 Welcome back. Now let us look at gas as a working fluid for thermometers. This brings us to the idea of gas thermometry where we use a system containing some gas as a thermometer device to measure temperature. Now let us consider for simplicity that our system is a gas enclosed in a cylinder piston arrangement. Some defined gas that is our system. We can have a pressure gauge which measures the pressure P of the system. We can have a calibrated scale which tells us the location of the piston which can be converted into the volume of the gas. Now since our system is a simple compressible system, the state will be defined by two variables and any property including temperature will be a function of two variables. In this particular case, the most convenient being P and V. Now the moment we have two properties defining temperature, things are going to become complex. So we constrain ourselves, set up some constraint. For example, option 1, we fix the piston at one place in which case what happens is the volume cannot change and for this fixed volume now we can say temperature can be defined as a function of pressure. This system or this scheme is known as a constant volume gas thermometer. The other possibility is keep the piston exposed to a fixed external pressure. So P remains unchanged. If we have a frictionless piston, it is not difficult to maintain P unchanged. So temperature can then be defined as a function of the volume and this scheme leads to a constant pressure gas thermometer. Considering the ease of measurement and considering the required or obtainable accuracy, the constant pressure gas thermometer is considered a better scheme than the constant volume gas thermometer. For the constant pressure gas thermometer, all that we have is a system essentially a cylinder piston arrangement in which a predefined gas, say nitrogen or oxygen or helium or hydrogen is kept that is our system. P is maintained at a constant value, say one atmosphere most convenient. It is the volume which is measured at various states and temperature is defined as a function of volume. As we do the experiment, we find that as the temperature changes volume will undergo a change. So you will get some line like this which will calibrate our temperature to the values of volume and then we can measure the volume at say ice point. Assuming that ice point and steam points are still our fixed points. So let us say this would be the state at the ice point, this could be the state at the steam point and then this would be V at the steam point. This is the V or volume at the ice point. We can define for example a Celsius scale based on this. Let us say this would be 0 degrees C, this would be 100 degrees C and some system which is in thermal equilibrium with a volume say V. From this calibration chart, we will say that it has this temperature. If this is the volume as indicated by the system, this will be the temperature on this constant pressure gas thermometer. Now there is still some arbitrariness in this. First which gas? It turns out that if you fix the ice point and steam point and 0 degrees C and 100 degrees C as the reference temperatures, then at a given state in between 0 degrees C and 100 degrees C, the temperature which you obtain depends on which gas you use because the behavior is not exactly linear. Not only that, it also depends on which pressure you fix the gas at and of course such a arbitrariness is not good for precise measurement of temperature. So as people did experiments, it was discovered that low pressures are better. It was Robert Boyle who experimented with various gases and plotted isotherms on the PV plane and what he noticed that he plotted isotherms for different temperatures, ice points, steam point. These are various temperatures. This is the T1 isotherm, this is the T2 isotherm, this is the T3 isotherm, this is the T4 isotherms. So Boyle discovered that isotherms of a gas approximately follow the relation that pressure and volume product is a constant. The constant is not an absolute constant. The constant is different for different isotherms which is good. The value of the constant can be used as a measure of temperature but it is also different for different pressures or different masses for the same volume. If you increase the pressure, you are increasing the mass of the gas in our system and it also depends on which gas and he discovered that this approximation becomes better as we reduce the pressure. That means this approximation is good at low densities of any gas. This that at low densities the isotherm of a gas are representable by a relationship PV equals constant is known as Boyle's law. Thank you.