 So we saw that a state of a thermodynamic system can be represented by a point in the so called thermodynamic state space. The question which arises is this, is it always possible to represent a state, by state we mean the thermodynamic state of a thermodynamic system by a point in the thermodynamic state space. Now remember that if you have to define a point in the geometric space, all the required coordinates have to be precisely defined. You cannot have any confusion in any of the coordinates, x has to be some precise value, y has to be some precise value, z has to have its precise value. Suppose this is true, if the answer is yes, then we have a depiction something like this, this is the state, this point and we could have the three coordinates say for example, pressure, mass, temperature. This is only for illustration depending on the system and the type of relevant properties, the coordinates will change. They could be 2, they could be 3, they could be more. But sometimes it is possible that when we do the measurement, we find that the pressure perhaps is not uniform. If we stir the gas, if the gas is fluid, reasonably dense and it is being stirred, pressure may not be uniform. If the cylinder is exposed to the sun on one side, it is possible that part of the gas is warmer than the other part. In which case one or more coordinates may not be uniquely defined and if they are not uniquely defined, it may not be possible for us to represent that so called state by a point. We will get some sort of a nebulosity, we do not know what the state is. So remember that if the answer to this question is yes, we have a state represented by a point in the thermodynamic state space and our definition is that this state is in thermodynamic equilibrium. We say that the state is in thermodynamic equilibrium when all the relevant properties are uniquely defined and hence the state can be represented precisely by a point in the thermodynamic state space. If the answer is no, then here we have a crude depiction of a state not in thermodynamic equilibrium. The idea of equilibrium is important in thermodynamics, the idea of thermodynamic equilibrium because when we say that a state is in thermodynamic equilibrium, we have unique and known values of its properties so we can proceed with appropriate calculations and further study of thermodynamics. We cannot do much when the depiction is that of non-equilibrium because we do not have a point which we can precisely locate in space. The idea of equilibrium is not unique to thermodynamics, we have just now defined thermodynamic equilibrium. But there are other equilibria, for example we have mechanical equilibrium, from mechanics, from chemistry we have chemical equilibrium. The definitions of these equilibria are different and we pick up no fight with them. Our definition of thermodynamic equilibrium is as explained that a state in thermodynamic equilibrium has all its properties uniquely defined and hence is represented or representable on an appropriate thermodynamic state space by a unique point. Even in thermodynamics we will later consider when we look at zeroth law another equilibrium known as thermal equilibrium. So this is just to make ourselves clear that the idea of equilibrium is not unique to thermodynamics. We have defined thermodynamic equilibrium in one particular way. There are other equilibria in other branches of physics. Even in thermodynamics we will have another idea of an equilibrium known as thermal equilibrium which we will come across when we study the zeroth law of thermodynamics. Thank you.