 As I mentioned in the introduction, among all the properties, we have chosen temperature for further discussion primarily because temperature, both temperature as well as its measurement pose some unique fundamental difficulties which the other properties do not have. So there is actually no formal definition for temperature, temperature may be understood as that property which determines whether two systems are in thermal equilibrium or not. So the definition appears to be not very, I mean not quantitative and there is a reason for that. I mean that is one of the fundamental conceptual issues with temperature. In fact, this conceptual difficulty was realized only much later historically so the zeroth law of thermodynamics. So it had to be called the zeroth law because it was enunciated after the other laws and so this formally states that when two systems are individually in thermal equilibrium with the third system, then they are in thermal equilibrium with each other. So what do we mean by this? So let us say that we have three blocks, let us call this block A, let us call this block B and let us call this block C. So when I bring these two blocks in contact and let us say they are in thermal equilibrium and then let us say I bring these two blocks in contact and they are in thermal equilibrium, then what this means is that A and B need not be brought together, they will be in thermal equilibrium. Now what exactly do we mean by thermal equilibrium? By thermal equilibrium, what we mean is that properties which are dependent on temperature will no longer change and or will be the same for the two blocks, that means the two blocks are in thermal equilibrium. So some of these properties are like volumetric expansion of the block. So let us say the block A is hotter and block C is colder when I bring them together. So the hotter block will start to contract and the colder block will start to expand and eventually when they reach thermal equilibrium neither of the block will expand or contract. So that means that equilibrium is attained. So we have used the thermal expansion property of the block to measure the level of thermal disequilibrium and establish that they are in equilibrium later on. We could also for instance have measured the electrical resistance of each one of these blocks and notice that they keep changing as the blocks go towards equilibrium. Once they go towards equilibrium, the values do not change anymore. So that is how we define thermal equilibrium and the property that we have used for this is called the thermometric property. In fact, this is a property that is actually eventually will be used to measure temperature of the system. Notice that the way this definition goes, it talks about thermal equilibrium, but does not assign a number. We are used to seeing a number for temperature and someone says or when someone asks what is the temperature outside today, we probably would say 25 degrees Celsius. Depending on the country that we live in, if you are in India, then you will say 25 degrees Celsius. So this definition actually does not give a number. How do we come up with that number is what we talk about next. That comes under the category of measurement of temperature. But notice that the definition of temperature itself is actually not quantitative. It only talks about thermal equilibrium and properties which depend on temperature alone being used to determine whether some, whether two systems are in thermal equilibrium or not. So that is a fundamental issue or fundamental difficulty with the definition of temperature. Let us look at measurement of temperature. So here we are looking at the simplest of thermometers, namely the humble liquid in glass thermometer. So we have a liquid inside the bulb here. It could be mercury or alcohol or any other liquid whose property change with temperature we know. And what we do is we start by calibrating the thermometer. That is when the number that we talked about comes in. So we bring this bulb in contact with water that is freezing at zero, I mean water that is freezing. Everyone agrees that when water freezes under normal conditions, its temperature is 0 degrees Celsius. So we note down the level of mercury in the bulb when we do this and mark that off as 0 degrees Celsius. So that is called a fixed point. So fixed points are points whose temperatures are agreed upon by everyone. So everyone agrees that under atmospheric condition water freezes at zero degrees Celsius. Next we bring the bulb in contact with water which is boiling at atmospheric pressure. And again this is another fixed point called the steam point and it is universally agreed that the corresponding temperature is 100 degrees Celsius. So we see how far the mercury rises up in the bulb and then we mark that off as 100 degrees Celsius. Now what we do is we divide the distance in between these two markings equally or we assume the scale to be linear. We divide them into equal segments and then mark 10, 20, 30, 40 and so on, degrees Celsius and so on. Now the question that arises next is let us say we have two liquid in glass thermometers. Let us say we have liquid in glass thermometer with mercury and we have a liquid in glass thermometer with alcohol. And we bring the two thermometers in contact with an object whose temperature we want to measure. And just for the sake of argument, let me exaggerate a little bit and say that one of the thermometers gives the reading as let us say 45 degrees Celsius and the other one gives the reading as let us say 50 degrees Celsius. So naturally you know the question that arises is which one is more accurate? Can we tell? This highlights the fundamental difficulty with the measurement of temperature. We already talked about certain fundamental difficulty in the definition of temperature. Now we are talking about a fundamental difficulty in the measurement of temperature. It turns out that neither one of the thermometers is incorrect, but both of them are correct primarily because we calibrated the both the thermometers at two fixed points, the ice point and the steam point. And by definition the readings of these two thermometers will agree with each other only at these two points. They cannot be expected to agree with each other at any of the intermediate points because we assumed a linear relation for the coefficient of or for the volumetric expansion of the thermometric liquid with temperature. So we assumed a linear expansion and then marked them like this. So the expansion coefficient between the two different materials will always be slightly different, which means that there will always be a slight difference in the readings between the two. So there is always going to be a difference in the readings unless we start calibrating at every one of these intermediate temperatures. So we take a fixed point at 10 degree Celsius and 20 degree Celsius, 30 degree Celsius and so on. But that sort of becomes hopeless exercise because we would have to calibrate at every temperature that we want to measure. Then we ask the question, what happens in between? So we have to reduce the difference between these scales or the readings to a small value and start calibrating with almost an infinite number of fixed points which generally are not available also. It is not worth the effort. But we understand that there is a fundamental issue with this and we will have to see how we can actually deal with this. So that illustrates the difficulty with measurement of temperature or the values that we ascribe to temperature. Now regardless of whether we use the liquid in glass thermometer or any other thermometer, so here we have given a list of direct contact thermometers. These are called direct contact thermometers because they are brought in direct contact with the object whose temperature we want to measure. So it could be a liquid in glass that we just saw. It could be a resistance thermometer or a thermocouple. And in the case of the liquid in glass, we use the thermometric property that is used is the volumetric thermal expansion of the liquid. So we know how or we establish how the liquid expands with temperature and then use the relationship in marking the scale in the thermometer. In the case of a resistance thermometer, of course we use the electrical resistance. Here the relationship is much more complex because the range of temperatures covered by resistance thermometers is actually much wider than the 0 to 100 degree Celsius for that we saw. So since it is much wider, a polynomial in temperature is used. Actually the scale is non-linear and usually involves a polynomial. Now if you look at a thermocouple which uses the Sieberk effect as the thermometric property, again the range of temperatures covered is actually quite large and this also uses a polynomial temperature. So if you actually draw a scale similar to what we saw here, the markings will not be linear but the markings will be non-linear, they will not go like this. But regardless of which one we use, the fundamental issue with the measurement of temperature namely that two thermometers will not agree with each other except at the fixed points that issue remains. Probably the most accurate temperature readings which do not depend on the working substance to some extent. So basically what we are saying is the temperature readings that we get depend on the nature of the working substance. So to some extent on the or to some irreducible extent on the nature of the working substance, probably a practical thermometer whose readings are almost independent of the nature of the working substance is the so-called constant volume gas thermometer that is shown here. And it is a very, it is a simple setup but the procedure to measure temperature with this is quite involved. So basically it consists of a bulb which contains a certain amount of gas. The gas could be helium, argon, nitrogen, whatever. So it is pre-calibrated, there is a scale here and so there is mercury in this reservoir and there is a flexible rubber tube and the mercury goes up to a certain level here depending on the pressure and by looking at the level to which it rises, we can actually determine the temperature. It is all calibrated and marked here. So basically, we bring the bulb and the gas inside in contact with the system whose temperature we want to measure. In this case, this particular bath. So the gas expands and then pushes the mercury down and we adjust the reservoir so that the mercury level is maintained at the same level. So we may push it up or down so that the level of mercury coincides with this marking and then we note the difference between the heights and we can work out the temperature. So let us say initially we start with 1 gram of say helium in the bulb. So after having taken this, we repeat the experiment by reducing this to let us say 0.1 gram of helium. We take the reading again. We reduce the mass of helium further to 0.01 grams and so on. So we keep repeating this until we reach reasonably practically small values or small amounts of gas inside the bulb. Then we redo this entire set of readings by using argon for instance instead of helium. We go through the same procedure. Then we go through the same thing with let us say nitrogen, oxygen and so on. Then from all these readings, we actually will get, if you work out the temperature, you will notice that you get a single value for temperature which does not depend on whether we are using helium, argon, neon, O2 or N2 and which does not depend on the mass of the gas in the bulb. So you get a reading which is truly independent of the nature of the substance in this case. Of course, the caveat that the gas should still behave as an ideal gas that remains because that is a fundamental principle that is used to calculate the temperature from the pressure. Basically, we are measuring a pressure difference here and that is used to convert, I mean that is used to evaluate the temperature. So it assumes that the gas behaves as an ideal gas. So as long as the range of temperature that you are looking at ensures that it behaves as an ideal gas, this probably is the closest to a thermometer that we can get which gives readings irrespective of the working substance. There is only one exception to this and we will discuss that as we go along. So to summarize what we have said so far, readings of different thermometers agree only at the calibration point, that is very, very important. And irrespective of the method used, it is known that the measured value of temperature depends to some irreducible extent. We cannot quantify this. If we can quantify this, then of course there will be no uncertainty anymore. So it depends to some irreducible extent on the thermometric substance used or the assumed calibration relation. As we will see later, the only exception to this is the corner engine. So if we can fashion a corner engine with which we measure temperatures, then the readings that we get would be independent of the working substance that is used inside the engine. We will demonstrate how this happens as we go along or much later when we discuss second law of thermodynamics. So that completes the introduction module where we talked about some seemingly simple concepts but we brought out very, very subtle aspects of system control volume and also temperature and its measurement. These are probably concepts that you are familiar with but most likely you may not be familiar or you may not have been familiar with some of the subtleties that we brought out in our discussion.