C will be what 0 work done from D to A will be 0 because both are constant volume process we have so delta V is 0 work done for C to D if I write that will be what the pressure is 5 minus 5 into the final pressure is 4 and initial pressure is 8 which is 20 yes and what is this it is minus 40 total work done is what all these you have to add you will get minus 20 okay so now you see one thing also you can observe A to B we are going means this is what this is expansion we have volume is increasing C to D it is compression expansion means what work done by the system means work done must be negative that is why you see we are getting negative value here right compression means what work done on the system must be positive you are getting positive value here like this you can cross check okay now another way is what since you see the next method which is the easier one I think you all have done like this or what yes or no you all have done like this only one thing suppose if you have an axis Y and X and if I have to find out the area of any curve on this axis how do we find out will find out Y into X as we multiply the two axis that we have right here also you see if you have to find out the work done of this right then what you have to find out the area of this curve that you have the graph that you have work done we know it is minus P delta B so P into V if you do it gives you work done into volume gives you work done right so this pressure into this volume axis if you have pressure volume axis then you can directly find out the area of this that gives you the what work done in this process now you see this difference is 4 right this is 5 from here to here and this difference is what 4 so length into breath is nothing but the area of this length into breath is what 5 into 4 gives you 20 right so this gives you the magnitude actually the area method gives you magnitude right but how do we get this sign that is another question right and for that what I told you if clockwise is there see the arrow I have given you clockwise it means it is clockwise clockwise means what work done by the system work done by the system means what it is negative so answer will be what minus 20 did you get this so if you have pressure volume thing is given then you can find out this easily directly by calculating the area ok directly by calculating the area into this ok now one more question in this will see for cyclic process I have given you del u del h del s del g right delta t all these will be 0 all state function chain in the state function will be 0 right now if I ask you one question because the graph related question they often ask in this particular chapter so you have to you have given you have this graph ok this is let me draw the graph first suppose the graph we have this this is pressure and this is temperature pressure temperature axis we have ok this is a see and the process is going like this now this graph you have to convert in pressure and volume right and one more conversion will see that is volume and temperature because sometimes you know what happens if you have pressure volume graph then you can easily find out the area and you will give the what is the time now ok ok ok we'll do this after this only I'll give you the break ok because after this we have to start reversible reversible process ok so that will take some time yeah give me 5 minutes ok 5 10 minutes you give me I'll give you the break ok so you see why why this is important because sometimes if they want to twist the question suppose you have pressure volume graph then you can easily find out the work done right and we are we have to mainly deal with work done in this chapter right so pressure volume graph you can find out the area and you will have the work done but sometimes if they really want to ask a question they will not give you pressure volume graph they will give you pressure temperature graph or volume temperature graph ok then how do we convert this into this ok so now how do we approach this particular graph that we have to understand first of all you try to identify what all process we have here you see I have given this line from here to here it means this line is passing through the origin and when passing through the origin it means for process A to B volume is constant yes or no tell me A to B yes volume is constant what about B to C what about B to C isothermal process constant temperature and C to A is what isobaric process constant pressure now we have to draw the graph in such a way that all these condition are satisfied ok so A to B is what A to B is volume constant so volume we have here right so A to B we cannot go like this right we can go like this or from top to bottom or bottom to top so obviously we have one line like this yes now in this point this can be A also and this can be A also that we are not sure right now right this can be A also this can be A also when I write this A it means the process is going in this direction when I write this A it means the process is coming in this direction right now B to C is what B to C is isothermal process so for PV graph isothermal process we know the graph goes like this for Boyle's law we must have done know the graph of PV is like this in Boyle's law constant temperature right so constant temperature graph is this now C to A graph is isobaric isobaric means pressure constant so pressure constant graph will be like this right now you see A to B we are going A to B we have constant volume but pressure is increasing right like I said this point can be A or this point also can be A so which point will be A that we are going to decide now right you see from A to B the pressure is increasing at constant volume so if you write this A and this B then the pressure will decrease correct so we have to write A over here B over here and third point is C if I put the arrow then A to B pressure you see the pressure is also increasing volume is constant right B to C the pressure is decreasing you see pressure is decreasing and volume is constant C to A constant pressure you see C to A we have constant pressure this is the graph we have of pressure volume graph did you understand this now if you have to convert this into pressure temperature graph now you see PV is equals to NRT if you apply NRT volume and temperature we have to think means pressure is constant so for constant pressure the line must passes through what origin right constant pressure graph what we have C to A right so C to A must pass through origin like this suppose so I'll give this is C to A right now which point is C which point is A that we have to identify again right C to A if you are going you see temperature is decreasing right so obviously in this process temperature must decrease right so you must have to write down C over here and A over here correct now AB graph is what constant volume so constant volume obviously AB graph will go like this parallel to the yx this perpendicular to this y axis exactly right and C to B B to C is isothermal so you see this B to C is isothermal this is B point okay so if I write down arrow here B to C you see constant temperature but volume is increasing B to C constant temperature pressure is decreasing means volume will increase right C to A C to A you see constant pressure temperature is decreasing C to A constant pressure temperature is also decreasing right A to B constant volume but temperature is increasing right so A to B you see constant volume but temperature is increasing this is what the graph of BT we have understood so like this if you have any graph given whether it is pressure temperature graph you have or volume temperature graph we have we can easily convert this into pressure volume graph and then we can solve the question okay so we'll take a break it's 615 almost okay at what time will start you tell me 630 correct will start at 630 sharp okay make sure you are present okay don't go anywhere because we have to discuss reversible irreversible process that is very important okay 630 will start 630 sharp yeah hello can we start who are there hello who are there so the next thing we have we are going to discuss is reversible and irreversible process okay reversible and irreversible process see before discussing this reversible and irreversible process one thing I want to ask you must have done the derivation of isothermal reversible process right isothermal reversible process and then in that we have done the derivation that is DW is equals to minus integral of P dv we want to V2 and then what I what we have done into this we have taken this pressure outside dv and then we derived the relation if you remember yes we have done this derivation did we take this pressure outside or not oh it is reversible no we haven't done this right okay let it be this one we have to actually way here either we can take this pressure out or we can let it be this pressure inside and we can substitute this as NRT by V dv and then we can you know integrate yes so since it is reversible right so we have done by this way not by this way okay means in this thing the pressure is not constant yes that is what you have to understand here if you try to recall you have done this derivation and we have done in this DW is equals to minus P delta V and since this reversible process we can't take this pressure outside the integral shine sign and then we substitute this as NRT by V and then we have done the derivation into it right so now the point here some of you must have this doubt that why we not take this pressure outside because the expansion or whatever it is takes place against the constant external pressure right so for that you have to understand reversible and irreversible process first okay generally what happens reversible process we do that we say that these are the process which takes place in both direction forward also in backward direction right it is bi-directional process okay any state we can anytime we can convert or we can reverse the process itself okay and we can go to the initial position right that is what the definition generally given right but that won't help you solving the question okay so first of all you have to understand this reversible and irreversible process and for that I am going to draw two piston cylinder system here and with this I am trying to explain what is reversible and what is irreversible process this is the one system we have and is the another one okay suppose the first one we have a movable piston right and this piston is somewhere here we have some gas over here which is not actually required but I told you this okay and this gas will apply some pressure on the piston and this piston will also the external pressure will also apply some pressure on the gas and wherever we have this equilibrium then the piston will be static okay so what happens here suppose if I put some particle here suppose if I put some sand in a bag like I take some bag okay and in the bag I put some sand and then I place this entire bag here on this piston right like this bag filled with sand over here right now this because of this bag will have some you know pressure downward and then the piston and the gaseous pressure wherever it is equal that the piston will be static right now if you want to remove this sand bag from here right we can do this in two different ways what are those you see all of a sudden if I remove the sand bag completely right then piston all of a sudden will go up and then wherever the atmospheric pressure and the pressure of the gas will be equal there the piston will stop right further it won't go up okay another way is what we can remove the sand slightly from this bag right little bit like we remove the sand little bit then again the piston will go up equilibrium will maintain again will remove the sand again the piston will go up equilibrium maintain and this process also takes place okay suppose this is state 1 we have and this is the state 2 right so from state 1 to state 2 if you have to go right this thing or this like the position this final position we can achieve in two ways one is what all of a sudden you remove the sandbag or second way is what you keep on removing the sand particles slightly like in a given time interval right so you remove the sand particle it goes up static again you remove again it goes up and it goes till here when all this when the bag you will remove completely right so two process I have discussed two way I have discussed when you remove the sandbag completely what happens this piston all of a sudden will go up right this process is what this process is very fast process right and this process we call it as irreversible process irreversible process right the second way that I explained you that you use you keep on removing the sand particles slowly and then you again achieve the final state okay that process is reversible process reversible process so now you think on it a little bit okay in reversible process what happens continuously we are removing the sand particles right means the pressure that is exerted by the bag is continuously changing right that's why in this method iso thermal reversible process what we say that this pressure is the function of volume here right and we cannot take this outside so we substitute this pressure in terms of volume and then we integrate understood any doubt till here any doubt who are there tell me hello okay yeah I could not okay I could not see the messages that's why I stopped okay anyways so you see basically there are few points you have to keep in mind here right reversible process like I said okay it is a step a voice process okay in irreversible process what happens all of a sudden piston go up goes up right in irreversible process so actually this expansion or compression whatever it is it takes place against a constant external pressure okay so there are few points in this you write down which is important okay this is important with respect to your board exam also okay they ask question on this okay so write down in irreversible process first it is a unidirectional process it is a unidirectional process and it cannot be reversed it cannot be reversed along the same path easily it cannot be reversed along the same path easily the next one we have it has it has an eight number of steps it has finite number of steps it is a fast process fast process and the system is at is at thermodynamic equilibrium at only initial final step initial and final step it takes place it takes place against constant external pressure constant external pressure right now if this equilibrium we have initial and final step only so we can apply this ideal gas law PV is equals to NRT at initial and final step only right at initial and final step only the next for reversible process you write down reversible process that's why one more thing if I tell you here any any work done calculation right TW is equals to minus PDV V1 to V2 if you have to do in irreversible process then we can simply take this pressure outside because it says simply that it takes place again the constant external pressure so we can take this minus P outside V1 to V2 TV which finally gives us minus P delta V as the work done in irreversible process but this thing this pressure we cannot take out in case of reversible process why external pressure is not constant because as I said that we are continuously removing the sand particles from the bag right from the bag so if you remove sand particles continuously so the external pressure is continuously changing as the pressure is decreasing this piston is slowly going up right to the final state right since the piston is slowly going up that's why we call it as a very slow process right which takes place against the which takes place against variable external pressure we have actually okay and since it is slowly going up to the final step so it contains infinite number of steps okay in finite number of steps this is on one point each step will be in thermal thermodynamic equilibrium each steps step is in equilibrium okay so here we can apply this PV is goes to NRT at every step basically okay P external external pressure is not constant okay and it is a very slow process and since suppose you are removing one sand particle from here and the piston slightly goes up again you put the same sand particle into the bag the initial position will be restored piston again comes down okay so in this what we say that we can reverse the process reverse the process anytime anytime and the original position will be restored original position will be restored okay now if I try to make you understand these two things with the help of graph right with the help of graph if I try to make you understand you see we are drawing this only one graph I'll make you understand in this suppose we have pressure volume graph right this is pressure volume I'll try to make you understand isothermal isothermal irreversible process isothermal reversible process okay isothermal irreversible and isothermal reversible process since it is an isothermal process so the pressure volume graph will always be like this okay suppose initially like I take this piston cylinder system right initially the piston is here right this is state one right and we here we have the bag actually okay sand particles right so here we'll have some pressure because the same part the pressure will be obviously more suppose initial pressure is somewhere here right it is the pressure we have P1 and when since irreversible we are talking about this bag you remove all of a sudden and the piston goes up and we get the equilibrium here at some point position here this is the final position initial position is the final position so there will be expansion right so volume increases so initial pressure suppose we have here and all of a sudden when you remove the bag the process goes like this since it is isothermal and this is what the pressure P2 right here we have the pressure P2 right so this is what this is this is one step from here you remove this bag all of a sudden this comes over here right and the volume increases you see the initial volume we have here V1 and the final volume is V2 right now the same thing the same state we can also achieve reversibly also and what happens in reversible process now you pay attention here right suppose if you are removing the sand particles so pressure slightly decreases right so first step you see if the pressure slightly decreases suppose the pressure comes over here right this is the pressure we have right it is P1 P2 suppose if this is if I write P dash so we remove the sand particles slightly pressure decreases and in this course expansion takes place a bit so this is the expansion we have so according to this also will have some volume here again you remove sand particles right again from here from here the pressure decreases right and in this course expansion takes place this is suppose we have P double dash again you decrease pressure it comes down here right and again in this course some expansion takes place like this and this pressure is suppose we have P finally if the pressure becomes P2 the expansion will be like this okay so you see in irreversible this the blue one blue one we have here is what this blue one is the expansion we have for isothermal irreversible process and the red one is the expansion we have isothermal reversible process right you see the number of steps involved in isothermal irreversible process is equals to one one single step from here to here it comes right number of steps here is one two three four four steps we have basically okay so one more thing we can conclude from here as the number of steps as the number of steps increases then the process has tendency has tendency tendency to behave behave more like reversible process without you have in this you can ask me okay so if you increase the number of steps on the basis of this also they can ask you some question okay you see each step will be in equilibrium in reversible process right but this kind of equilibrium only exist in initial and final step in case of isothermal process isothermal irreversible process right so that is why you see this expansion this expansion takes place from here to here this expansion takes place against this external pressure this expansion takes place against this external pressure this expansion takes place against this external pressure like this you see in case of reversible process the external pressure is continuously changing right that's why while we do the derivation of isothermal reversible process we we cannot keep this pressure term outside the integral sign and then we then we substitute this pressure in terms of volume with the help of ideal gas equation PV is equals to NRT by V PV and then we integrate that and we'll get the expression okay did you say in reversible reaction there are infinite steps but does not it have doesn't it have finite steps in the graph see the graph see the point is we decrease you remember one thing in isothermal reversible process we decrease the pressure by very small amount DP this is this graph I made for you to understand actually if you decrease suppose pressure we have an atmospheric initially right so from ten if you decrease the pressure by point zero zero zero zero one then also some expansion we have here again you decrease further pressure point zero zero zero zero one then also some expansion we have here that's why we are saying it is it has infinite number of steps possible what I said you have a sandbag here you remove one particle from this one sand particle what is the mass of that negligible okay but that also leads to the some expansion into this okay that's why we say infinite number of steps okay so if you have this concept clear they ask this question and board exam also the difference of reversible and reversible process so everything four five steps you can write down if you draw this graph you'll get full marks okay there's nothing more than this and that is how you can understand wherever we have irreversible process take pressure constant P del V will give you the walk done but in case of reversible this pressure is a function of volume accordingly you have to solve okay so I hope you all have done that derivation of isothermal reversible process and all so I'm not going to derive that one okay that will get 2.303 and RT log of V2 by V1 like that we'll get some expression yes or no okay so that derivation I am skipping okay that I'm not doing you can go through it is given in the book we don't have that much time okay so now you see the graph of isothermal and adiabatic process so if I draw the PV graph here for isothermal process it is like this and the same kind of graph we have for adiabatic process also PV graph this is for suppose isothermal isothermal and this is adiabatic okay so it is important to identify it is important to identify the graph okay for this one you see since it is isothermal so we can always write PV is equals to some constant K and for adiabatic we have PV to the power gamma is equals to constant okay this also we can derive okay again derivation we are not doing very skipping that okay only concept we are discussing okay derivation you can go through in the book if you have doubt you can ask me okay I'll explain that okay now you see if I calculate the slope of this graph right the slope what any graph if you have y or x the slope will write what dy by dx okay similarly we have PV graph so slope will be dp by dv okay so dp by dv if I calculate from this that will be minus k by v square yes or no tell me and k we can write as PV so finally we will get the graph as p by v minus p by v the slope in isothermal process is minus p by v yes or no correct similarly if I calculate the slope in adiabatic process dp by dv that will be equals to minus of k into gamma right divided by v to the power gamma plus one right further if you simplify this we can write what minus gamma into k by v into one by v to the power gamma and k by v from this expression from this expression k by v sorry we have this constant k will write here so one by v to the power gamma is equals to what we have p by k is equals to p by k if I substitute this here will get what minus gamma into k by v into p by k k and k gets cancelled and we get gamma into minus of p by v okay this minus of p by v is what it is the slope in isothermal process so when I know equate all these p minus v from these two expression will get slope in adiabatic process is equals to gamma times slope gamma times slope in isothermal process okay is it clear is it clear slope in adiabatic process is equals to gamma times slope in isothermal process now if you see for monoatomic gamma value for monoatomic gamma value is 1.66 for diatomic gamma value is 1.4 for polyatomic gamma value is 1.33 whatever the value we have gamma is always greater than 1 right since gamma is always greater than 1 so work done sorry for the that's why we can say the slope the slope for adiabatic process is always greater than the slope for the slope for isothermal process is it clear adiabatic process so if you see the graph you can understand what slope we have right but what graph we have actually okay so if I again can I rub this off now you see if you have two graph given right this is very important right now if you have two graph given you have to identify which one is for isothermal and which one is for adiabatic the first case we are taking that is expansion only small graph we have expansion expansion means what work done by the system here you see we have two graph right one graph I am giving you let me draw the axis first one graph I am giving you when the final pressure is same right this is suppose the initial thing we have this graph and okay you see the final pressure in this graph is same okay this is the initial pressure PI and this is final pressure PF since it is expansion so it is coming like this it is going like this okay this is the one graph we have and this is another graph you have to identify which graph is isothermal and which graph is adiabatic okay this when final pressure is same another one when final volume is same like this when final volume is this is VF this is VI and this is pressure axis volume axis and volume axis can you draw the isothermal and adiabatic graph together in the same that is what we are doing here you see we can see don't mix this thing with the you must be thinking about whether a process can be isothermal and adiabatic both at the same time okay that is not the concern the concern is if you have any process which is isothermal so we can draw the graph same we can draw if the process is adiabatic also right that is what it is it is it has nothing to do with the process whether the process can be isothermal or adiabatic at the same time that is not the meaning we are just trying the two graph we are trying to compare the two graph here okay adiabatic and isothermal okay so you see in this if the suppose if the graph if the process is isothermal right isothermal process means what happens the temperature must be constant right adiabatic process means what happens that the heat exchange is zero so since the expansion is taking place so system is doing work work done by the system we have so in case of adiabatic process what happens system is doing work at the cost of its own internal energy since it cannot take energy from outside while the process the process the process is adiabatic is it clear so adiabatic process you write down system is doing work at the cost of its own internal energy system is doing work the cost of its internal energy capital U right so now with them in the system internal energy is decreasing it means what its final temperature is also decreasing because internal energy is a function of temperature right so when the internal energy is less obviously it's temperature is also less okay and when the temperature is less right final pressure is constant we have for both the process so from pv is equals to nrt we can say its volume is also less yes or no tell me correct did you get this okay now you see this graph now it is very clear what what we like conclude from this in adiabatic process final temperature will be lesser and hence final volume is also less correct so where we have less volume the lower graph right this is the lesser volume we have it means the lower graph is for adiabatic process and this graph is for isothermal process is it clear see what did I say that we are discussing about this to graph isothermal or adiabatic so let's talk about adiabatic process first okay see since expansion is there volume is increasing and we know expansion whenever it is there work done by the system we have okay work done by the system we have correct means when the system is doing work and since the process is adiabatic so it cannot take energy from outside right so it has to do work system has to do work at the cost of its own internal energy right and hence what we say that its internal energy decreases well internal energy decreases it means temperature is also decreases right and when temperature decreases and temperature and volume are directly proportional why we see because the final pressure is same this is the condition we have for final pressure to graph here right down here when pressure is same when the final volume is same right when pf is same here these two condition we are taking and when vf is same here you will get graph like this only correct so when the final pressure is same so we know the final temperature is directly proportional to final volume right so when final temperature is decreasing so final volume will also decrease correct so that's why both of these graph which one will have the lesser volume that will be adiabatic and higher volume will be isothermal clear understood now the same logic you see you can apply when the final volume is same right final again adiabatic process the work is done at the cost of its internal energy so internal energy decreases so temperature decreases temperature decreases since final volume is same here so we can talk about final pressure here when internal energy decreases so final pressure will decrease so final pressure we have here for this graph so this graph is again adiabatic and the upper graph is isothermal like this we can identify the graph how many of you understood this quickly we have 10 15 minutes we have to do some questions on this ok this graph things are important yes now this thing we just get reverse in the case of compression ok what you have to keep in mind whenever you have expansion the lower graph is adiabatic and the upper graph is isothermal but in case of compression when final pressure is same and final volume is same then always we have the lower graph is isothermal and upper graph is adiabatic just to write down here the same thing in case of compression in case of compression you can think on this ok lower graph is isothermal and upper graph is upper graph is adiabatic this you must remember ok adiabatic and isothermal graph ok you can think on this like we have explained this you can think simply on this if you do it at home ok if you have doubt you can ask me I will explain this in the next class ok how it is lower in upper one ok now you see one question I am giving you actually we will solve two questions one question I am giving you which they have asked in J exam ok that we will discuss on to this graph thing ok so suppose we have this graph given like pressure and volume graph we have three different graphs one two and then three right this is the first graph we have second graph we have and this is third ok now you have to answer which of these graph represents monoatomic gas or diatomic gas polyatomic and this is the expansion we have here ok expansion graph is given you have to identify which one is monoatomic gas which one is diatomic gas and which one is polyatomic gas mono is three which one is diatomic gas ok you see first of all you tell me one thing whether this since it is a pv graph whether it is adiabatic graph or isothermal first you tell me that what graph it is it is adiabatic graph or isothermal what graph we have it is adiabatic or isothermal where is shweta shweta tell me the answer why it is adiabatic aditi sanjana what is the answer prathik where is prathik urvik ok you see if you see the isothermal graph isothermal graph never intersects you must have seen the graph isothermal like this ok so this isothermal graph never intersects write down ok that is what I am telling you sanjana isothermal graph you must have seen a different temperature pv graph they never intersects they are parallel like this ok so that's why this graph is what this graph is adiabatic graph here which is given since they are intersecting at one point so now the first thing we have to identify in this whether this graph is isothermal or adiabatic since they are intersecting so they are adiabatic graph now you see the graph that I have drawn in the last this thing just before this that is one is adiabatic another one is isothermal what is the case we have here it is expansion and expansion we know the lower graph is what the lower graph is adiabatic and the upper graph is isothermal for isothermal what condition we have pv is equals to constant adiabatic the condition we have what pv to the power gamma is equals to constant ok so can we say one thing because what is the power of v over here we have here you see the power of v we have one in case of isothermal in case of adiabatic the power of v is gamma which is more than one yes or no correct so can we say one thing as the power of v increases right when the power of v increases the graph starts shifting down right it is shifting towards this side ok it is coming down yes or no can we say this the power of v increases the graph shifted this side ok towards the down right down side downwards it is shifting correct it means more value of gamma more shifting of graph will be there downwards right and we know the value of gamma is maximum for which one we have value of gamma is maximum for monoatomic then we have what diatomic and then we have polyatomic so maximum value of gamma it means the graph will be downwards maximum so this third represents monoatomic gas second represents diatomic gas and the first represents polyatomic gas is it clear have you understood this ok now you see one question which was asked in j 2012 ok it is a multiple correct ok j 2012 question we have pv graph is given let me draw the graph pressure volume graph is given ok here it is given it is p1 v1 and t1 at this point at this point it is p2 v2 t2 and at this point it is p3 v3 and t3 ok expansion graph we have ok expansion so which one is isothermal and which one is adiabatic which one is isothermal and which one is adiabatic the answer is clear right the upper one is what isothermal and the lower one is what adiabatic but this is not the question perfect the question is something else it is given in the question that the upper one is isothermal and lower one is adiabatic it is given in the question ok the question is what first option we have you have to tell t1 is equals to t2 possible or not means you have to tell me the answer more than one correct we have into this second option we have t3 t1 third option we have work done in isothermal process is greater than work done in adiabatic process ok fourth one del u for isothermal process is greater than del u for adiabatic process who said both are adiabatic the upper one is isothermal same here the upper one is isothermal and the lower one is adiabatic see you don't confuse with this that the graph is getting graph is intersecting at one point see it is not like we are not talking about the one same process which is isothermal and adiabatic both the same question that swetha probably asked that time ok the thing is we are just giving you two graph one is isothermal and other one is adiabatic ok one is isothermal and other one is adiabatic the upper one is isothermal the lower one is adiabatic ok and on the base of this graph you have to tell me which all options are correct which temperature is different that is what that is what you have to answer say may you have to answer that only if it is isothermal process then the temperature must not be different all are saying one and three one is very clear right because the temperature because the process is isothermal so obviously t1 is equals to t2 is correct no if the process is isothermal then t1 is equals to t2 is obviously correct do we have t3 greater than t1 possible no because what I said because this process is this process is adiabatic and this expansion takes place at the cost of its internal internal energy so that's what I have given you there that the temperature decreases in this process so obviously this t3 should be less than t1 ok so this answer is not correct the correct answer of this is what t3 should be less than t1 this one is correct yes what about isothermal and adiabatic third one is correct or not third one is also correct because you see if you have to find out the work done in isothermal and adiabatic process what you will see you will see the area under curve right so area under curve in case of isothermal process is this right area under curve in case of adiabatic process is only this right so obviously the area under curve in case of isothermal process is more so obviously the work done in case of isothermal process is more than to that of adiabatic process okay but since you see one more thing here you just keep in mind work done by the system we have to that must be negative okay so if you take this the magnitude of work done in isothermal process is more than the magnitude of work done in adiabatic process right this mod is not given in the option but we have to think like this if you include minus sign here then the sign will reverse okay now you're coming now you come to this fourth option right you see change in internal energy in case of isothermal process is always zero since the temperature is constant because internal energy is a function of temperature itself right change in internal energy in case of isothermal process is always zero but change in internal energy in case of adiabatic process when expansion is taking place in this case right expansion again means what work done by the system right work done by the system means what internal energy decreases since the process adiabatic system cannot take energy from outside it has to do work at the cost of its own energy right that's why the internal energy decreases and when the internal energy decreases the change in internal energy in adiabatic process is always less than zero correct correct question right so obviously the isothermal process will have larger internal energy then adiabatic process okay so if I write down mod here right then it is correct third option I'm talking about okay but in the question if they didn't give you this mod here then this option will be wrong you must take care of one thing because what I said graph only gives you magnitude that one question we have discussed no on by the system or clockwise anti-clockwise if you talk if you calculate work done by the like the logic of this area under this curve that gives you only magnitude right the magnitude of work done in case of isothermal process is more than adiabatic process so this option is only true when you write down magnitude here right if you remove this mod then this option will be wrong in that case is it clear third option is it clear yeah so with magnitude the correct answer will be one three and four but if magnitude you remove correct answer will be one and four okay so like this you can compare and you can do this okay so like we are done for today okay we'll wind up the class here only we are left with only that gives free energy some concept we have there and then entropy thing okay so that will discuss in another class okay since this was this is the this was the extra class we have so we'll take one more and then we'll do that also okay second law of thermodynamics we are left with see I tell you one thing this chapter is quite big okay and all these you see every single concept if you have to understand you have to solve a lot of question and you have to think on this okay one more section of this chapter we have that is thermochemistry that has its law and all in helping and all right so that also we'll have questions from that also that portion is also important for J point of view okay this chapter is quite big you are going to have one question from this particular chapter okay so we cannot skip anything okay you you must have to be you know clear with your concept in this okay so the thing that is left in this thing is in this chapter is enthalpy enthalpy we have done gifts free energy and entropy okay and then some physical significance of that also okay so we'll probably finish this in next class okay when we'll take that class we'll let you know okay so like my suggestion is just go through with the previous year questions okay you will see that many questions we many things we haven't discussed today we could not discuss today okay but then we'll discuss that later on but what all things are there related to first law and this work done in various process those questions you can go through graph related questions you must do okay so we'll see this in the next class again okay thank you any doubt