 Welcome back, we were discussing the HS diagrams of adiabatic work transfer systems and we had drawn two diagrams one for the turbine and one for a compressor. So let us now discuss the turbine in slightly greater detail. So let us just draw the HS diagram again for a turbine. So we had drawn the HS diagram as follows for a turbine and this is the inlet isobar, this is the exit isobar. So the inlet pressure is higher than the exit pressure and that is what is happening in a turbine. So let us just write P i is greater than P e. If the process was ideal that is if it was reversible apart from the fact that it was adiabatic then we know we would have got an isentropic process and in that case the ideal state would have been e star that is you would have gone through the same entropy here. So s i would have been equal to s e star. Now what happens is that the process is not reversible it is not ideal and it leads to production of entropy and we know from our second law for an open system that m dot s e minus s i is equal to s dot p which should be greater than or equal to 0 as long as the system is adiabatic which is what we are investigating and hence s e will be greater than s i greater than or equal to which means s e will be greater than or equal to s e star. Now in this case the inlet enthalpy is higher than the exit enthalpy. So it is h i is greater than h e which means that w dot s which is equal to m dot h i minus h e is a positive quantity. This is what we expect from a turbine we are extracting work out of it. So the system does work on the surroundings it is a positive quantity and this is what we expect. Now you also see that this difference here is the delta h that is ideal or let me call it delta h star and this difference from the same h to this here this is delta h actual. So delta h star is h i minus h e star and delta h actual is h i minus h e this is what is happening in the real process. So obviously delta h star is greater than delta h actual. So h i minus h e which is the actual work output is less than or equal to h i minus h e star which implies of course that w dot s which is the actual work output is less than or equal to w dot h star. This is related to this this is related to this of course in both the w dots are positive that is we are extracting work out of the system. So let me write both. So this is what happens for a turbine. So please note again we have two pressures we go from a higher pressure to lower pressure which means we go from a higher enthalpy at the inlet to a lower enthalpy at the exit and the ideal work output is definitely going to be greater than what we see actually and this is of course agreeing with our notion of what is an ideal process whenever we are trying to extract work output between set of pressures what we get ideally is more and what we get actually is less and hence we will get w dot s is less than w s star. Now because of this we can actually go ahead and define an efficiency. So let us see how we will do that. So the efficiency of a turbine and we will call it the isentropic efficiency this is because we are going to base it on the isentropic process. So in the isentropic process what we get of w ideal is m dot h i minus h e star and we are going to base it on this so called ideal work and hence we will define something called as eta s t which is the isentropic efficiency of a turbine this t stands for turbine. We will define this as actual work output upon the so called ideal work output and this will turn out to be h i minus h e upon h i minus h e star and since w s star is greater than w dot s this number will be greater than sorry it will be less than or equal to 1 and this is so called isentropic efficiency of a turbine. Of course we could have other efficiencies related to mechanical behavior of the turbine etcetera but this is a purely thermodynamic quantity that we are discussing here. We could have extracted a certain amount of work if the turbine was reversible and if we had got the exit entropy the same as the inlet entropy but that does not happen and hence we define something called as an isentropic efficiency which is defined that it is the actual work output divided by the ideal work output and it is going to be a number which is less than 1. Thank you.