 Welcome back. Now it is time for us to look at an important idea in thermodynamics known as the equation of state. We go back to two premises. The first state postulate it said that the state of a thermodynamic system can always be defined using primitive variables. Then the second postulate it says that the number of independent intensive properties required to define the state of a system is the number of two-way work modes plus one. This means that if you have a simple compressible system containing a solid, a liquid or a gas, two properties are required to define the state of a system of fixed mass because we are talking of a set of intensive properties. So that means if we have a, for example, a fluid system, system containing a fluid, we may even consider a solid to be an extreme case of a fluid, then two primitive properties would define the state of a system. So this could be pressure and volume and to make it intensive properties, we may consider them to be pressure and specific volume. Specific volume is nothing but volume per unit mass of the system. So this implies that any other property say temperature must be some function of pressure and specific volume. Such relations, particularly the relation between pressure, volume and temperature is known as an equation of state. Another important equation, although we do not generally call it an equation of state but which from a thermodynamic point of view is an equation of state is this important relation. For a fluid system, how does the thermal energy depend on the state of the system? It is an equation of state but we may call it the thermal energy relation but it is as much an equation of state as is this. By default whenever you say equation of state it is the relationship between pv and t. Now here f is some arbitrary function depending on the type of fluid, this relation could be rather simple, this relationship can be very complicated. Now here we have used the first state postulate and written pv as our independent variables. But this relationship can be turned around and we can write this as p to be some function of t and v or v to be some function of p and t. It turns out that from a point of view of measurement it is very easy to control and precisely measure these two parameters pressure and temperature and that is why you will notice that in any tabulation properties of fluids, properties of steam, properties of gases the table is in terms of these two independent variables pressure and temperature. When we come to the study of steam tables you will see this in action and perhaps a most general relation is to say that look rather than decide whether pv is independent or tv is our independent pair of variable or even pt. Sometimes we say that the equation of state is represented by a function like a general function of pv and t which is 0. Where again here remember this f, this f and this f do not represent any specific function, they represent some well defined function as required in that particular case. Thank you.