How does gas spin the turbine in a jet engine? I am confused about how the energy from the ignited gas spins a turbine in a jet engine, as pictured below
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I know it works in the same way as a water mill, but don't understand how that works either. So how does this work. In the back of the engine is where you will find the turbine labeled.
 A: Let's walk through the stages of a jet engine. The first part is the compressor. The compressor is generally made up of multiple stages and each stage is designed to compress the air a little bit more (increase the pressure). This is done because high pressure air is high density air (and hot air), and the combustion that will occur later is more efficient at high pressure and density. The compressor stages themselves are a big wheel of blades, and each blade looks like a little wing. As the wheel spins, the wing generates some lift and pushes the air deeper into the engine, compressing it as it goes. Compressing the air requires energy and the compressor is driven by a shaft connecting it to the turbine. 
The second part is the combustion chamber. The air entering here can be up to 40 atmospheres pressure. Fuel is injected and burns, releasing the chemical energy. This chemical energy release increases the temperature (a lot, but one must be careful that it isn't too much or your turbine will melt). 
The last stage is the turbine. There is hot, high pressure air in the combustion chamber and it moves rapidly into the turbine. Like the compressor, the turbine will generally have multiple stages. Again, if you look at each individual blade in a stage, it looks like a little wing. These wings generate lift as the air moves past them, which in turn spins the turbine. The air moves past because it is high pressure in the combustion chamber and low pressure outside the engine. This spinning of the turbine drives the shaft that spins the compressor. Once the cycle gets started, it is self-maintaining (at least, until you run out of fuel). Of course, the turbine cannot extract too much energy or there wouldn't be anything left for thrust. Unless of course you are using a turboshaft or turboprop, where you want the turbine to extract all the energy possible and what isn't used to spin the compressor is used to drive the shaft or propeller.
There's obviously a start-up problem. If the turbine spins the compressor and the combustion needs the compressor running and the turbine needs the combustion, something has to spin it to start. This can be done with giant blowers that force a large amount of air through the compressor so it begins to spin. Or it can be done with another power unit on board (APU) which is designed to get the compressor started so the combustion can take place and the turbine can drive the compressor.
That is jet propulsion in a nutshell. There is way, way more involved when you get into the nitty-gritty details, but that's an overview of what each step does and how it connects to the others. 
A: There are basically 4 major parts to a jet engine: 


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*the compressor, whose role is to compress the air (to make it ready for combustion that's gonna take place in the next step. The air is basically compressed so that there could be more air in the combustion chamber i.e. more fuel can be used in order to move the heavy aircraft onwards (not upwards, as the movement upwards is ONLY handled by the wings). The more stages in the compressor, the more compression. 

*the compressed air enters the combustion chamber and mixed with fuel and combusted (this bears a lot of science in combustion kinetics, fluid dynamics, fuel injection, mixing of the fuel and air ...). The combustion technically increases the enthalpy of the mixture, and in simple words enthalpy is a measure of how hot and powerful a fluid is.

*so now the very hot and still partially compressed air which has a lot of energy hits the turbine blades and turns them. During this process 2 main phenomena happen: 1. the thermal energy of the fluid mixture (exhaust gas of combustion chamber) converts into kinetic energy of the turbine which rotates the compressor; 2. The blades of the turbine shape nozzles increasing the velocity of fluid. 

*nozzle also increases the velocity of the fluid passing through it and the high velocity exhaust gas exits the nozzle i.e. the jet engine with a very high velocity. This velocity pushes the aircraft forward based on Newton's third law (each action has an equal and reverse reaction), just like when you blow a balloon and release the end of it, the balloon discharges the air and moves forward.
These are the main 4 parts of a jet turbojet or turbofan engine. The fan in a turbofan makes job of compressor a little easier by compressing the air a bit also contributes to the lower sound of the engine. And the ducts act as delaval nozzles which add to the speed of the exiting fluid thus increasing the efficiency of the overall engine.
