 The next thing we're going to take a look at is the Carnot heat engine. This is a heat engine that operates on four reversible processes and consequently it is an idealization. However it's a very famous one that we quite often refer to within thermodynamics. So let's take a look at the Carnot heat engine. Now the Carnot heat engine consists of four reversible processes and what we'll do we'll take a look at it on a PV diagram. So we will begin with an isothermal process. Actually there are two isothermal processes involved in a Carnot heat engine. One of those isothermal processes is taking place at T hot and the other is taking place at T low. So if you recall when we talked about sources and sinks that would be the source temperature and the sink temperature. To begin with what we go through is an expansion process from state 1 to state 2 and that expansion process takes place at constant temperature. Now remember we said that when you expand a gas rapidly it gets cold. Well here in order to prevent the gas from cooling we have to have heat addition. So with the Carnot cycle we have heat addition during this expansion process. So 1 to 2 is reversible isothermal, so constant temperature, expansion. The next step in the Carnot heat engine is a reversible adiabatic expansion and that on our cycle or on our diagram would look like this and that takes us to state 3. So we can say process 2 to 3 that is reversible adiabatic expansion. So remember adiabatic means that there is no heat transfer and if there is no heat transfer while you're expanding a gas the gas is going to get cooler and that's why we drop down to the lower temperature. The next step that we have is we have an isothermal compression process taking us from state 3 up to state 4. Now if you recall when we talked about compressing a gas the gas usually gets hotter and if we want to have this as being isothermal so we're saying reversible isothermal compression and whenever we compress a gas it's going to get hotter so in order for it to be isothermal we need to reject heat to the environment and that would then become Q subscript L and the final component to make it a cycle for the Carnot heat engine is one of reversible adiabatic compression taking us from state 4 up to state 1. So with the compression process we have heat that is being or the gas is getting hotter it's adiabatic and so the result of that is the temperature of the gas or of our working fluid is increasing and that's why we go from isotherm TL up to isotherm TH through that process so that is the four components of the Carnot heat engine cycle and it is an idealization because in reality these processes would take a long time you would have to have infinite areas for the heat transfer like we said we have to have heat transfer over pretty much an infinitesimal temperature differential so it is an idealization. However what we can do we can write out an expression for the efficiency the thermal efficiency of this cycle so let's take a look at that now. So for a reversible heat engine it can be shown that the ratio of the heat transfer and the Qh divided by Q low is equal to the ratio of the temperatures and both of the temperatures need to be in Kelvin and from that what we can do we can write out that the thermal efficiency for a reversible process a reversible heat engine that is the Carnot engine so that becomes an expression for the thermal efficiency of the Carnot heat engine. Now there are a couple of comments that we should make about the Carnot process and in particular the Carnot heat engine and these are referred to as being Carnot principles. So the first comment that we can make is that the thermal efficiency of an irreversible heat engine is always going to be less than the thermal efficiency of a reversible engine the Carnot heat engine being a reversible heat engine so we can write that as the thermal efficiency of an irreversible engine is always going to be less than the thermal efficiency of a reversible engine so that's the best that we can possibly do would be the reversible in reality we will never achieve it. A second Carnot principle is the second Carnot principle is that the thermal efficiency of all reversible heat engines operating between the two same reservoirs so two reservoirs at the same temperature you'd have one at T high and one at T low all of those any type of heat engine so here we have heat engine we have heat flowing that way that way and then work out any reversible heat engine operating between those two temperature sources so a source and a sink will have the same thermal efficiency.