 Welcome back, now we look at a model of the behavior of a gas known as an ideal gas. We know that real gases, oxygen, nitrogen, air, they obey Boyle's law only approximately and this approximation becomes better and better as the system density is lowered and which happens at low pressures or high temperatures. The combination of reasonably low pressures and reasonably high temperatures is good in that zone Boyle's law is obeyed to an excellent approximation for any gas. If we imagine a gas which will obey Boyle's law throughout its state space not just at low densities that is low pressures and high temperatures but at any pressure, any temperature and any density, we will call such a gas an ideal gas. An ideal gas is a gas or a fluid which obeys Boyle's law all over its thermodynamic state space and we should remember that any gas at a low density or low pressure approximates an ideal gas. For an ideal gas if you plot the isotherms on the PV plane, we will get at low temperature figure like this, a high temperature, still higher temperature, still higher temperature. At different temperatures, we will get different isotherms and each one of these isotherms would be represented by PV equals some constant C1, this will be PV equals some other constant C2, this will be PV equals a third constant C3 and this PV equals some constant C4. So each isotherm is represented by PV equals constant, a different constant for different isotherms and that means on a PV diagram these are what we call rectangular hyperbolas. Now notice that for a given isotherm say T2, the temperature is fixed at T2, any state on this isotherm as the temperature C2. PV product for any state on that isotherm is represented by C2 and that means we can use the value of C that means the PV product to measure temperature of the system of the ideal gas. This brings us to the idea of ideal gas scales of temperature. Notice that I said scales of temperature and not just one scale because you will soon see that depending on the fixed point used and the relationship used for interpolation we can have different ideal gas scales of temperature. How does this scale of temperature work? The ideal gas thermometer would be a system say a cylinder piston arrangement which would enclose our system, we will measure its pressure, we measure its volume and this is an ideal gas of a fixed mass say m. Because it is an ideal gas in principle like any gas the temperature would be a function of pressure and volume. However because of Boyle's law it would be a function only of the PV product and hence we can use the value of the PV product to measure the temperature. So the first step is this is our thermometer, the second step is because this is a very simple relationship we need only one fixed point. Let us say that we define the reference state and we define the fixed point and we define this reference system and its state. And then we can define or obtain T in terms of the temperature of the fixed point, the PV product of our system at the fixed point and the PV product at the state where we want to determine the temperature. So this would be something like an interpolation law. I am putting interpolation within codes because it is not really an interpolation, there is only one fixed point and from that point we define the temperature over the range. Now it should be clear to you that why I am saying scales of temperature depending on the reference system and its state depending on the value of the fixed point temperature and depending on this relation we will get different ideal gas scales of temperature. However, it turns out that the ideal gas scale of temperature is a very useful scale of temperature and hence scientists have come together and define a single standardized ideal gas scale of temperature and that is the Kelvin scale of temperature, thank you.