 What we're going to do now is we're going to take a look at the efficiencies of different components that you may have within any of the different cycles that you're analyzing within the course. We've looked at thermal efficiency already for reversible as well as irreversible heat engines. We also looked at it for heat pumps and refrigeration systems, although there it was coefficient of performance. So what we're now going to do is we're going to look at what are called component or adiabatic isentropic efficiencies for different things like nozzles, pumps, compressors, and turbines. So we've looked at thermal efficiency for complete cycles and the cycles that we've looked at consisted of heat engines, refrigerators, and heat pumps. Now for those latter two refrigerators and heat pumps it was the coefficient of performance that we were using to quantify them. But what we're going to do now is we're going to look at the efficiency of individual components and this is useful when you're doing thermodynamic modeling because what you are able to do is if you can determine the component efficiency for all of the different components that you may have in your cycle you can then go and study many different types of combinations of these components and evaluate the thermal efficiency for complete cycles but by changing different components. So it's useful when you're studying different types of cycles and their design. Now what we're going to do just like the title says adiabatic, recall that means no heat transfer. So that means q dot is equal to zero. So we're going to write out the first law and that's what we'll be using for each of the different components that we're looking at and we said that it was adiabatic consequently this here is gone. So what we're left with is work and enthalpy potential energy and kinetic energy. Now we said that this is for an adiabatic and isentropic efficiency. So if it's adiabatic isentropic that means that it needs to be reversible and what does that mean? That means that there's no friction, turbulence or really that should be viscous dissipation because you can have viscous dissipation for a laminar flow it does not necessarily need to be a turbulent flow and other losses such as rapid expansion so none or it's not quasi equilibrium. Another thing could be heat transfer across finite temperature differences. So the first thing we're going to begin with is the first component we're going to look at the turbine and our starting point here is going to be the first law for an adiabatic system and we're looking at a turbine that is sitting on the ground it's not moving anywhere so potential energy and kinetic energy go away and if you remember for a turbine our definition of work it's a work producing device and therefore in the first law work is positive and so with that what we're left with for the equation and so that is from the first law. Now the adiabatic efficiency for a turbine is written as eta with a subscript capital T to denote turbine and it is equal to the actual work divided by the isentropic work and we'll denote it with a little w a divided by a little w s so the little w would originate in this equation here which we would then have m dot times h1 minus h2 to apply the sign to it so what we're going to do we're going to work with a diagram that we talked about close to the beginning of the course it's called the moly a diagram and what you're looking at here is a plot of enthalpy versus entropy so looking at the moly a diagram for a turbine we have h on the vertical and s for entropy on the horizontal and we're going from a higher pressure to a lower pressure in some sort of expansion device in our turbine now what we're going to do is we're going to reference everything to an isentropic process which goes from state one down to state two s now that would be an ideal process it is reversible and adiabatic and for the enthalpy we will start from enthalpy value h1 and we will go down to an enthalpy value h2 s now in reality what happens whenever we go through a turbine or an expansion process we have irreversibilities and consequently entropy is increasing and the process when we have the entropy increase would actually look more like this so that would be a real world process we end up at state two actual and it will have an enthalpy value h2a so now looking at the definition that we had for the component efficiency for an adiabatic turbine and coupling that here with this our first law taking both of those together into this equation here and what we end up with is on the top the actual work is going to be minus h2a plus h1 the mass flow rate is canceling out here because it would be the same for both turbines for both the isentropic and the actual so this expression here becomes the component efficiency or adiabatic efficiency for a turbine next what we will do is we will look at a compressor again we're going to begin with the first law so our compressor is not moving anywhere kinetic energy on the inlet and the x that are negligible and work in a compressor is negative by our definition of work because we're doing work on the system and consequently the first law becomes this and we can then rearrange that by dividing by the mass flow rate and we get little w is equal to h2 minus h1 so the component efficiency for a compressor is a ratio of isentropic work to actual work and this will be expressed as ws over wa for actual so isentropic to actual again we're going to look at this on the molier diagram and what we're doing we're going from a lower pressure to a higher pressure we begin at state one we go vertically up to state 2s and in reality what will happen is we will increase an entropy through this compression process and we end up at 2a here we have h2s for the enthalpy and then h2 actual and h1 for down here and with that we can write out the adiabatic efficiency for the compressor as being the following and again what i've done here is i've used a combination of our first law and our expression for the adiabatic efficiency of a compressor and that is what results