The thermodynamic cycle for a jet engine consists of four processes:
(a) adiabatic compression in the inlet and compressor (1-2), (b) constant pressure heat addition in the combustor (2-3), (c) adiabatic expansion in the turbine and exhaust nozzle, and finally (3-4), (d) constant pressure cooling to get the working fluid back to the initial condition (4-1).
As discussed, in a turbojet engine, the air enters the engine through a diffuser, which lowers its speed and increases its pressure. The air then goes into the combustion chamber, and each unit mass of air absorbs energy Q, increasing its internal energy. Finally, the gases expand in the nozzle to the ambient pressure and leave the aircrafts at high velocity.
According to first law of thermodynamics, the change in internal energy of a system is equal to the heat added to the system minus the work done by the system, ΔU = Q - W = ΔH + ΔE
The above expression gives the conservation of energy for open stationary systems with a constant mass flow rate. W is the work per unit mass performed by the air inside the open system. (W = 0 for the diffuser, the combustion chamber and the nozzle in which there are no movable parts). In the ideal case, the turbine work is assumed to be equal to the compressor work. Hence Q = ΔH + ΔE
ΔH is the difference between the exit and inlet specific enthalpies and ΔE is the difference between the exit and inlet kinetic energies per unit mass.
If the exit temperature is the same as the initial external temperature, all the thermal energy that is given to the system in the combustion chamber will be used to increase the kinetic energy of the air, leading to maximum thrust. Q = ΔE
However, the second law of thermodynamics implies that the complete conversion of thermal energy into work (or into kinetic energy of the air) is impossible and that the most favorable situation (maximum production of work) is realized if all the processes are reversible. The processes in the diffuser, the compressor, the turbine and the nozzle are assumed to be reversible and adiabatic. In an ideal jet-propulsion cycle, the power generated in the turbine equals the power consumed in the compressor.