 Welcome back, we saw the purpose of creating a map of corresponding isotherms in the state space. Here we had as an illustration two systems A and B and again as an illustration we had plotted four pairs of isotherms corresponding player of violet or pink isotherm pair of black isotherms, red isotherms and green isotherm. The green isotherm in the state space of A corresponds to the green isotherm in the state space of B and so on and the question which we could answer using this map of isotherms is given some state A star of A and B star of B are A star and B star isotherm and then we saw that if for example A star happens to be on the red isotherm and B star also happens to be on the red isotherm then we will say these two states of the corresponding systems A and B are isotherm however if the two systems one of A and one of B do not lie on corresponding isotherms for example here we have one candidate state of system A which is on the black isotherm but the other system which we are checking is on the red isotherm of B then they are not on the corresponding isotherms and hence the two are not isothermal and the question is if two states are isothermal two systems are in isothermal states then when you bring them in contact with each other across a diothermic wall in spite of that wall being a diothermic wall no heat transfer will take place. So whether a heat transfer process takes place or not is what we can decide using these maps of isotherms. Now remember that here we have created the isotherms using color because I am able to sketch lines in different colors but if I were to use only say paper and pencil then perhaps I would use a thinner line, a thicker line, a dashed line or a dotted line or a chain line and things like that or instead of colors or the design of a line we could simply say that the label of this line is one the label of this line is two the label of this line is C the label of this line is Z and corresponding labels here this would be label one this would be label two this would be label C this could be label Z. What do these labels mean? So here now we will say that A star and B star the same question are isothermal if they have or if they lie on isotherms which have the same color or the same nomenclature here in labels these labels on isotherms is what we call temperature and the requirement is corresponding isotherms in this state space of any system should have the same label this is important. Now more important thing is here we have considered just four different isotherms but isotherms would move continuously for example I am sure between states on isotherm one and states on isotherms two there will be intermediate states which belong neither to isotherm one or nor to isotherm two and it is possible that our candidate state one is here for A and another is here for B what we now need to do is create more intermediate isotherms. So some sort of an interpolation would now be necessary and now when you have a large number of isotherms giving them labels like A, B, C, D or assigning them colors like black, blue, red, green, pink becomes difficult. So we need to have something which is easily manageable and something which is easily interpolated. So a convenient method to assign labels is to use numbers and then this assignment of labels leading to numerical values of temperature leads to what we call thermometric scales. And the process of doing this assigning labels and creating thermometric scales and using that to measure temperature of a given system in a specified state is known as thermometry. We will look at various types of thermometric devices but let us say that the simple system which is used to do this is known as a thermometer, is a system usually rather simple to use often rudimentary that is used for a specific type of thermometer. Let us look at a simple thermometer. This is the type of thermometer which all of us have seen at home in schools in various offices. This is earlier known as the mercury in glass thermometer now better known as the liquid in glass thermometer. And this system has a long capillary I am exaggerating the bore and at one end there is a bulb. It is a closed system usually enclosed in glass and there is a liquid earlier mercury but since mercury is considered not an environmentally friendly fluid some other fluid and the remaining part of the bore is evacuated. Now what type of a system is this? It is solid glass so you cannot twist it, turn it, extend it, compress it. It has no electrical property so you cannot charge it, discharge it. So the whole system as shown by this the outer line itself can be considered as the system boundary is a rudimentary thermodynamic system. Because it is rudimentary thermodynamic system the number of properties which are required to define the state of this system it is simply one. And what would be that property? That would be the length of the liquid thread in the capillary. As you play with this you will find that if you put it in cold water the liquid may be up to here. If you put it in warm water the liquid may be here. If you put it in frozen ice or something it may go right up to here. Let us not do dangerous things like putting it in an oven and see whether it shoots out that is possible. Now using this how do we label isotopes? For the labeling we have to do is prepare a scale. The simplest scale which is still used is Celsius scale. We will take this as an example. And what I will provide you is the historical development of the Celsius scale. What is done is we decide on two reference points which are known as fixed points. One is the ice point in which we have a system of ice and water at one atmospheric pressure. System containing ice and water in equilibrium. This is known as the standard ice point. And what we do is we bring our thermometer in contact with such a system wait till thermal equilibrium is reached. And then we mark on this the location of the liquid length at ice point. This is the T ice point. Then we create another system in which we have what is known as the steam point. Here we boil water and keep it in such a stage such a state that we have water and steam together and the system pressure is again one atmosphere. We bring this thermometer in contact with such a system across a diathermic wall, wait till thermal equilibrium is reached and then again mark let us say this is the length of the thread at steam point. What we have actually measured is length of the thread at the ice point and length of the thread at the steam point. Let us call this as L naught and let us call this as L 100 from some reference location. Now again arbitrarily but for the Celsius scale we define the ice point. First Celsius scale has these two fixed point. The first fixed point ice point, the second fixed point steam point. And then we define that ice point temperature in 0 Celsius or 0 degree Celsius. The steam point temperature is defined to be 100 degree Celsius. So on the Celsius scale the ice point temperature is defined to be 0 degree C. The steam point temperature is defined to be 100 degree C. Using standard diced systems as that of the ice point system and the steam point system. And then suppose you have to measure the temperature of some other system. Say I have to measure my temperature then what shall I do? I will bring this thermometer in contact with myself. If it is not mercury and if I am not going to be very aggressive I can put that bulb in my mouth or put it under my armpit or you know tape it up to my chest. Bring it in thermal contact. Be cool, sit tight till thermal equilibrium is reached. And that means the mercury or the liquid thread which was somewhere in the capillary will finally find a position such that the temperature of the thermometer and temperature of my body would be the same. Thermometer and myself would be a pair of isothermal state. And let us say that I find my state to be in thermal equilibrium with this. Let us say LG for Gaithonding. And then we have an interpolation law which says that temperature of this system G will be, if LG happens to be 0 it will be 0 degree C. If LG happens to be 100 it will be 100 degree C. So this will be something like LG minus L0, simple interpolation law L100 minus L0 multiplied by 100 units of degree Celsius. This would be the interpolation law. So notice that even the simple Celsius scale requires the following things. First thing it requires is the thermometer. We need a simple system known as the thermometer. Then we need at least one fixed point. In this case we have two fixed points. Third we need to define the temperatures of those two fixed points. And finally for readings which are intermediate we need an interpolation law which would finally give us a method to assign the label of the isotherm on which the system which is in equilibrium with the thermometer at its state LG lies. And this is the interpolation law which gives me my body temperature at say 36 degree C or 37 degree C. We will discuss more about thermometry and associated thermodynamic concepts soon after this. Thank you.