 In the last two sessions, that is thermodynamics one and two, we have studied basics of thermodynamics, systems, surroundings, then interaction, work and heat interactions, process, state points, then basic thermodynamic processes like constant pressure, constant volume, mediabetic, polytropic and so on. You have also learned to calculate, evaluate the work done for the particular process. Now we are going to study important aspects of thermodynamics, that is the genesis of first law of thermodynamics and the calculation or evaluation of specific heats and the discussions thereof, which are very important for the thermodynamic analysis. As usual, we are going to see what are our objectives or outcomes that we expect. At the end of this session, you will be able to explain the genesis of the first law of thermodynamics. You will be able to define and evaluate specific heats for various processes and we will demonstrate that Cp is always greater than Cv. Now see, very important thing is for any topic, genesis is a very important thing because that gives you an idea that exactly what we are doing in a subject. Now before we go into the genesis, let us recapitulate or let us check how much you have learned and exactly how we can apply that particular knowledge. Now suppose I tell you that this is a PV diagram that I have, this is P and V. I go from 1 to 2 by path A and I come from 2 to 1 by path B and my simple question is, whether this cycle, now why it is cycle because system is going from 0.1 to 2 and coming back to 0.1. Now in this cycle, whether it is a work producing cycle or work absorbing cycle. Now logically you know that point 1 and point 2, if I go by process A, volume is getting decreased. Now you know that by common sense or by the law of nature that gas or working medium will not be compressed on its own, we have to do some work. So if I take area under the process 1 to 2 and show it by shaded region say by black recolor and if I ask you to find out the area under the process 2 to 1 by path B, then you will find that this area which is a shaded in red is greater than the area in black. So what does, what it indicates that work done, that is work output is greater than work input. Now if this is a situation, what is the net work positive, so this is the power producing cycle because it is clockwise, it is a clockwise cycle. On the contrary, if I say this is my PV diagram for another process and for your simplicity or understanding I just say that these are the volumes and these are the pressures. If I write this as V0 and this is a 2V0, this is say P0 and this is say 2P0 and this is a perfect circle and if I say that the process is from this direction. Now as a understanding or challenge you evaluate the delta W and tell me the answer whether it will get less than, greater than or equal to 0. You know that if it is equal to 0, no work is done. Some work is done because there is area under the work say PV diagram, if it is less than 0 work is being supplied, if it is greater than 0 work is being obtained. So, find the answer for this and then now we proceed for our first law genesis. Now you know that whenever we supply heat, take for example a standard system accepted by the international committee is a piston and cylinder assembly in which there is a gas. Now if I supply heat, if I supply heat to it then what happen because of supply of heat the gas will expand, the piston will move to this particular side if there is no constraint. So as a result there is a displacement and because of this there is some work done. So the work done if I show it by symbol W, actually it is wrong to show it by absolute number because work and Q, work and heat are both are path functions. And already we know that how we define work and heat, once again I repeat it here for your clarity that work and heat both are energies in transit and unless and until they cross the boundary we do not call them as work and heat that is first part and it depends upon the path. Means if it is isobaric process, if it is isochoric process or isometric process, if it is a polytropic process, if it is adiabatic process or if it is isentropic process then Q and W both change. But very important thing about say this proper path function is that it is just like Newton's law. So if I say, if I find out the difference between say Q minus W regularly means I supply heat and I measure the W. If I supply some another heat Q2, I measure W2. I supply Q3, I measure W3 means I made it right here I and I. So W1 minus Q1, Q1 minus W1, Q2 minus W2 a very wonderful result has been observed. It is just like Newton's law which stated that F is equal to MA and he stated in a different way that F upon M is equal to some constant. Means if I take a force applied for a particular mass, one parameter remains constant. He doubled the force, doubled the mass ratio remains same and that we called as an acceleration. Similarly, when I take a difference of heat supply and work obtained then I got a parameter which is remaining constant. So that is called as change in internal energy. Now this is very important concept in thermodynamics that the subtraction of two path functions leads to a point function. Now what is the meaning of this? Means suppose on the PV diagram, say suppose on the PV diagram I go from 0.1 to 0.2 and suppose energy associated with this is U1 and internal energy associated with this is U2. Then whether I go by path this, path this or path this one, it makes no difference if I go by this way. Important thing is U2 minus U1 is always equal to QI minus WI and this is nothing but this is the first law statement that we get in this form. If I want to write in differential form I write dQ minus dw is equal to du, actually this d and d should be made some hypenation because this is not exact differential. In calculus du on the right side is a exact differential but dQ and dw are not exact because we call those properties exact which are path independent. So du is a point function. Now you may wonder that what is the concept of internal energy and how it is to be measured? Can we measure the internal energy? No. We can measure only difference. We can measure the difference in internal energy but before that I will just bring to your notice that how we find out the internal energy. Now you know that this U is an internal energy it is divided into two. One is say we call say for example suppose I have an object it is a gas a chamber in which there is a gas molecule and gas molecules are moving in random direction and if I give a velocity to this some velocity say V instead of U I will use a symbol V. Then what happens with reference to this datum line this cylinder has some potential energy because of it motion there is some kinetic energy. So kinetic energy and potential energy of the object in total is different than the kinetic energy, potential energy and vibration energy of the molecules within the system. So you will find very interesting thing that this kinetic energy one half m e square and the potential energy suppose this height is say h mgh has nothing to do with the internal energy of the system. Because internal energy is because of the vibratory motion, translatory motion and rotational motion of the molecules. And we do not include see for ideal gas there is no interact in intermolecular forces they are absent there is no inter ionic forces. So here we have got say two forces one is intermolecular we call them as intermolecular and inter ionic. So both these are absent in ideal gas. So if in ideal gas if you see these are absent then there remains three quantities one is known as kinetic energy which is translational then rotational kinetic energy and there is a vibrational energy. And here comes the main theorem of thermodynamics which is known as principle of equipartition of energy principle of equipartition of energy. Now this equipartition of energy says that the energy per molecule is given by one half k t the proof of this will be seen in data in afterwards and if it is per degree of freedom is per degree of freedom. If there are f degrees of freedom it is f to k t if there are number of molecules avagato number of molecules it is Na into k t and f by 2 it becomes RT. So this is our symbol for say that is equation for energy in each degree of freedom for monatomic there are three degrees of freedom for diatomic there are say five degrees of freedom and for nonlinear molecule there are six degrees of freedom. Now we come to the concept of a specific heat. Now specific heat is defined as delta Q is equal to Nc delta t. Now the question is when we define this delta Q Nc delta t so we write c is equal to delta Q upon Nc delta t. Now if you do not supply heat if delta Q is 0 then we get c is equal to 0. If delta Q delta t is equal to 0 that is isothermal c is equal to infinity then if I expand slowly c is positive and if I expand suddenly c is negative. So you think over how can you imagine that specific heat can be negative and last question is Cp is greater than Cv. You know that in a cylinder and piston assembly for example this is my piston and cylinder assembly if I constant this and if I want to increase the temperature volume remaining constant if I start heating there is no expansion no work done so no cooling. So I require minimum amount of heat to raise the temperature by one degree if it is a constant pressure there is expansion and there is a cooling so to raise the temperature by one degree I have to increase the temperature I have to supply more heat therefore Cp is always greater than Cv and we are seeing after our Cp minus Cv is equal to R in detail. So we have studied the genesis we understood the specific heat and we have seen that we can evaluate that Cp minus Cv is equal to R and Cp is greater than Cv. So thank you for this session.