Why does air get bigger when it gets hotter?
This happens anywhere and not just in a jet engine but it concerns us because we need to add energy to the engine to get thrust (energy), or power (energy) out.
(Note that piston engines develop power but jet engines develop thrust. We shall look at that later.)
When energy is added to air, or anything else, the energy (normally 'heat') spreads through the air causing all the molecules in the air to get excited. Watch a football crowd, when they get excited they start to jump around and wave their arms. They are, individually, taking up more space. Molecules do that. Their mass (weight) remains the same but they take up more room - they expand. They become less dense (less 'crowded together'). If they are not allowed to expand they will press against one another, they will have increased pressure.
In the jet engine we allow them, the molecules of air, to have more space by keeping the pressure (nearly) constant. They will spread out and become bigger; to escape they will need to accelerate.
The engine is a tube.
Air goes into the front and comes out the back.
Let's forget 'velocity' for a moment and think in terms of the weight of air.
Suppose that, over a one second period of time, one pound of air goes into the front of the engine.
We now have a "Mass Flow" (Wf) of 1 lb/sec. We should reasonably expect that we should get 1 lb/sec of air out of the back of the jet engine. If we only get half a pound/sec where has the other half a pound gone? If we get 2 lb/sec then we have miraculously created 1 lb of air, every second, within the engine. Wow! That would be something wonderful!!
No. what goes in the front comes out the back. But the air coming out of the back is a different size. It is bigger - much bigger. To maintain a mass flow of 1 lb/sec it has to come out MUCH faster.
Momentum = Mass x Velocity
Same mass going in as coming out but the velocity has changed because we have added energy to it.
More velocity? More momentum.
More momentum? More reaction - more thrust.
See how simple Jet Engines are?