 Yes. Hello guys. Good evening. So I hope all of you are here. All right. Okay. So last class we were doing thermodynamics. What was the last thing we were discussing? One second. Okay. So we had discussed it. Work done, right? Formula of work done we have seen. Okay. Thermodynamic quantity till work we have discussed. Yes, cyclic process like work done in cyclic process, right? Okay. Okay. The next thermodynamic quantity we have all of you write down the next thermodynamic quantity is that is he write down. Okay. So next write down thermodynamic quantity we have heat is represented by q. Okay. Small q, capital q you can write it is represented by q. Okay. So what is heat? Heat is again a form of energy. Correct. It is basically the energy transfer. Energy transfer which takes place because of the difference in temperature form of energy. So it is the energy transfer takes place because of difference in temperature. So whenever you place a hot object, a hot body and cold body together in contact, right? Then energy transfer from hot to cold body happens, right? So what happens? Suppose we have an object, we have an object at two different temperature and these two are connected through a conducting wire. Okay. This one is at temperature T1. This one is at temperature T2. If T1 is greater than T2, here we have only one option. So since I have given the arrow over here, this heat will transfer from this object to this object only when T1 is greater than T2. Okay. This transfer takes place unless the temperature in the two objects becomes equal. Okay. Till then the transfer of heat from hot to cold object takes place. Okay. Right. See we had the assumption in case of work done like work done by the system is negative work done on the system is positive. Similarly, we have, we have assumption or convention we can say in case of heat also. And what is that convention? The convention is heat given to the system, given to the system or we can also say the same thing as heat absorbs by the system. Right. System is absorbing heat. Okay. Heat given to the system or heat absorbs by the system is always positive and heat released by the system is always negative. So this is the sign convention we have. Okay. Like we have for work done, we have signed convention over here for heat. Copy this down. Next you see heat capacity and under this only we don't have new topic. So topic is heat only. So we have two, three terms over here. One is total heat capacity, total heat capacity. Total heat capacity is the amount of heat required. It is the amount of heat required to change the temperature, the temperature by one degree Celsius means per unit change in temperature. Okay. One degree or we can have rise, we can have degrees. So per unit change in temperature, the amount of heat required is called the total heat capacity. The unit of this is, is Joule is the unit of energy. Kelvin is the unit of temperature. Right. Here we have change in temperatures, whatever unit you take that does not make any difference. Joule per Kelvin we can write. Okay. Now this total heat capacity is classified now into two kittings, two types of total heat capacity we can have. The first one is molar heat capacity, molar heat capacity. It is C. I'll change the notation so that it will be easier for you to understand. Molar heat capacity, suppose I'm taking a C M and you will get this notation in some book in like most of the book, the simply write it as C. But why I've taken this as different, you will understand this after some time. Molar heat capacity you see it is the same thing amount of heat required to change the temperature by one degree Celsius of one mole of substance just you need to add. Okay. So molar heat capacity is for one mole of substance. So definition would be amount of heat required to change the temperature, the temperature by one degree Celsius of one mole of a substance. So if you take one mole of a substance, so it is molar heat capacity. If you look at the unit here for molar heat capacity, the unit is obviously the energy is Joule per mole Kelvin because of one mole. Got it. The second one we have is specific heat capacity, specific heat capacity. See, it is exactly same. But the only difference is here we are taking CS we represent this as like here we are taking one gram of substance. So instead of one mole, just you place one gram. That is the only difference we have. Okay, so unit I'll write down here unit of specific heat capacity is Joule per gram Kelvin, because it is defined for for one gram unit mass of substance. So if I write down the heat exchange, whether it is total heat capacity or molar heat capacity or specific heat capacity, we can write C. I'll write down this way. DQ is the heat change we have is equals to we can write C DT is equals to we can write N number of moles C M DT M is the mass CS DT. Okay, change in heat you need to find out that is delta Q if you need to find out. So for that you need to integrate the given expression, integrate and integrate this. So what you will get delta Q is equals to C delta T is equals to NC M delta T is equals to M CS delta T. Now this I have written and we can only write this we can write this only in one condition. What is that condition pretty tell me the condition is that specific heat or any heat capacity. See that you have, right. This we can write only when only when heat capacity, whether it is specific or molar molar heat capacity is independent of temperature independent of temperature, which is mostly the condition. Okay, heat capacity generally it is independent of constant temperature we don't have much effect on heat capacity with temperature, but sometimes what happens, we have relation of C with temperature given. Okay, in the question. So if it is given then that expression you need to put over here and then you need to integrate. If it is not given, then we'll assume that heat capacity is independent of the temperature. Clear. Now you see calculation. We are doing under heat only everything right calculation of heat capacity what could be the possible value of heat capacity under different different condition. Okay, possible value of heat capacity. Suppose we have suppose first process I'm assuming we have suppose isothermal process isothermal process I want you to consider I want you to consider this expression. That is delta q is equals to C delta t. Okay, delta q is equals to C delta t this expression we need to consider. So if the process is isothermal what is the value of delta t could you tell me what is the value of delta t isothermal process delta t is zero. And when delta t is zero, what is the value of see see is nothing but infinity this expression, right, this could be the possible value of C in isothermal process right. Okay, similarly, if we are assuming adiabatic process what is the condition of adiabatic process delta q equals to zero. So we'll have here delta q equals to zero, which means when q is zero, see is also zero. So depending upon the process, the value of C could be anything from zero to infinity. Third one you see this is a range we have isochoric what is isochoric process constant volume. Right on at constant volume at constant volume, the heat exchange that is delta q is nothing but delta u of the system. This we are writing it down, writing it down with the help of first law of thermodynamics if you remember a bit of because we haven't discussed this, but we will discuss this. The first law of thermodynamics the expression is what we have delta u is equals to q plus w. Right, so this w would be zero, because we know it is PDV right, this w would be zero if volume is constant. This is zero q is equals to delta u we have, right, so at constant volume, this is the relation we have. So, see is equals to what we can write. So the first law stands for first law of thermodynamics. Okay, we'll discuss it. I'm just taking the reference of it. Okay, I'm just taking the reference of it will discuss after sometime the first law of thermodynamics. Okay, you have to keep this in mind that constant volume, the internal energy change is nothing but the change in heat content of the system. Okay, so the heat capacity is c is equals to we can write delta q by delta t. Or we can also write it as dq by dt. dq is nothing but du. So it is du by dt. It is a heat capacity at constant volume. This is the volume is constant here. So, we write C as CV, CV is equals to du by dt. Remember, this is for one mole, right, for one mole, CV is the heat capacity at constant volume. It is a molar heat capacity we have. CV is the molar heat capacity at constant volume since we have taken one mole over here. Now the next one is we have isobaric process isobaric process isobaric process as we know delta p is equals to zero pressure constant delta p is zero. So molar heat capacity, molar heat capacity isobaric process is represented by CP. Okay, that was CV, this one is CP. And dq, when the pressure is constant, dq is nothing but dh over here, where h is the enthalpy. It is the definition of enthalpy basically. So this enthalpy is the heat content of the system of the system constant pressure. This is the definition of enthalpy. We will discuss enthalpy also later. In this case, CP is equals to dh by, I'll write down this way, wait. The general formula is dq by dt. But this is at constant pressure. So dq becomes dh at constant pressure, so dh by dt. So the formula is CP is equals to dh by dt. So we have at constant pressure, one mole we are considering. How? We won't get du by dt. Pressure is constant. So dq in first law becomes dh, first of all. The definition is that only. So dh is equals to du plus pdv we can write. But we are concerned with dq. So dq is dh only, that is it. You don't, you know, require here first law of thermodynamics. So this is the, what we say, enthalpy change and cpcv relation we have. We'll come back again to this cpcv relation. Very important. This one is also right. We'll come back to this point again after first law of thermodynamics. So cpcv calculation we'll see for ideal gas for after first law of thermodynamics. Right. So before going into first law of thermodynamics, we have another thermodynamic term that we need to understand and that is the internal energy. Right down the third thermodynamic term, which is internal energy represented by capital U or capital E, both you can take. So capital U or capital E internal energy. Correct. So the internal energy of any system is what internal energy is the sum of all kind of energy basically. We can talk about kinetic energy. We can talk about potential energy. We can talk about chemical energy as well. Basically internal energy we defined at the micro level. Like suppose you have a cylinder in which the gaseous particles are present. So we are considering the energy of the gaseous particle, the internal energy, right. But we also consider all kind of energy of the gaseous particles. We can talk about kinetic energy, potential energy, chemical energy of the gaseous particles. Kinetic energy is what means all kind of energy you add, whatever energy are possible and you can think of. Like for example, kinetic energy could be translational, rotational, you know, all this kind of potential energy is what it is because of the height. Right. Because of, you know, height or we can say the position of the particles. Chemical energy is what? Bond making, bond breaking, all the nuclear reactions are there. All kind of reactions we can consider over here. Everything, whatever it is possible. Okay. So this is the internal energy of the system. Okay. What is internal energy? Internal energy is a state function. Right. And what is a state function? State function, could you tell me? What is a state function? State function is what? Does not depend upon path. Right. So it is independent of path. Right. Does a state function. It depends mainly upon temperature. Right. Internal energy depends mainly upon temperature. Okay. I'll come back to this point again. Now you see one thing here. Have you seen this formula? DU is equals to NCVDT. Have you seen this formula? First time. You haven't done this in physics? You haven't seen? Okay. Let it be that. This chapter you are done in physics. Thermodynamics? That's why. Okay. Anyways, let it be. Okay. See, I can give you this expression in a simpler way. Okay. But the thing is you won't understand the actual thing if I simply give you the expression in a simple way. So if you try to understand the actual thing over here, you need to go from this expression. You see kinetic energy, we know it is a function of only temperature. Right. It depends upon temperature. Similarly, potential energy is the function of, we can say volume. Why volume? Because if volume is less, contraction is there, molecules are closed. Right. So they can have more interaction, which affects the potential energy. But if the volume is high, the molecules are far apart. Again, the potential energy will be different. Right. So potential energy is a function of volume. It depends upon the volume of the molecule of the system. Right. Because that will affect the relative distance of the molecule. Okay. So what we can say this U, internal energy U is the function of temperature and volume. Is it fine? So we have two variables on which internal energy depends. Mostly it is temperature because volume change we do not have over there. But we can discuss with these two examples. Now, if you find out the change in internal energy, du, this would be dou U by dou T at constant volume into dt plus dou U by dou V at constant temperature into dV. This we can write. This expression, you do not have to think about it. Okay. It is not there in the syllabus. This we call it as Euler's formula. E-U-L-E-R-S. Euler's formula. Once again. Okay. Euler's formula. Euler's formula we use when a variable, independent variable depends upon more than one variable. Then in order to find out the change in this variable, we use this formula. Once again, I will discuss. Right. So dou is the, this dou is the, dou means partial derivative. It means partial derivative. You do not have to think about it. Right. You will not get any questions on this. Partial derivative. What is partial derivative? We are differentiating U with respect to T keeping V constant. That is what the meaning of this. Differentiation of U with respect to T keeping V constant into dt. Differentiation of U with respect to V keeping T constant into dV. This is what the Euler's formula we have. Clear enough? D by dx is completely derivative. There is no partial derivative into this. D by dx we use when there is only one independent variable and one dependent variable. Correct. When we have only one independent variable, then we use d by dx. Differentiation. Clear enough? Yes, tell me. Now, you see I am taking for n moles or let it be l. I will just introduce n in the last. So we have dU is equals to what is dou U by dou T at constant volume into dt and the second part of this we have dou U by dou V at constant temperature into dV. What is this term? Dou U by dou T. Could you tell me? Just now we did. Dou U by dou T is nothing but cV when volume is conscious. So cV dt it is and it is plus the same expression we have. Dou U by dou V at constant temperature into dV. Is it clear? Just go back and check. dU by dt is equals to cV we have done. So change in internal energy. In terms of calculation, there is no change. It just means we have partial derivation. That is it. We are differentiating one with respect to the other variable keeping the other variable constant. In terms of calculation, we do not have any difference. Definition wise we have difference. Dou we use for partial derivative and d is for complete derivative. Clear? Dou U by dou T also is made like means change in internal temperature divided by the change in internal energy divided by the change in temperature. dU by dt also means the same thing. So calculation wise the answer that you get will be same. But we use dou only to represent the partial derivative. That is it. All the method of differentiation you can apply for dou also. Correct? So for n number of moles what we can write? For n moles we can write dU is equals to n cV dt. This is for one mole. So for n mole we multiply by n dou U by dou V at constant temperature into dV. Tell me, anyone has any doubt till here? If you are not getting Euler's formula, you can skip that. That is not in our syllabus. Okay? Could you speak? Anyone of you? Could you respond all of you? Done? No doubt here? Clear? Okay. Now you see what is this term? This is important here. This is the change in internal energy. If they ask you to find out the change in internal energy, you need to do this. And I am sure you have never seen this kind of formula. You have done this chapter in the school? Yes. Have you seen this formula? No. You must have seen dU is equals to n cV dt, right? Have you seen that? Or that also you haven't seen? Maybe some of you have seen. Some of you haven't seen. Anyways, so you see actual... Oh, fine. Maybe it was deleted. So fine. Let it be. So actual change in internal energy is this. This is what you need to find out in order to calculate the change in internal energy. Okay? Now this term that is written over here, this dou U by dou V. This is called the internal pressure of the system. Internal pressure of the system. If it is a gas, then it is the internal pressure of the gas. Internal pressure. Okay? How it is internal pressure? Okay. You cannot accept this. It's just because I am saying you should not accept this, right? You can understand this term, how it is the pressure actually. You see, U is what? We have basically U by V. If you look at the dimension here, U by V dimension, correct? U is what? Internal energy. Internal energy is energy itself. So we can write down this as pressure into volume. Why? Because we have U plus PV, you know, work done and this. The dimension of this and this must be same. So U, you can replace with PV. That's what I have done. Just to understand this. Okay? U plus PV divided by V, we already have V and V will get cancelled without pressure. Means this expression dou U by dou V at constant temperature represents the internal pressure of the system. Now, if you apply this, like if you try to find out the change in internal energy for ideal gas, for ideal gas. What is the internal pressure in ideal gas? P internal in ideal gas is what? We know in ideal gas, there is no interaction or everything you forgot about. Do we have internal pressure in ideal gas? No, we do not have. Last chapter only we had discussed. We do not have internal pressure. So P internal would be zero if we are considering ideal gas. So P internal zero means what? Dou U by dou V is equals to zero. This means the change in internal energy here, if you find out du is equals to, we have n Cv dt. This is the formula we have. So if you memorize this formula simply, du is equals to n Cv dt, you must take care of that this is applicable for only ideal gas. And mostly we will be dealing with ideal gas only, hence this formula is given in the book. du is equals to n Cv dt. Correct? This is one case. Another case is what? Suppose we are considering real gas. Real gas in, in a rigid container. What do you mean by a rigid container? Real gas in rigid container. dV is equals to zero. dV is equals to zero. So again you see this if you substitute in the previous expression, what we get again? du is equals to n Cv dt because dV becomes zero. Isn't it correct? Is this correct? Correct? It means what? This formula we can use for ideal gas. We can also use for real gas. But real gas under what condition? When the container is rigid. If the container is not rigid, then the formula is the previous one that I have done in the previous page. You have to use that formula in order to find out the change in internal energy. What denominator? No, no, no. You see the term is this. The second term is this. du by du v at constant temperature into dV. This you cannot put at zero because this is a different term. It is change in volume obviously, but it is the change in internal energy with respect to volume. dV will substitute over here and hence it is zero. I am not getting your issue. I think if I turn off the video, is it fine then? How about this? I think all of you are fishing some issue. Could you tell me what is happening? No issues. Is it fine now? I think I need to remove this chat box. Could you see that chat also? Maybe I think some network, I have seen this issue before also because of some network error, I guess. I could not figure it out, but anyways, I think if I remove this chat box, then it would be better. Now it is fine, better. You can raise hand guys. You can click over there in the raise hand. I will get the answer from your side then. It is better now if I place it here. So we will remove it then. If it is required, I will open the chat box, otherwise I will close it. It is fine now. Okay, understood. Okay, so we have done this. So always keep this in mind. You see one thing. du is equals to ncvdt. What is cv over here? It is the molar heat capacity at constant volume. Listen to me very carefully here. Molar heat capacity at constant volume. We haven't applied any condition of constant volume in this expression. You see, we got this expression here, but we haven't applied any condition of constant volume. Just we differentiate this partial differentiation and we got this. So this formula that we are getting here du is equals to ncvdt. It is not at all necessary that it is applicable only for constant volume process. No. Are you getting my point? Since we haven't applied the condition of constant volume, this formula is applicable for all processes, whether the volume is constant or not. It is applicable for all processes. Generally it is a misconception students has since we are right down cv here, which is for constant volume. This formula we can use only when the volume is constant. No. It is applicable for all processes. If ideal gas is there, or if real gas is there with rigid container, did you understand this? Let's keep that in mind. du is equals to ncvdt. This is also applicable for all processes with this two things. Okay, so we had discussed work done, we had discussed heat, we had discussed internal energy. Based on this, we will have a law and we call it as the first law of thermodynamics, right down on a few, the heading. Real gas, so we have discussed know this. What if gas is real or in rigid container? Real in rigid container, we can use du equals to ncvdt. That is the second case we have. Real and rigid container, we can use that. Okay, write down the heading. First law of thermodynamics. In short, we write it as FLOT, first law of thermodynamics. This law is completely based on the conservation of energy. Conservation of energy. So suppose we have state one, and from this, you want to go to a state two. There are many different ways. We are assuming the internal energy is Ui and internal energy is Uf final initial. So how this change in state is possible? There are various processes by which change in state is possible. We can have isobaric, isothermal, adiabatic, no isocoding, many different processes we have. In which what we do, either we allow heat to flow in to the system. We can allow heat to flow in, or we can take heat outside the system, or we can work done on the system, or system does some work. All these possibilities are there in order to change the state. Yes or no? Any object, any system, if you want to change the state of the system, you can do any one of these four things, correct? Either you will do some work on the system, or you allow system to work, right? Or you give some energy from outside, or you take energy from the system out. Anyone think you can do? So what condition I am taking here? You see, I am assuming Q amount of heat absorbed by the system, by the system and W is the work done, W is the work done on the system. Since we have work done on the system, internal energy decreases or increases. U, internal energy increases, correct? So the final internal energy is Uf is equals to, we had some initial internal energy, Ui. And in this, you have given Q amount of heat and work done on the system is also positive, plus W. This is the relation we have, energy we have conserved. We have this internal energy, you given Q amount of heat and work done on the system. So Q plus W, you need to add. This total becomes the final internal energy. Uf minus Ui, we are writing it as delta U is equals to Q plus W. So this is the first law of thermodynamics here, expression. Just a change in internal energy, okay? One more condition you see. I will go to the next page, copy this down first. Now the same condition I am taking. Q amount of heat is absorbed, Q amount of heat absorbed and work done, work done by the system, work done by the system. So what we can do? Uf is the final internal energy is equals to Ui and Q amount of heat is absorbed by the system. But W amount of work is done by the system, means the internal energy will decrease. So minus of Wi, work done by the system is this. So what we can write delta U is equals to Uf minus Ui is equals to Q minus W. And hence we can write Q is equals to delta U plus W. This is the expression we have, expression. Delta U plus W, when you write down this expression, this is work done by the system. That is the only difference we have. And when you write down this expression, which is delta U is equals to, is equals to Q plus W. This W is the work done on the system, on the system. Just once again guys, just hold on. Yeah. Now you see two, three things can conclude from this, conclusion. Suppose we have a process, any process. And in the process, the change in internal energy is zero. So we are assuming different, different conditions and based on the condition, what is the result we have? That is what we are going to understand. So for example, if we are taking a process in which delta U is zero. For example, if you have a cyclic process. So we know in case of cyclic process, delta U is zero, right? So delta U is zero means DQ plus DW equals to zero. So DQ is equals to minus DW or we can also write this as plus DQ equals to minus DW. Plus DQ means what? Positive energy means energy absorbed, energy is taken, is given to the system, right? So we can write down here, system absorbs energy, absorbs energy, plus DQ means, correct? And minus DW means work done on the system or by the system, work done by the system. Means if you have any process in which a change in internal energy is zero, then two possibilities are there. One is if the system absorbs energy, equal amount of work done by the system. You can also understand this theoretically. You don't have to go for the mathematical expression like this. You have a system and the system does not want to change its internal energy. Means there should not be any heat absorbed, net heat absorbed by the system. Suppose if it takes 10 joule of heat if it takes, then it has to work 10 joule out so that the internal energy remains constant. Is it clear? Yes, that is what the mathematical expression we have. Plus DQ equals to minus DW. We can also have the another possibilities. What is the another possibility? If we can write plus DQ equals to minus DW, then why can't we write minus DQ is equals to plus DW? Can we write this? And what do you mean by this expression? Minus DQ is equals to plus DW. What do you know? This equation that I have written, minus DQ is equals to plus DW. How do you write down this in a sentence? The amount of heat released by the system, which is negative. So this we can write the amount of heat released by the system, by the system. This is equals to work done on the system. So basically also you can understand if the system is absorbing heat, right? System is releasing heat, suppose, like this 10 joule of heat it is releasing. Then 10 joule of work you need to do from outside so that the delta E won't change. Hence the expression we have, correct? So when DU is equals to zero, these two possibilities we may have. Just let me put this in the charge. The second point, if WD, work done is zero, then what you can write? We can write DU is equals to DQ. This is what we can conclude. So when there is no work done, if the internal energy increases, means plus DQ plus DU, correct? Or minus DUQ minus DU. So what we can say, the change in internal energy or we can say the increase in internal energy is equals to heat absorbed by the system or released by the system. Heat absorbed or heat released. One second I'll go back to that. We can say if internal energy increases, then heat absorbed by the system. And if internal energy decreases, then heat released by the system. Copy this down. I'll go back. Done. What is the third condition we can apply over here? Anybody? Could you tell me? What is the third condition we can take? DW zero we have taken, delta U zero we have taken. Another one is what? When DQ is equals to zero. There's no exchange of energy, adiabatic process, right? DQ is equals to zero means what? Adiabatic process. No exchange of energy. So what we can write, DU is equals to DW. So it depends upon, internal energy depends upon whether work done by the system or on the system. If we have work done on the system, on the system, means what? DW greater than zero, which further means DU greater than zero, which further means internal energy U increases. If you have work done by the system, DW less than zero, DU less than zero, internal energy decreases. This is the three condition you can think of. So this is it for first law of thermodynamics. One question we'll discuss on this. One question guys. A gas contained a cylinder fitted with a frictionless system expands against a constant pressure, constant pressure, one atmospheric from four liter to 10 liter. In this process, in this process, it absorbs 800 joule energy need to find out delta U. Delta U is equals to what? Try this question. Yes. So what is the answer you got? 192, 190, 14, 0, and see what the wide range of answer you get. No one is getting the correct answer. Archit is close, but not correct. 794, no. Correct answer is around 200 something, 213 to 14 approximately. See what happens here. No, one second. A gas contained a cylinder fitted with a frictionless piston expands against a constant pressure. This. So what is the work done in this process? Could you tell me? The work done is equals to minus P external delta V. Since it says against a constant pressure, right, means what it is irreversible. So we can apply P external to delta V. Correct. So that would be the negative sign. You let it be pressure is one. DV is 10 minus four. And we are getting six. ATM leader, six ATM leader. Which I think. Yeah, I think one of the answer is correct. Because one data is I have changed here. Correct. Six ATM leaders. So we have to convert this in the June. Correct. So minus six into. What we say minus six into 100, zero. Sorry, 101.325. Okay. This is one thing. W we got absorbs 800 Joule of energy. So Q is what Q is plus 800. Correct. We use the expression of work done by the system. That is delta U is equals to delta Q plus W. That is 800. Plus what is this value? We are getting 607 something we are getting. Negative. So 193. Right. Huh. Correct. So 193 approximately. We are getting 192. Point something in the answer. How did you get 607? The value. Okay. Fine. Yeah. That approximation you can do our shit depending upon the options, what options are given. When the options are closed, you need to take the exact value in June. Okay. Now next. Thermodynamic term. We have, you see. Is enthalpy. Heading on of your right down enthalpy. Enthalpy is represented by edge. Definitions write down. It is the heat content of the system. Heat content of the system at constant pressure. Constant pressure. So do is equals to what the first law of thermodynamics. DQ plus DW. Right. At constant pressure, what we can write simply, we can write this as DU is equals to DQ. W is PV. So D PV here. Yeah. Okay. So at constant pressure, at constant pressure, we can write DU is equals to. DQ P is constant. We're going to take this outside PDV. Right. So this is the heat content. DQ at constant pressure. We have. Right. I missed one negative sign over here. W is minus PBO. So negative sign. So here we are. So what is DQ? DQ at constant pressure is equals to. DU plus P. DV. At constant pressure, we know the heat content of the system is. Enthalpy. So this DQ P is nothing but the heat content of the system. Okay. So we have the heat content. Okay. So we have the heat content. So we have the heat content of the system. Right. So we have the heat content of the system. dqp is nothing but the dh of the system. So dh is equals to du plus pdv. This is the mathematical definition of enthalpy. That enthalpy equals to internal energy plus pressure volume work done. Okay, then this is important. Okay, I'll come back to this equation again. You will get a lot of questions on this. Okay, now enthalpy you see. Enthalpy is a function of pressure and temperature mainly. Mainly depends upon pressure and temperature only. Right? So the change in enthalpy again by using the islet's formula here, which is it is doh h by suppose I am writing down here doh t keeping the other variable that is pressure constant into dd. What should be the other expression here? Could you tell me doh h by by what doh p keeping temperature constant into dp? Correct? Doh h by doh t at constant pressure. If you go back and see, I have told you that this is cp dt. This is cp into dt. If you have n number of moles, ncp dt plus doh h by doh p at constant temperature into dp. This is the overall change in enthalpy we have. The actual formula is this. Now we can apply conditions on this and we can get the reduced form of this particular change in enthalpy. Okay, like we had in case of d. Actual formula is this. This is this formula is applicable for all process, for all process, all condition. For all process, all condition. Once again, Rajita, I'll go back. Second line is you. This is you only. Yeah. Okay, this is for all condition. Now if you look at the condition of ideal gas, now this is the actual change in enthalpy we have. Now we can apply conditions into this. Since we will be dealing mostly with ideal gas equation, so we'll apply the condition of ideal gas. So for ideal gas, what we can write h is equals to u plus pv. This is the enthalpy formula we have. And we know this internal energy mainly depends upon the temperature because pressure is already constant for enthalpy. Right. So u is a function of temperature only pressure is not changing. Correct. And this pv is also we can write nRT. For ideal gas, gas will have so pv is also nRT, we can substitute. Right. So overall what we can say for ideal gas enthalpy is only a function of temperature for ideal gas. This is only for ideal gas guys. Okay. Only for ideal gas. However, it depends upon pressure, temperature, number of moles also mainly it is pressure and temperature. So h is a function of temperature for ideal gas. And hence, if you write down this doh h by doh p, what do you mean by this expression? T. What do you mean by this? This frame of sentence for this particular expression which is written. It is that derivative of h with respect to p keeping T constant. Isn't it? Yeah, that also we can say internal pressure. So for ideal gas also internal pressure is 0. Or simply the definition of this expression is what? Derivation of derivative of h with respect to p keeping T constant. So p is already a constant here. Or we can also say it is the internal pressure of the molecules. This is equals to 0 for ideal gas. It is internal volume. One second guys, DP we have no. So it is internal volume. That also we can take it as 0 because internal volume is what? Is negligible for gaseous for ideal gas molecules. So 0. Or we can also say this equals to 0 for doh h by doh v at constant T. This is internal pressure. This is internal pressure. Both will be 0 over here. Okay. So if I substitute this in the previous expression, DH is equals to we get NCP DT. So again you see DH is equals to NCP DT is applicable for all process for ideal gas. Process is not a constraint here. Constraint is the gas should be ideal. Don't get confused that CP is written here molar heat capacity at constant pressure. It means we can apply this only when the pressure is sponsored. No. It is applicable for all processes. This formula we can also apply for real gas. But the condition for real gas is what? Real gas at constant pressure. Real gas at constant pressure. DP is equals to 0. And hence we can substitute this. DH is equals to NCP DT. So for real gas also it is applicable. But the condition is the pressure must be constant. Correct? Understood? Okay. Now another expression we are going to see. See, thermodynamics is all about conditions. Okay. You have one expression. And in the question also one of those conditions will be given. So you need to understand that how do we apply conditions in a given expression? What we can conclude under a given condition? Okay. See, we have this expression. DH is equals to du plus PDB plus PDB. Correct? Can we divide both sides? Can we divide by DT? No problem with this? Yeah. What is DH by DT? What is DH by DT? Anybody? What is DH by DT? N into CP. Very good. So N into CP is equals to N into CV plus N. So we can write what? We can write CP minus CV is equals to easy derivation. Clear? Okay. For any number of moles it's possible. That is one thing. Another formula of CP by CP and CV is the ratio of CP by CV we call it as gamma. Gamma is Poisson's ratio. We'll use this later on. We'll use this to write it down. One of the formula is this. What is this CP and CV? Is it molar or specific? CP and CV, molar or specific? It is molar heat capacity. Okay. No, no, no, it's not. That is there. And what is that symbol? Yeah. What is that symbol? This is gamma. We call it as gamma. Okay, sir. This is gamma. Poisson's ratio we call it as. Okay. Now on this you see one question they asked in neat exam, not in J but for J point of view, I'm sorry, for J point of view also it is important. What was that question? I'll show you.