 We talk a lot about the relationship between heat and work, that is, after all, where the name of this class comes from, thermodynamics, heat and work, and one of the primary aspects of our power production is going to be in the form of expansion and compression. When we describe operating efficiency of a compressor or an expansion process like a turbine, we are describing an isentropic efficiency, because the best-case scenario for a compression and expansion process is an isentropic process. So when we describe operating efficiency, we are saying how does the work compare to that ideal case? For the isentropic efficiency of the compressor, we are comparing ideal work and actual work, and the easiest way to think through the order of that proportion is to imagine, do you have more work into a compressor if everything is perfect, or in the real world where there's friction and losses and stuff? You're right, it takes more work to compress something in the real world with friction and losses and stuff. You're right, it takes more work to compress something in the real world where there's friction and losses and stuff, and as a result of that, that means that we are expressing the proportion of ideal to actual work in the compressor, and the ideal work is the work if everything is perfect, therefore the work of an isentropic process. Now, same question. In a turbine, do you get more work out in a perfect world where there's no losses, or in reality where there's friction and losses and stuff? You get more work out of a turbine in the ideal case. The presence of losses decreases your work. Therefore, in the isentropic efficiency of a turbine, we are describing the proportion of actual work to ideal work. We can write the isentropic efficiency of a turbine is the actual work over the ideal work, and we can express that on a specific basis, a total magnitude basis, or on a rate of power basis. For compressor, we can express the isentropic efficiency of a compressor as the proportion of ideal work to actual work, because the actual work required is bigger, therefore our isentropic efficiency will be less than or equal to one, and that proportion represents the total work, the specific work, and the rate of power. To figure out what to plug in for the specific work for the actual and ideal basis, let's consider an energy balance. For an energy balance on a compressor, if I'm assuming everything is perfect, I have an adiabatic process because delta S of the surroundings is also going to be zero, then I have the work in is equal to H2 minus H1. For a turbine, the ideal work is going to simplify down to H1 minus H2. Therefore, when I'm comparing the actual work to the ideal work, what I'm comparing is the delta H's. For the ideal case, I have an isentropic process, which means that I have H1 minus H2 if it were perfect. We call that a new state point called 2S. 2S is a hypothetical state point, and it represents what the output would be if everything were perfect. So in the isentropic efficiency of our turbine, we have the proportion of actual work to ideal work, which is going to be H1 minus H2 divided by H1 minus H2S. When I talk about compressors, remember that I have the proportion of ideal work to actual work, which means that I'm writing this as H2S minus H1 divided by H2 minus H1. So the eta here represents the isentropic efficiency, H1 represents the enthalpy at the inlet to the device, H2 represents the actual outlet enthalpy, H2S represents what the enthalpy would be if everything were perfect, if there were no losses, if we had a reversible process.