 Welcome back. We are now going to look at a specific thermodynamic temperature scale and that will be the thermodynamic Kelvin scale of temperature. A while ago we noticed that if we use this relation for defining scales of temperature using of course a reversible 2T engine or even refrigerator then we will get a scale of temperature which is a thermodynamic temperature scale. There is a certain amount of arbitrariness in this because this function G of temperature is yet to be defined. Let us now define that in a simple way and then we will come to one specific scale which we will call the thermodynamic Kelvin scale of temperature. Remember that we basically have to define a function G of T and then once it is defined temperature can be defined using this relation where Q1 and Q2 are the heat interactions of a reversible engine or even a reversible refrigerator working between T1 and T2. And remember that for this relation it does not matter whether T1 is higher than T2 or T1 is lower than T2. If T1 is higher than T2 Q1 and Q2 will be in the direction at shown whereas if T1 is lower than T2 then Q2 and Q1 will be in the direction opposite to what we have shown here if we are working with an engine. Now what is the choice for G? Let us make the simplest of choices. G of T is T itself. In that case the definition of our thermodynamic temperature scales would be some temperature by some reference temperature will be Q by Q reference for a reversible machine. So again let me draw this diagram. For this definition what we will have is a reference temperature and a reference system and also a value for that a reversible engine working between our system at temperature T and the reference temperature system. This heat interaction is Q, this heat interaction is Q ref. Of course there will be work interaction but we are really interested in only the measurement of the heat interactions. Now remember that T ref and the definition of the reference system is yet to be done whereas this gives us the measurement formula. So now we have to define a reference system, its reference state and we also have to define T ref. We will now proceed to do this. Now for the thermodynamic Kelvin scale we will define our reference system to be a closed system containing water steam ice that is the water substance in some phase and the reference state would be the triple point. So remember that this reference system and the reference state is the same reference system and the reference state which was used to define the ideal gas Kelvin scale. So it is the same reference system and the same reference state. And of course we have to define a reference temperature and this is defined to be as in the case of the ideal gas Kelvin scale 273.16 Kelvin and using this definition and our interpolation form which we have selected to be this, we do the following experiment. Suppose we have a system whose temperature T is to be measured. What we do is if the system is large enough and can be approximated to thermal energy reservoir then we use the system itself or at the same temperature T we create a thermal reservoir. Then we create a thermal reservoir which is at T ref that means it contains water at its triple point and then we run a reversible machine. If T is greater than T ref well it will be a reversible engine. If T is less than T ref it can be a reversible engine working the other way, does not matter. Anyway we measure the heat interaction Q with this system or the reservoir. We measure the heat interaction Q ref with respect to the reference system. And since we have defined T ref, T is calculated from the formula T by T ref is Q by Q ref and we will be conscious of the fact that this is reversible. We will be using this capital R symbol almost everywhere to indicate that what we mean is a reversible process or a reversible cycle or thermodynamic reversibility wherever involved. Now one thing, we now have a bit of confusion which we have to get rid of. We have a system at some state. Now whose temperature is to be measured? We can use either the ideal gas Kelvin scale or the thermodynamic Kelvin scale. Let us say we get the temperature measured to be T here on the ideal gas Kelvin scale. And now instead of calling this T just to be clear let me say that the same temperature on the Kelvin scale let us call it theta. The question is, is T equal to theta? We know that is there is one temperature level, the triple point of water where T is defined to be 273.16 Kelvin, theta is also defined to be 273.16 Kelvin. But at other temperatures higher or lower we do not know whether they will be equal or not. And till that question is resolved which we will do in a few moments let us say that we will be using the symbol theta whenever the temperature is measured on the thermodynamic Kelvin scale. And we will be using the symbol T when the temperature is measured using the ideal gas Kelvin scale. Our effort now would be to do something which will resolve this question. In fact the end result should be that well there is no difference between T and theta. And then after that there will be no need for two distinct symbols T and theta. After that we will continue using T for temperature because we would have demonstrated that the temperature measured on the ideal gas Kelvin scale in the same temperature measured on the thermodynamic Kelvin scale leads to the same result. Thank you.