 Good morning all of you, before we start the topic a few questions, I think to begin with I will take just one question per center, so there are two questions here, one from Trichy and one from Jaipur, let me first take the question from Trichy. One question at a time, if there are many hand holdings, hand raising then maybe I will come back to that center for the second question, PTT student video, good morning Trichy, over to you for your question. Sir, you reduce first law that behavior between adiabatic and non adiabatic that is about the work heat interaction and later to zero et ala existence of isothermal state and being isothermal is a trans state in the state space of all system you said, then in the second law you say that which is possible which is not possible and the direction of energy transfer. So, you studied the in the zeroth law is that any temperature is clearly explained or in the only in the second law the temperature is clearly explained I want to know, over to you sir. Temperature exist in basically two laws the zeroth law and the second law and when we discussed second law we reviewed the status of temperature from the zeroth law. In the first law the way we developed it there is no mention of temperature at all it is only adiabatic processes and initial state and final state and work interaction. Zeroth law tells us that there is something called thermal equilibrium that is the existence then we said that being in thermal equilibrium of the property of two states being in thermal equilibrium is a transitive property and that is what we traditionally know as zeroth law that A is in thermal equilibrium in B and B is in thermal equilibrium with C that means and then A is in thermal equilibrium with C. So, now this existence and transition transitive laws tell us that in the state space of any system there will be pair of isotherms actually corresponding isotherms. So, there will be a set of isothermal states in the state space of system A the corresponding set of isothermal states in the state space of system B and a corresponding set of isothermal states in the state space of any system and just for convenience we label these states as with some labels. So, that we can identify whether a given state from the state space of system A and another given state from the state space of system B are isothermal or not. Zeroth law just tells us that if they are isothermal then by definition there will be no heat transfer and then because isotherms have the label called temperature we say such states have the same temperature. If we find that the two states say A 1 and B 1 of two different systems or two systems A and B happen to be non-isothermal from zeroth law point of view we can only say that heat will be transferred between them if they are brought into contact with each other across a diathermic wall. It does not tell us in which direction the heat will be transferred because the labels called temperature mentioned in the zeroth law they do not mention any higher temperature or a lower temperature. The numerical value of higher temperature and lower temperature gets assigned when we map those isotherms onto some convenient thermometer that is why we have 0 Celsius and red Celsius 30 Celsius 50 Celsius. Here the idea of a higher temperature simply means higher on a Celsius scale it is not thermodynamic higher or lower and this is where zeroth law ends when it comes to second law. Second law is much more detailed than either the zeroth law or the first law that we would have noticed. First law has one simple statement and two derivations one the idea of energy or change in energy of a system and second the heat transfer in non-adiabatic processes these are the only things which come out of first law. Out of zeroth law comes the idea of temperature and then thermometer takes over about how to label those isotherms conveniently. It is in the second law that we have many many things involved we start with just a single statement that is the Kelvin Planck statement and then using definitions of an engine a 2 T heat engine a reversible process and a reversible cycle and a reversible engine would derive a lot many things. For example, we derive that the there is a we derive first that there is a hierarchy of temperature and using second law we define temperature as higher or lower. What is our definition of a higher temperature given two isothermal two non-isothermal states at say T 1 and T 2 take a system at T 1 another system at T 2 try to work a 2 T heat engine reversible or otherwise does not matter all we need is that it P I engine between the two systems one at T 1 and one at T 2 let us say system 1 and system 2. If you find that the engine works by taking heat in from the system at 1 rejecting heat at 2 and producing some positive amount of work then we say that the temperature of 1 is higher than the temperature of 2 that is our definition of higher and lower temperature. If it is the other way round if it takes it from 2 rejects it to 1 and produces work then we say T 2 will be higher than T 1. So, among other things second law also helps us define the gradation of temperatures higher and lower. Now, this definition of higher and lower it just to be consistent with the temperature scales in which higher numbers are given to so called hotter stuff. We have psychologically decided that the steam point is at is hotter than the ice point for a system at the steam point is hotter than the system at the ice point. So, using second law when it comes to defining a higher and lower temperature we define it appropriately. So, this is just for being consistent and there is nothing more in it over to you. Thank you. Good morning doctor Brahmara over to you. Good morning sir the question is related to free expansion. Let us say there is a closed system with a gas in it at some pressure and temperature. If it expands against free expansion and reaches a final volume V 2 can we calculate the work done as PDB work or since it is against no resistance is the work done 0. The question is about free expansion. Let us discuss it with some detail because here it is important to sketch the system diagram. If you are thinking of free expansion in a vessel and we have a problem somewhere where a vessel had a wall in between and there was a gas here and there was vacuum here. And here the free expansion or sudden expansion was initiated by removing this wall. So, the gas would expand occupy the vacuum of course, a non quasi static process all that you would know is initially the volume was V 1 finally, the volume was V 2 initially may be the pressure was something this was the initial state 1. Finally, the pressure would reduce any gas because the volume is higher but we do not know what is the path in between. So, it is not a quasi static process and it is not a it is not the process in which the work can be the expansion work can be determined. The same thing is true of you know the argument then goes like this. Suppose I have a gas but instead of a partition let us say let us say this thing is open, but I have a piston and say on this side is vacuum and we have a gas initially at some pressure P naught and the initial volume is V naught. And then I will argue that look the piston will suddenly get accelerated. So, the situation is very similar to this and the V 2 will be the point where the piston is made to stop for some reason or something else happens. Then the but you can say that look the gas will provide a force on the piston of P naught a and then you say I can make the piston of a very heavy mass m. So, that this under this influence this mass will not suddenly move the piston it will accelerate it slowly. Well if it accelerates slowly and during the acceleration if you can measure the pressure and volume that means at any instant you are sure of the position of the piston at if in any instant by means of measurements if you are sure that the pressure in the gas is uniform then under that assumption you can have a quasi-static process. So, if you have a heavy piston which moves or accelerates slowly then under in that condition you will be approaching a quasi-static process, but if you say it is a lightweight piston it shoots off it is unlikely to be quasi-static over to you. Thank you sir over T. Now, I will go to PSG Coimtour. PSG Coimtour good morning over to you. Hello sir good morning sir there are two questions here first one can you please explain me once again the character statement of second law. The second question is what is the difference between vapor and gas over to you sir. I will take the second question first there is in the thermodynamics as well as in normal English the distinction between a vapor and a gas is a bit confusing you can use either and it does not make any difference except that when you have a gas which is in contact with a fluid its own liquid may be it is in equilibrium may be it is not in equilibrium or may be it is in a stage which is superheated but reasonable reduction in temperature or a small increase in pressure can liquefy it then we tend to call it a vapor when it is far away from the liquid vapor dome in the state space we tend to call it a gas. For example, at room temperature at one atmosphere pressure we will call nitrogen a gas whereas the same nitrogen when it slowly evaporates from a liquid nitrogen flask will generally be known as nitrogen vapor. So, that way the two words are more or less interchangeable except that generally when you are near the liquid vapor zone you tend to call it a vapor when you are far away from it you tend to call it a gas there is nothing special about it. For the Karatheodori theorem or Karatheodori formulation of the second law we do not really have to worry about it but remember we have sort of derived it indirectly from our Kelvin Planck statement. The Kelvin Planck statement says that a 1 T heat engine is not possible we have derived from that the following thing. We have said that d s is greater than or equal to d cube by T this is the entropy principle. This means that for any adiabatic process this is for any process for any adiabatic process we will have d s is greater than or equal to 0. That means if we start from a state of a system and execute only adiabatic processes we will reach states which will be either at the same entropy or at the higher entropy. We know that in the state space there will be an isentropic line this is isentropic. So, if you execute adiabatic processes we may have d s equals 0. Let us say this is higher entropy states and these are lower entropy states. And if this is our state by executing adiabatic processes we will reach states which are anywhere on this side at higher entropy or in the limiting case the same entropy. We will never reach states here and this is what we have derived this is what it means what Karateo Dori has done is rather than start from the Kelvin Planck statement of the second law of thermodynamics. He started with this as the statement but they are calling it an entropy. It says that in the neighborhood of the state space of any point there are states which you cannot reach through quasi-static adiabatic processes that is it. That means you can reach some states you cannot reach some states and using this he derived all the characteristics that we have derived of the second law. However the mathematics is very involved there are actually his paper is very informative unfortunately it is in French. There are two books for some reason neither of them in mainstream thermodynamics which give a compact but concise and reasonably complete introduction to the Karateo Dori formulation. One is by S Chandrasekhar the Nobel laureate I think the title of the book is introduction to stellar structure. First or second chapter of this will have the Karateo Dori's form explained and the second one is a technical book Bolli and Weiner. I am not sure whether this is EI or IE it is I think introduction to thermal stress analysis or theory of thermal stresses or something but thermal stresses are the key words in the title. Both are well known books a good library should have this in the physics section and this in the solid mechanics or stress analysis section. You will find in these books enough introduction but if you look up there are many many other papers etc which have argued for against try to analyze Karateo Dori's derivations in detail. They go into deep mathematics which is not so easily understandable. Karateo Dori's work itself is from 1909 and it is in French. The paper is available I think it is downloadable from some sites but since it is in French it is a bit difficult to understand because although it is mathematical so it is full of symbols but there are arguments also which are purely in French. Sir good morning my question is regarding entropy is there any physical definition for entropy over to you sir. That is the last question I am taking from your center because half an hour is over. There is no physical definition of entropy the way entropy we have we have defined entropy using a integral dq by t for a reversible process that is our first final and proper definition of entropy for us. Jaipur engineering college I hope you are able to hear me but when I say over just start asking questions because I am able to hear you over to you. Sir if internal energy is the function of temperature only then if you refer the steam table at 100 degree Celsius 1 bar pressure there are two different value of energy and you have why it is so. Remember internal energy internal energy is a function of temperature only only for an ideal gas is water and water vapour and ice etcetera an ideal gas no moment they are not the ideal gases or it is cannot be modelled as an ideal gas the question of you being a function only of temperature does not arise. For any other gas vapour fluid you will be a function of temperature and something else pressure volume drainage fraction some other variable of state over to you. I will just take one question each from NIT Calicut and Amrita then we will start the formal session today. NIT Calicut good morning and over to you. The question is about the perpetual motion machine of the first kind and the second kind. This has already been discussed so I am surprised that the questions are coming up the same questions are coming up again and again are being asked on Moodle. I will just quickly say that perpetual motion machine of first kind is something some process which violates the first law of thermodynamics PMM of the second kind is a process or a machine which violates the second law of thermodynamics that is it there is nothing more about this. So over and out I am going to the other centre Amrita Kohimthur good morning over to you. Good morning sir I am Ravindran from Amrita I have a question regarding test 2 sir in test 2 one question is there that is an adiabatic process which one which statement is correct the answers were P equal to constant PV power gamma equal to constant V equal to constant PV equal to constant usually we are using if it is an adiabatic process immediately we answer PV power gamma equal to constant gamma is an adiabatic index but after finishing our examination we found that all 4 statements were correct is it correct sir if it is correct how is it sir please explain with examples. Just remind me in the afternoon late afternoon I will give you illustrations of all 4 processes being possible with the condition that it be an adiabatic process this actually it was a bit surprising to us because of you know usually our undergraduate students in the initial quizzes make this error that the moment is see the word adiabatic adiabatic is equivalent to PV raise to gamma is constant it is a simple pattern matching they do and they forget that adiabatic only means no heat transfer across the wall because it is defined as work transfer only so no heat transfer across the wall. So, as you attend the lecture on open systems let me nicely sketch situations which are adiabatic and which have the 4 possibilities pressure equals constant volume equals constant temperature equals constant and as well as PV raise to gamma is constant. So, I will do that homework and I will display those things in the afternoon we already have some illustrations of these in the exercises sheet if you wish to look at them in detail over and that brings us to the end of the morning discussion session