Comprehensive Thermodynamics Revision Guide

Thermodynamics, the study of heat, it's a very vast chapter and today we'll try to cover the revision of this chapter, its theory and formulae as fast as possible. This video will give you a lot of information in a very small time so please focus, please pay a lot of attention. You can pause this video wherever you want so that you can focus more on the formulae. Here we go. First of all, the terminologies of thermodynamics, system, surrounding, universe and boundary. System is the part of the universe which is under observation. Surroundings are whatever is not a part of the system, so remaining part is the system. surrounding and the system is separated from the surrounding via the boundary. Yes, so the boundary could be imaginary. I could just say this is my system or it could be a real boundary like a box. So the walls of the box would be the boundary. Moving on, you could have different different types of systems. Open system, which can exchange both energy and matter with the surroundings. Yes, closed systems, they can exchange only energy but not matter with the surroundings. And isolated systems can exchange neither energy nor matter with the surroundings. The idea of energy over here is classical, not modern. So we don't say that energy and mass are the same over here. Fine. So an example of an open system would be the human body. We can exchange mass with the surroundings. We eat food and we can also... Exchange heat with the surroundings. Pretty obvious, right? Isolated systems are ideal systems, okay? These do not exist in nature. These are just imaginary. Fine. Now, a system can be defined by its state variables, okay? So, pressure, volume, temperature, number of moles, these describe the condition of a system and changing these variables will change the state of the system. Fine. The system could have different different types of properties. They could be extensive properties. Extensive properties depend on the extent of the system. Intensive properties do not depend on the extent of the system. So extensive properties are total energy, volume, mass. Bigger the system, bigger is the volume, more is the mass. Intensive properties, pressure, density, refractive index, doesn't matter how big the system is. To distinguish between extensive and intensive, there is a trick. Think about a huge system and cut out a small chunk from that system. If both of these now have the same value of a property, it is an intensive property. Fine, chalo aage badenge, types of thermodynamic processes there are are isothermal processes where delta T is equal to zero, isobaric processes where delta P is equal to zero, isothermal means temperature remains constant, isobaric means pressure remains constant. Then you have isochoric processes where delta volume remains constant, delta V is equal to 0 and then you have adiabatic processes where the transfer of heat is 0. So, heat is denoted by Q and Q is 0. Then there could be certain processes which are cyclic in nature. So, whenever a system undergoes different number of processes and finally returns to its initial state. You go out, roam around the entire world, come back to where you are sitting right now, displacement equals to 0. So such a process is known as a cyclic process. Fine, moving ahead, heat which is denoted by Q. you is the energy transfer due to temperature differences between system and surrounding. You know that heat moves from higher temperatures to lower temperatures. Then you've got work. Work could be of different types. You could do work on a system by putting electric electricity, you could do work on the system by shaking that system all over, you can do work on the system by either compressing or expanding it and this is the kind of work we consider for simplicity in thermodynamics. This is known as mechanical work okay and it could be compression work or expansion work. So you could put some pressure on the gas or you could make the external pressure lesser so that the gas starts expanding. Yes, now the formula for work done is equal to minus P external dV is integration, which implies that if you have a PV graph, alright, if you have a pressure versus volume graph, the area under that pressure versus volume graph will give you the work done, okay, very simple, let's move on. Now, the sign convention is very important and this sign convention that I am discussing right now is the sign convention for chemistry, okay. So if heat is supplied to the system, we call it positive. If heat is taken out of the system, we call it negative. Essentially, whenever we are giving energy to the system, we call it positive. Whenever we are taking energy away from the system, we call it negative. So heat supplied to the system is positive. Work done on the system, when you are compressing the system, then work is positive. Okay? And work done by the system, when it expands, then W is considered to be negative. This is the sign convention of chemistry. Fine. Now, let's talk about internal energy. Internal energy is simple. It's just the sum total of the components of energy of the system due to internal factors. So... Kinetic energy plus potential energy of the internal components. For an ideal gas, there is no potential energy because there are no intermolecular forces in an ideal gas. That's how they are defined. So for an ideal gas, the internal energy is just the addition of kinetic energy of the gaseous particles. And if you remember the gaseous state chapter, you would know that kinetic energy depends only on temperature. So for an ideal gas, the internal energy depends only on temperature. Fine. Then we have this very famous equation, delta U is equal to Q plus W. People, do you remember what this is? It is nothing but the mathematical equivalent of the first law of thermodynamics. The first law of thermodynamics states that energy can neither be created nor destroyed. It can only be converted from one form to the other. Yes, and when we simplify it for thermodynamics mathematically, we can say that internal energy of a system remains constant Unless energy is transferred from the surroundings in terms of heat or work. Very obvious and hence comes the formula delta U is equal to Q plus W. You could also write the differential form delta U ki jaga DU is equal to DQ plus DW. That is also something that you can write if the question demands. Alright, so this is what we have written over here. Then let's talk about enthalpy. Enthalpy is the net heat content of the system and mathematically H equals to U plus PV. Now once we manipulate these formulae, we get this beautiful thing that we need to remember. Delta H is equal to QP. What is QP? QP is the heat under isobaric conditions. Heat exchanged under constant pressure conditions is QP. And if you manipulate these formulae, this is what happens. what you get. Similarly, delta U is equal to QV. QV boleto, heat under isochoric conditions, when volume isn't changing, heat exchange, QV. Fine. So, these two are universal. These forms that we got, delta H equal to QP, delta U equals to QV, you have to remember this, these are applicable for all processes whatsoever. Fine. Now, let's move on. Reversible processes. Remember, I am pretty sure you remember this. In a reversible process what happens is, the process is so slow that just with an infinitesimal change, you can change the direction of the process. Yes, you can make the system and the surrounding revert back to its initial condition. These reversible processes are ideal. These do not actually exist in reality. You must be saying, but sir, I charge my phone's battery every day. It charges again and again, reversible process, see. The reversible process's definition in thermodynamics is a little different. In thermodynamics, a reversible process is one in which both the system and the surroundings get reverted back. When you are charging your phone, you take energy from the wall socket and some heat is released into the atmosphere. Now, Can you take that heat back from the atmosphere, put it in the phone, put it in the wire, put it in the wall socket? Can you take the energy from your battery and put it back in the wall socket and back into the universe? No, right? In real conditions, reversible processes do not exist. These are absolutely ideal. So how are these defined? These are defined by quasi-static states, which means that this process is under an almost static condition. It is so slow. that you can't even distinguish whether the process is happening or not. Again, theoretical ideas, you can imagine anything. So, in a quasi-static state, the system is always in equilibrium with its surroundings. Fine, badiya. So, this implies that we can always write P internal equals to P external for reversible processes. Makes our life simpler in some cases. Moving on. Let's talk about heat capacity. Heat capacity is the heat needed to raise the temperature of the system by 1 Kelvin. We all know this. So C is equal to Q by delta T. Very simple. Now if I talk about heat capacity per mole, I have to just include the factor of N at the bottom. So C molar is equal to Q by N delta T. Now if I am talking about molar heat capacity at constant pressures, I will write it as CP and this is something that we all remember. QP by N delta T, we know what QP is, just discussed. CV is equal to QV by N delta T. Very simple, awesome. And now these two formulae, we have just expanded them a little bit. You have to remember these. Okay, these are very important. I hope everyone remembers this. I hope everyone remembers this. So, delta H is equal to QP is equal to NCP delta T. Delta U is equal to QV is equal to NCV delta T. Fine, let's move on. Do you remember this table? This is something that we also discussed in the gaseous state chapter whenever you learnt. So for monoatomic gases, you have only one atom in the molecule. So this has only 3 degrees of translational freedom. Hence Cv becomes 3r by 2. Cp is Cv plus r. Do you remember this? Cp is equal to Cv plus r. So Cp becomes 5r by 2. And you have gamma. Gamma is the? Poisson's ratio, CP by CV, the values are given over here. For diatomic gases or linear gases, any linear gas or any diatomic gas, the molecule could look like this. The molecule could look like this, three atoms in a line, two atoms in a line. So whenever you have a linear gas, it has five degrees of freedom. Three translational and two rotational. And then if you have a nonlinear poniatomic gas, something like this. You have 6 degrees of freedom. This 3R is essentially 6R by 2. Fine. So, please pause the video over here if you want. Take a good look at the table. Note it down if you want to. Let's move on. So, these formulae are also important. And these formulae that are there on the screen are applicable only for ideal gases under reversible conditions. Because we all... want to simplify things in this chapter. So for isothermal processes delta T is equal to 0, NCV delta T 0, NCP delta T 0, delta U and delta H are 0. The formula for work which you should remember. Okay, just remember one of these, everything else is just a corollary of the first one. W is equal to nRT ln V1 by V2. I am sure you can remember at least this much. Or you can remember Q is equal to nRT ln V2 by V1. Over here, do you realize that Q is equal to minus W? Because delta U is 0. Right? So W is equal to NRT ln V1 by V2. And the other formulas are just a manipulation of the first one. Okay? Then you have isobaric processes. Over here the change in pressure is equal to 0. Isobars. Right? Pretty obvious. So in isobars, change in pressure is 0. So work simply becomes minus P delta V. No need to integrate anymore. Minus P delta V. and we are talking about reversible processes so you can simply take the pressure of the gas no need to think about external pressure. So W is equal to minus P delta V can also be written as minus nR delta T because we are talking about an ideal gas. Then you have isochoric processes so in isochoric processes delta V is equal to zero yes so there is no compression there is no expansion. W is equal to 0. QV is equal to delta U is equal to N CV delta T. Very simple now. Because work is 0, so Q is QV which is equal to delta U and we just discussed this. Cool. Then you have adiabatic processes. In adiabatic processes, heat exchanged is equal to 0, so W is equal to delta U which is always equal to NCV delta T, so when you expand this, this is what it becomes, P2V2 minus P1V1 over gamma minus 1 or this is equal to NR delta T over gamma minus 1, this is something that you can remember. Also the most important result. The most important result for adiabatic processes is that PV to the power gamma is a constant value. Remember, this is here. PV to the power gamma, I will write it in a bigger way over here. PV to the power gamma is a constant value. Yes, fine. So, this is something that you have to remember. When you combine this equation with PV is equal to nRT, you can get these ideas as well. constant, T to the power gamma, P to the power 1 minus gamma constant, you don't need to remember these, just remember PV to the power gamma is a constant. Fine, again, pause the video if you want to, have a good look at the formulae, write them down, take a screenshot, now I am moving on. Entropy, entropy is the degree of randomness of the system, yes, and it's a very interesting phenomena. finds its applications in second law of thermodynamics and mathematically we call delta s of the system to be Q reversible by T. Heat exchange in a reversible process upon temperature. So second law of thermodynamics states that the entropy of an isolated system or universe, considering ourselves in a universe not a multiverse, universe will be an ideal system because there is nothing outside it as far as we know. So the entropy of an isolated system always tends to increase, always increases. Fine? Which also means that in a spontaneous process, if a process has to happen on its own, the entropy of the universe is always increasing. If there is any process in this universe that is happening, it is causing an increase in the entropy of the universe. If there is a process which causes a decrease in the entropy of the universe, it will not happen on its own. Okay, so you have to combine multiple processes together so that all of these processes combined together cause an increase in the entropy of the universe and only then these processes can happen. Just look at the ceiling fan that you have in your house. Why is it moving? It is moving because the overall process that is happening is allowing the universe's entropy to increase. So for example, think about the overall process by which the fan is working. A river is flowing somewhere, that river is passing through a turbine, that turbine is rotating and hence generating electricity via dynamo. Then the electricity is passing through so many variables and then coming to your house. And then the fan is working. All of these processes combined together will increase the entropy of the universe and that is why your fan is running. Fascinating. So you have to remember that delta S total or delta S universe has to increase so that your process is spontaneous. So it implies that the entropy change of the system plus the entropy change of the surroundings has to be greater than zero. So remember that in a reversible process the entropy of the universe remains constant. First of all reversible processes are ideal, they don't really happen in nature but if you think about them theoretically, since the system and surroundings are changing in a way that they can be reverted back to initial position, essentially no change is happening right? So that is why Entropy of the total universe remains unchanged in a reversible process. Let's move on. So, for an ideal gas in reversible conditions, for the system, okay, in reversible conditions for the universe entropy change is zero, for the system of course there will be some entropy change. So, entropy for the system for ideal gases, okay. The formula is equal to nCV ln plus nR ln. Now for different different processes you can modify this formula which sounds like a poem nCV ln, nR ln. So, for isothermal processes T2 by T1 is equal to 1, so this part becomes 0, so the formula becomes Nr ln V2 by V1. Similarly for isochoric processes, formula is simple, NcV ln T2 by T1. For isobaric, NcP ln T2 by T1. For adiabatic processes, heat exchange is 0, I told you that we are thinking about reversible processes here yes. So Q rev is 0, hence entropy change is 0. Now, talking about the universe is good, but we should be able to determine spontaneity based on just the system, right? And that is where Gibbs free energy comes into picture. Gibbs free energy gives us a very convenient parameter to judge the spontaneity of a process from the system's perspective. So at constant temperature and pressure, delta G is equal to minus T delta S total. What is this total? This is the delta S of the universe. So if delta S of the universe has to increase for spontaneity, this formula implies delta G has to decrease for spontaneity. So inside a system, if its Gibbs free energy is decreasing, the process is spontaneous. At constant temperature, Pressure, this formula is very important, delta G is equal to delta H minus T delta S. Direct questions can come from this formula. Please keep this in your mind. Okay, moving further. Then we discussed about different different types of enthalpies. The first one is enthalpy of formation, delta HF0. Heat absorbed or released when one mole of a compound, one mole of a compound is formed from its constituent elements under their standard elemental forms. Let's try to understand what this means quickly. We are creating one mole of H2O in its liquid form. We are creating one mole of H2O. What are the... Elements that it is made out of? Hydrogen and oxygen. What are their elemental forms? Elemental form means that there is only one type of atom in that entire form. Yes, so hydrogen gas, this is the natural occurring way of hydrogen. O2 gas, this is the naturally occurring way of oxygen. So we have to use these naturally occurring ways of the constituent elements and form the final thing, one mole of it. That's the definition of standard enthalpy of formation. So you are creating 1 mole of H2O using hydrogen and oxygen. Do not worry about these fractions. So finally what's happening is delta HF0, the enthalpy of this reaction is known as the enthalpy of formation. I hope you remember that negative enthalpy is exothermic, positive enthalpy is endothermic. Fine. Now... For certain standard elemental forms that exist in nature already, the enthalpy of formation is considered to be zero. This is a convention, this is a standard that we have set. Since these forms are already present in nature, no one needs to create them, so we said their enthalpy of formation is already zero. Standard elemental forms. So what are these? A few examples are O2 gas, carbon graphite, bromine liquid, rhombic sulfur, white phosphorus, aqueous protons. Yes. So for all of these, their standard elemental form, enthalpy of formation is zero. Let's move on. Enthalpy of combustion, whenever you burn something, energy released or absorbed is known as enthalpy of combustion. So methane, oxygen, jala do, you get enthalpy which is most of the times exothermic, enthalpy of combustion. combustion. Now, obviously you have to burn just one mole of a substance for standard reasons. Enthalpy of solution, dissolve something, how much? One mole of something. Dissolve one mole of anything, the energy released or absorbed will be called. the enthalpy of solution, you have to dissolve it in excess of a solvent, water. So when you dissolve it in water excess you get an enthalpy, you call it enthalpy of solution. Then comes enthalpy of hydration, this is a little more interesting. Heat released or absorbed when one mole of anhydrous or partially hydrated salt undergoes hydration by the addition of water of crystallization. You realize over here we are using just a limited amount of of water, CuSO4 plus 5 H2O gives you CuSO4.5 H2O. We have created this complex now. So, over here the enthalpy of hydration is what we call it. We don't call it enthalpy of solution. In solution, excess water in hydration. only a certain amount of water of crystallization. Then you have enthalpy of neutralization, very simple, one equivalent of acid plus one equivalent of base, add them together, they will release some energy. I can also say that one mole of H positive combines with one mole of OH negative to form water and the enthalpy of this process is known as the enthalpy of neutralization. Fine, let's move on. Bond dissociation energy, energy needed to break a bond. How much bond? 1 mole of a bond. So if you break 1 mole of H2 molecules into its constituent atoms, you will need to put some bond dissociation energy into it. How much energy is needed over here? 436 kJ per mole. Okay, then do you remember resonance from organic chemistry? Resonance in most of the cases is a stabilizing entity. In anti-aromatic cases it's different, but every other case resonance is a stabilizing entity. So because of resonance what happens is the actual enthalpy of formation of something is lesser than what is expected. It takes less energy to form it. Yeah, you are getting the point right? Since this thing is already a little more stable, you don't need to put that much effort to form it in the first place. Pretty obvious, you can have a So, resonance energy is the delta HF0 actual minus delta HF0 calculated or I can write over here expected. Now, you are wondering sir, these formulas are fine but how do we know the applicability of these? See, as I told you earlier as well that this session is for revision of thermodynamics. Number one, we are trying to do is as fast as possible so that we save our time. We don't have enough time because our exams are very close. Second of all, If this video is going out today, tomorrow there is a video at the same time which will deal with questions of thermodynamics. So we will do that as a separate video, as a separate session. Don't worry about that. Please focus on this one right now. So resonance energy is here. Very good. It is a stabilizing force. Hence we give it a negative sign. More stable. Fine. Then comes Hess law. Remember Hess law? Hess law uses the fact that enthalpy is a state function. First, let's think about what a state function is. State function me, it does not matter how you achieve the final state. Final minus initial, that's all. For example, displacement. You get up from your chair, roam around the entire world, come back and sit in your chair. Displacement equal to zero. So similarly, in enthalpy, it depends only on what the final state is and what was the initial state. Similarly for internal energy, similarly for entropy, all of these are state functions. That is why they have universal formulas. Because it doesn't matter how you achieve the final state. You achieved it, okay, use the same formula that you used for any other process. Fine? So enthalpy, entropy and internal energy, these are state functions. Q and W. Heat and work, they are path functions. It matters what path you take. Fine? So in Hess law, it uses the fact that enthalpy is a state function. Essentially, if this is reaction 1, this is reaction 2, this is reaction 3 and this is reaction 4. Do you realize that reaction 1 plus reaction 2 plus reaction 3 gives you reaction number 4? The same calculation that you've done with these reactions, you can do with their enthalpies. Delta H1 plus delta H2. Plus delta H3 is equal to delta H of the final reaction. So the way in which you combine the reactions, in the same way you can combine the enthalpies. Because enthalpy is a state function. More details when we do questions. And finally, free expansion. This is a very interesting imaginary process once again. We consider an isolated system. Expansion of an ideal gas in an isolated system. It's a very, very, very ideal imaginary process. What's happening is you take a system like this. There is a piston over here which can be moved. Okay. So this is a movable piston. Fine. And outside there is vacuum. So pressure external is equal to zero. So the gas is expanding under zero external pressure. Yes. P external zero. P external is 0, so W is equal to 0 because W is equal to minus P external dV. Okay, work done is 0. Also, it's an isolated system, so there is no exchange of energy with the surroundings. It's in vacuum. Q is equal to 0, no exchange of heat or anything. This is also an ideal gas. So, W is equal to 0, Q is equal to 0. Do you understand that the change in internal energy is 0? And since the internal energy of a gas depends only on temperature, delta T is equal to zero, which implies N Cp delta T is also equal to zero. The only thing that is changing in this process is the entropy. See this process is happening because if there is a gas you keep it in vacuum it's obviously going to expand on its own without putting any effort. But what's happening is that you are giving the gas more space now. More space implies more entropy. So delta S is something that increases and that is consistent with the second law of thermodynamics. Delta S is greater than zero for an isolated system. Yes, very nice. And finally, we have something called the polytropic process. It is just a generalized mathematical form of any thermodynamic process where pv to the power n is a constant value, n is a real number. This is something that they will give you in the question or they will tell you how to... find out this value of n. And using this, you can do the rest of the question. Some standard cases are isothermal processes may this n is equal to 1, PV is a constant. For adiabatic processes, n is equal to gamma. This is not y, this is a gamma. Fine. So for adiabatic processes, PV to the power gamma is a constant. So polytropic process is something where PV to the power n is a constant value. Fine. So people, what we've done, till now is we have covered all the theory and formulae that were there in the thermodynamics chapter in a very quick manner. Yes, it's a very vast chapter so it did take a little bit of time. Now to make your life even more simple, I will include the PDF of whatever we have discussed in the description box down below. You can download it. Also, this video serves the purpose of quick revision. It is not meant for you to learn the entire chapter from. Alright, so if you wanted to revise, I am pretty sure this video was helpful to you. Hit that like button. If this video is going out today, then tomorrow we are going to do the question solving session of thermodynamics. Do not worry about that. Download the PDF. Stay subscribed to the channel because you do not want to miss these awesome things. Until next time, bye bye. Take care.

First of all, the terminologies of thermodynamics, system, surrounding, universe and boundary. System is the part of the universe which is under observation. Surroundings are whatever is not a part of the system, so remaining part is the system. surrounding and the system is separated from the surrounding via the boundary.

Yes, so the boundary could be imaginary. I could just say this is my system or it could be a real boundary like a box. So the walls of the box would be the boundary.

Moving on, you could have different different types of systems. Open system, which can exchange both energy and matter with the surroundings. Yes, closed systems, they can exchange only energy but not matter with the surroundings.

And isolated systems can exchange neither energy nor matter with the surroundings. The idea of energy over here is classical, not modern. So we don't say that energy and mass are the same over here. Fine.

So an example of an open system would be the human body. We can exchange mass with the surroundings. We eat food and we can also... Exchange heat with the surroundings. Pretty obvious, right?

Isolated systems are ideal systems, okay? These do not exist in nature. These are just imaginary.

Fine. Now, a system can be defined by its state variables, okay? So, pressure, volume, temperature, number of moles, these describe the condition of a system and changing these variables will change the state of the system. Fine. The system could have different different types of properties.

They could be extensive properties. Extensive properties depend on the extent of the system. Intensive properties do not depend on the extent of the system. So extensive properties are total energy, volume, mass. Bigger the system, bigger is the volume, more is the mass.

Intensive properties, pressure, density, refractive index, doesn't matter how big the system is. To distinguish between extensive and intensive, there is a trick. Think about a huge system and cut out a small chunk from that system.

If both of these now have the same value of a property, it is an intensive property. Fine, chalo aage badenge, types of thermodynamic processes there are are isothermal processes where delta T is equal to zero, isobaric processes where delta P is equal to zero, isothermal means temperature remains constant, isobaric means pressure remains constant. Then you have isochoric processes where delta volume remains constant, delta V is equal to 0 and then you have adiabatic processes where the transfer of heat is 0. So, heat is denoted by Q and Q is 0. Then there could be certain processes which are cyclic in nature. So, whenever a system undergoes different number of processes and finally returns to its initial state. You go out, roam around the entire world, come back to where you are sitting right now, displacement equals to 0. So such a process is known as a cyclic process.

Fine, moving ahead, heat which is denoted by Q. you is the energy transfer due to temperature differences between system and surrounding. You know that heat moves from higher temperatures to lower temperatures.

Then you've got work. Work could be of different types. You could do work on a system by putting electric electricity, you could do work on the system by shaking that system all over, you can do work on the system by either compressing or expanding it and this is the kind of work we consider for simplicity in thermodynamics. This is known as mechanical work okay and it could be compression work or expansion work. So you could put some pressure on the gas or you could make the external pressure lesser so that the gas starts expanding.

Yes, now the formula for work done is equal to minus P external dV is integration, which implies that if you have a PV graph, alright, if you have a pressure versus volume graph, the area under that pressure versus volume graph will give you the work done, okay, very simple, let's move on. Now, the sign convention is very important and this sign convention that I am discussing right now is the sign convention for chemistry, okay. So if heat is supplied to the system, we call it positive. If heat is taken out of the system, we call it negative.

Essentially, whenever we are giving energy to the system, we call it positive. Whenever we are taking energy away from the system, we call it negative. So heat supplied to the system is positive.

Work done on the system, when you are compressing the system, then work is positive. Okay? And work done by the system, when it expands, then W is considered to be negative. This is the sign convention of chemistry. Fine.

Now, let's talk about internal energy. Internal energy is simple. It's just the sum total of the components of energy of the system due to internal factors. So...

Kinetic energy plus potential energy of the internal components. For an ideal gas, there is no potential energy because there are no intermolecular forces in an ideal gas. That's how they are defined.

So for an ideal gas, the internal energy is just the addition of kinetic energy of the gaseous particles. And if you remember the gaseous state chapter, you would know that kinetic energy depends only on temperature. So for an ideal gas, the internal energy depends only on temperature.

Fine. Then we have this very famous equation, delta U is equal to Q plus W. People, do you remember what this is?

It is nothing but the mathematical equivalent of the first law of thermodynamics. The first law of thermodynamics states that energy can neither be created nor destroyed. It can only be converted from one form to the other.

Yes, and when we simplify it for thermodynamics mathematically, we can say that internal energy of a system remains constant Unless energy is transferred from the surroundings in terms of heat or work. Very obvious and hence comes the formula delta U is equal to Q plus W. You could also write the differential form delta U ki jaga DU is equal to DQ plus DW. That is also something that you can write if the question demands.

Alright, so this is what we have written over here. Then let's talk about enthalpy. Enthalpy is the net heat content of the system and mathematically H equals to U plus PV.

Now once we manipulate these formulae, we get this beautiful thing that we need to remember. Delta H is equal to QP. What is QP?

QP is the heat under isobaric conditions. Heat exchanged under constant pressure conditions is QP. And if you manipulate these formulae, this is what happens.

what you get. Similarly, delta U is equal to QV. QV boleto, heat under isochoric conditions, when volume isn't changing, heat exchange, QV. Fine. So, these two are universal.

These forms that we got, delta H equal to QP, delta U equals to QV, you have to remember this, these are applicable for all processes whatsoever. Fine. Now, let's move on. Reversible processes.

Remember, I am pretty sure you remember this. In a reversible process what happens is, the process is so slow that just with an infinitesimal change, you can change the direction of the process. Yes, you can make the system and the surrounding revert back to its initial condition. These reversible processes are ideal.

These do not actually exist in reality. You must be saying, but sir, I charge my phone's battery every day. It charges again and again, reversible process, see. The reversible process's definition in thermodynamics is a little different.

In thermodynamics, a reversible process is one in which both the system and the surroundings get reverted back. When you are charging your phone, you take energy from the wall socket and some heat is released into the atmosphere. Now, Can you take that heat back from the atmosphere, put it in the phone, put it in the wire, put it in the wall socket? Can you take the energy from your battery and put it back in the wall socket and back into the universe?

No, right? In real conditions, reversible processes do not exist. These are absolutely ideal. So how are these defined? These are defined by quasi-static states, which means that this process is under an almost static condition.

It is so slow. that you can't even distinguish whether the process is happening or not. Again, theoretical ideas, you can imagine anything.

So, in a quasi-static state, the system is always in equilibrium with its surroundings. Fine, badiya. So, this implies that we can always write P internal equals to P external for reversible processes. Makes our life simpler in some cases.

Moving on. Let's talk about heat capacity. Heat capacity is the heat needed to raise the temperature of the system by 1 Kelvin. We all know this. So C is equal to Q by delta T.

Very simple. Now if I talk about heat capacity per mole, I have to just include the factor of N at the bottom. So C molar is equal to Q by N delta T. Now if I am talking about molar heat capacity at constant pressures, I will write it as CP and this is something that we all remember. QP by N delta T, we know what QP is, just discussed.

CV is equal to QV by N delta T. Very simple, awesome. And now these two formulae, we have just expanded them a little bit.

You have to remember these. Okay, these are very important. I hope everyone remembers this.

I hope everyone remembers this. So, delta H is equal to QP is equal to NCP delta T. Delta U is equal to QV is equal to NCV delta T.

Fine, let's move on. Do you remember this table? This is something that we also discussed in the gaseous state chapter whenever you learnt. So for monoatomic gases, you have only one atom in the molecule. So this has only 3 degrees of translational freedom.

Hence Cv becomes 3r by 2. Cp is Cv plus r. Do you remember this? Cp is equal to Cv plus r.

So Cp becomes 5r by 2. And you have gamma. Gamma is the? Poisson's ratio, CP by CV, the values are given over here.

For diatomic gases or linear gases, any linear gas or any diatomic gas, the molecule could look like this. The molecule could look like this, three atoms in a line, two atoms in a line. So whenever you have a linear gas, it has five degrees of freedom. Three translational and two rotational. And then if you have a nonlinear poniatomic gas, something like this.

You have 6 degrees of freedom. This 3R is essentially 6R by 2. Fine. So, please pause the video over here if you want.

Take a good look at the table. Note it down if you want to. Let's move on. So, these formulae are also important.

And these formulae that are there on the screen are applicable only for ideal gases under reversible conditions. Because we all... want to simplify things in this chapter.

So for isothermal processes delta T is equal to 0, NCV delta T 0, NCP delta T 0, delta U and delta H are 0. The formula for work which you should remember. Okay, just remember one of these, everything else is just a corollary of the first one. W is equal to nRT ln V1 by V2. I am sure you can remember at least this much. Or you can remember Q is equal to nRT ln V2 by V1.

Over here, do you realize that Q is equal to minus W? Because delta U is 0. Right? So W is equal to NRT ln V1 by V2.

And the other formulas are just a manipulation of the first one. Okay? Then you have isobaric processes.

Over here the change in pressure is equal to 0. Isobars. Right? Pretty obvious. So in isobars, change in pressure is 0. So work simply becomes minus P delta V. No need to integrate anymore.

Minus P delta V. and we are talking about reversible processes so you can simply take the pressure of the gas no need to think about external pressure. So W is equal to minus P delta V can also be written as minus nR delta T because we are talking about an ideal gas. Then you have isochoric processes so in isochoric processes delta V is equal to zero yes so there is no compression there is no expansion.

W is equal to 0. QV is equal to delta U is equal to N CV delta T. Very simple now. Because work is 0, so Q is QV which is equal to delta U and we just discussed this. Cool.

Then you have adiabatic processes. In adiabatic processes, heat exchanged is equal to 0, so W is equal to delta U which is always equal to NCV delta T, so when you expand this, this is what it becomes, P2V2 minus P1V1 over gamma minus 1 or this is equal to NR delta T over gamma minus 1, this is something that you can remember. Also the most important result.

The most important result for adiabatic processes is that PV to the power gamma is a constant value. Remember, this is here. PV to the power gamma, I will write it in a bigger way over here. PV to the power gamma is a constant value.

Yes, fine. So, this is something that you have to remember. When you combine this equation with PV is equal to nRT, you can get these ideas as well. constant, T to the power gamma, P to the power 1 minus gamma constant, you don't need to remember these, just remember PV to the power gamma is a constant. Fine, again, pause the video if you want to, have a good look at the formulae, write them down, take a screenshot, now I am moving on.

Entropy, entropy is the degree of randomness of the system, yes, and it's a very interesting phenomena. finds its applications in second law of thermodynamics and mathematically we call delta s of the system to be Q reversible by T. Heat exchange in a reversible process upon temperature.

So second law of thermodynamics states that the entropy of an isolated system or universe, considering ourselves in a universe not a multiverse, universe will be an ideal system because there is nothing outside it as far as we know. So the entropy of an isolated system always tends to increase, always increases. Fine?

Which also means that in a spontaneous process, if a process has to happen on its own, the entropy of the universe is always increasing. If there is any process in this universe that is happening, it is causing an increase in the entropy of the universe. If there is a process which causes a decrease in the entropy of the universe, it will not happen on its own.

Okay, so you have to combine multiple processes together so that all of these processes combined together cause an increase in the entropy of the universe and only then these processes can happen. Just look at the ceiling fan that you have in your house. Why is it moving?

It is moving because the overall process that is happening is allowing the universe's entropy to increase. So for example, think about the overall process by which the fan is working. A river is flowing somewhere, that river is passing through a turbine, that turbine is rotating and hence generating electricity via dynamo. Then the electricity is passing through so many variables and then coming to your house.

And then the fan is working. All of these processes combined together will increase the entropy of the universe and that is why your fan is running. Fascinating. So you have to remember that delta S total or delta S universe has to increase so that your process is spontaneous.

So it implies that the entropy change of the system plus the entropy change of the surroundings has to be greater than zero. So remember that in a reversible process the entropy of the universe remains constant. First of all reversible processes are ideal, they don't really happen in nature but if you think about them theoretically, since the system and surroundings are changing in a way that they can be reverted back to initial position, essentially no change is happening right?

So that is why Entropy of the total universe remains unchanged in a reversible process. Let's move on. So, for an ideal gas in reversible conditions, for the system, okay, in reversible conditions for the universe entropy change is zero, for the system of course there will be some entropy change. So, entropy for the system for ideal gases, okay. The formula is equal to nCV ln plus nR ln.

Now for different different processes you can modify this formula which sounds like a poem nCV ln, nR ln. So, for isothermal processes T2 by T1 is equal to 1, so this part becomes 0, so the formula becomes Nr ln V2 by V1. Similarly for isochoric processes, formula is simple, NcV ln T2 by T1.

For isobaric, NcP ln T2 by T1. For adiabatic processes, heat exchange is 0, I told you that we are thinking about reversible processes here yes. So Q rev is 0, hence entropy change is 0. Now, talking about the universe is good, but we should be able to determine spontaneity based on just the system, right?

And that is where Gibbs free energy comes into picture. Gibbs free energy gives us a very convenient parameter to judge the spontaneity of a process from the system's perspective. So at constant temperature and pressure, delta G is equal to minus T delta S total.

What is this total? This is the delta S of the universe. So if delta S of the universe has to increase for spontaneity, this formula implies delta G has to decrease for spontaneity.

So inside a system, if its Gibbs free energy is decreasing, the process is spontaneous. At constant temperature, Pressure, this formula is very important, delta G is equal to delta H minus T delta S. Direct questions can come from this formula.

Please keep this in your mind. Okay, moving further. Then we discussed about different different types of enthalpies. The first one is enthalpy of formation, delta HF0. Heat absorbed or released when one mole of a compound, one mole of a compound is formed from its constituent elements under their standard elemental forms.

Let's try to understand what this means quickly. We are creating one mole of H2O in its liquid form. We are creating one mole of H2O. What are the...

Elements that it is made out of? Hydrogen and oxygen. What are their elemental forms?

Elemental form means that there is only one type of atom in that entire form. Yes, so hydrogen gas, this is the natural occurring way of hydrogen. O2 gas, this is the naturally occurring way of oxygen. So we have to use these naturally occurring ways of the constituent elements and form the final thing, one mole of it. That's the definition of standard enthalpy of formation.

So you are creating 1 mole of H2O using hydrogen and oxygen. Do not worry about these fractions. So finally what's happening is delta HF0, the enthalpy of this reaction is known as the enthalpy of formation.

I hope you remember that negative enthalpy is exothermic, positive enthalpy is endothermic. Fine. Now... For certain standard elemental forms that exist in nature already, the enthalpy of formation is considered to be zero. This is a convention, this is a standard that we have set.

Since these forms are already present in nature, no one needs to create them, so we said their enthalpy of formation is already zero. Standard elemental forms. So what are these?

A few examples are O2 gas, carbon graphite, bromine liquid, rhombic sulfur, white phosphorus, aqueous protons. Yes. So for all of these, their standard elemental form, enthalpy of formation is zero.

Let's move on. Enthalpy of combustion, whenever you burn something, energy released or absorbed is known as enthalpy of combustion. So methane, oxygen, jala do, you get enthalpy which is most of the times exothermic, enthalpy of combustion.

combustion. Now, obviously you have to burn just one mole of a substance for standard reasons. Enthalpy of solution, dissolve something, how much?

One mole of something. Dissolve one mole of anything, the energy released or absorbed will be called. the enthalpy of solution, you have to dissolve it in excess of a solvent, water. So when you dissolve it in water excess you get an enthalpy, you call it enthalpy of solution.

Then comes enthalpy of hydration, this is a little more interesting. Heat released or absorbed when one mole of anhydrous or partially hydrated salt undergoes hydration by the addition of water of crystallization. You realize over here we are using just a limited amount of of water, CuSO4 plus 5 H2O gives you CuSO4.5 H2O.

We have created this complex now. So, over here the enthalpy of hydration is what we call it. We don't call it enthalpy of solution.

In solution, excess water in hydration. only a certain amount of water of crystallization. Then you have enthalpy of neutralization, very simple, one equivalent of acid plus one equivalent of base, add them together, they will release some energy. I can also say that one mole of H positive combines with one mole of OH negative to form water and the enthalpy of this process is known as the enthalpy of neutralization. Fine, let's move on.

Bond dissociation energy, energy needed to break a bond. How much bond? 1 mole of a bond. So if you break 1 mole of H2 molecules into its constituent atoms, you will need to put some bond dissociation energy into it.

How much energy is needed over here? 436 kJ per mole. Okay, then do you remember resonance from organic chemistry? Resonance in most of the cases is a stabilizing entity. In anti-aromatic cases it's different, but every other case resonance is a stabilizing entity.

So because of resonance what happens is the actual enthalpy of formation of something is lesser than what is expected. It takes less energy to form it. Yeah, you are getting the point right? Since this thing is already a little more stable, you don't need to put that much effort to form it in the first place.

Pretty obvious, you can have a So, resonance energy is the delta HF0 actual minus delta HF0 calculated or I can write over here expected. Now, you are wondering sir, these formulas are fine but how do we know the applicability of these? See, as I told you earlier as well that this session is for revision of thermodynamics. Number one, we are trying to do is as fast as possible so that we save our time.

We don't have enough time because our exams are very close. Second of all, If this video is going out today, tomorrow there is a video at the same time which will deal with questions of thermodynamics. So we will do that as a separate video, as a separate session. Don't worry about that.

Please focus on this one right now. So resonance energy is here. Very good. It is a stabilizing force.

Hence we give it a negative sign. More stable. Fine.

Then comes Hess law. Remember Hess law? Hess law uses the fact that enthalpy is a state function.

First, let's think about what a state function is. State function me, it does not matter how you achieve the final state. Final minus initial, that's all.

For example, displacement. You get up from your chair, roam around the entire world, come back and sit in your chair. Displacement equal to zero.

So similarly, in enthalpy, it depends only on what the final state is and what was the initial state. Similarly for internal energy, similarly for entropy, all of these are state functions. That is why they have universal formulas.

Because it doesn't matter how you achieve the final state. You achieved it, okay, use the same formula that you used for any other process. Fine? So enthalpy, entropy and internal energy, these are state functions.

Q and W. Heat and work, they are path functions. It matters what path you take. Fine? So in Hess law, it uses the fact that enthalpy is a state function.

Essentially, if this is reaction 1, this is reaction 2, this is reaction 3 and this is reaction 4. Do you realize that reaction 1 plus reaction 2 plus reaction 3 gives you reaction number 4? The same calculation that you've done with these reactions, you can do with their enthalpies. Delta H1 plus delta H2.

Plus delta H3 is equal to delta H of the final reaction. So the way in which you combine the reactions, in the same way you can combine the enthalpies. Because enthalpy is a state function. More details when we do questions. And finally, free expansion.

This is a very interesting imaginary process once again. We consider an isolated system. Expansion of an ideal gas in an isolated system. It's a very, very, very ideal imaginary process. What's happening is you take a system like this.

There is a piston over here which can be moved. Okay. So this is a movable piston. Fine.

And outside there is vacuum. So pressure external is equal to zero. So the gas is expanding under zero external pressure.

Yes. P external zero. P external is 0, so W is equal to 0 because W is equal to minus P external dV.

Okay, work done is 0. Also, it's an isolated system, so there is no exchange of energy with the surroundings. It's in vacuum. Q is equal to 0, no exchange of heat or anything. This is also an ideal gas.

So, W is equal to 0, Q is equal to 0. Do you understand that the change in internal energy is 0? And since the internal energy of a gas depends only on temperature, delta T is equal to zero, which implies N Cp delta T is also equal to zero. The only thing that is changing in this process is the entropy. See this process is happening because if there is a gas you keep it in vacuum it's obviously going to expand on its own without putting any effort.

But what's happening is that you are giving the gas more space now. More space implies more entropy. So delta S is something that increases and that is consistent with the second law of thermodynamics.

Delta S is greater than zero for an isolated system. Yes, very nice. And finally, we have something called the polytropic process. It is just a generalized mathematical form of any thermodynamic process where pv to the power n is a constant value, n is a real number.

This is something that they will give you in the question or they will tell you how to... find out this value of n. And using this, you can do the rest of the question. Some standard cases are isothermal processes may this n is equal to 1, PV is a constant.

For adiabatic processes, n is equal to gamma. This is not y, this is a gamma. Fine. So for adiabatic processes, PV to the power gamma is a constant. So polytropic process is something where PV to the power n is a constant value.

Fine. So people, what we've done, till now is we have covered all the theory and formulae that were there in the thermodynamics chapter in a very quick manner. Yes, it's a very vast chapter so it did take a little bit of time. Now to make your life even more simple, I will include the PDF of whatever we have discussed in the description box down below.

You can download it. Also, this video serves the purpose of quick revision. It is not meant for you to learn the entire chapter from. Alright, so if you wanted to revise, I am pretty sure this video was helpful to you. Hit that like button.

If this video is going out today, then tomorrow we are going to do the question solving session of thermodynamics. Do not worry about that. Download the PDF.

Stay subscribed to the channel because you do not want to miss these awesome things. Until next time, bye bye. Take care.

Transcript for:Comprehensive Thermodynamics Revision Guide

Transcript for:
Comprehensive Thermodynamics Revision Guide