 We now consider the way property changed during a process because a process again is nothing but a change of state and hence this implies a change in properties, at least one property. Now one should realize that when a process takes place, the state changes say from 1 to 2. So at least one property will change from 1 to 2. It is possible that all properties will undergo a change but remember that property depends on the state. Hence the change in property during a process depends only on the end state. Let us take an illustration, let us take phi is a property of our system. So as the process is executed from 1 to 2, the change in property will be the final value of the property minus the initial value of the property. This is the change in our property. This is represented quite often by delta phi or sometimes to be specific that it pertains to the process 1 to 2, delta phi 1 to 2 and this change in property one should appreciate that depends only on the end states and not on the path because the path may take different roots from 1 or 2 but so long as the end states are the same, the property phi 2 of the final state and the property phi 1 of the initial state will not be different and hence the change in property over a process from a fixed initial state to another fixed final state will be the same. So if I consider a quasi-static process from 1 to 2 like this, I will have delta phi 1 to as a change in property. If I take another quasi-static process from 1 to 2, let us say the first process is A, second process is B, again I will have the same change in property. If I consider a non-quasi-static process from 1 to 2, let us say C, again I will have the same change in properties because the properties depend only on state 2 and state 1 and hence the change in property will depend only on the end states and not on the path. What is the implication of this for a cycle? Let us consider a cycle starting from an initial state I and coming back to the same state which is also F. So this is a quasi-static cycle A and maybe I have a non-quasi-static cycle with the same initial and final state B. In this case, because these are cycles, the final state is the same state as the initial state, hence the property of the final state equals the property of the initial state and hence the change in property, any property of a system which executes a cycle is 0. This is something which one should remember. From a mathematical point of view, in thermodynamics we say that properties depend only on the state of a system. From a mathematics point of view, any property is a point function because a point represents a given state in thermodynamic state space. So since change in property, final value minus initial value does not depend on the path. So if you consider a small part of the process with a change in property d phi integrated from 1 to 2, this integral becomes delta phi 1 2 and this is independent of the path. And hence in mathematical terms d phi is an exact differential. The mathematical property of any exact differential is that when you integrate it over from a given point to another point, the value of the integral does not depend on the path. In fact, this characteristic that the differential of a property is an exact differential will be used in reverse to define two of the most important properties that we come across in thermodynamics, energy and entropy. Thank you.