 Welcome back. Let us consider the entropy difference between two states for a simple compressible system at rest. Simple compressible system, this means that there is only one two-way mode of work and that is expansion compression and that means dw, this expansion compression would be pdv. At rest means there is going to be no change in the velocity or the position of our system. It is something like me sitting still at a desk and this means that changes in energy would be changes only in the thermal energy not in say kinetic energy, gravitational potential energy and so on. Now for such a system ds we have to calculate. Now remember that the first law will be applicable dq is de plus dw and with this assumption that de equals dw, this becomes du plus dw. Now we want to execute a process reversibly and that means this dw must be only two-way mode of work. So dq reversible will become du plus pdv because now we are restricting dw to only two-way modes of work. Since we have a simple system there is only one two-way mode of work and dw equals dw expansion which is pdv and because of this our ds which is defined as dq by t reversible is du plus pdv by t. It is this expression which we will need to integrate to obtain the change in entropy between two states. This relation relating to this relation relating ds to du, dv and pnt is sometimes known as the entropy relation for a simple compressible system at rest. That should always be at the back of our mind during these series of lectures. If there are other cases we will talk about them but otherwise simple compressible system at rest. This is known as the entropy relation and if I multiply both sides of this equation by t we will get tds is du plus pdv and this equation is known as the basic property relation again for a simple compressible system at rest. Now using the entropy relation if we want to determine the entropy change between two states that would simply be the integral of du plus pdv divided by t this whole expression from 1 to 2 across any convenient path of course from 1 to 2. Thank you.