How does a turboprop engine use a gas turbine to turn a propeller?

A turboprop engine functions by utilizing a gas turbine engine as a prime mover to drive a propeller. Unlike a turbojet, which generates thrust primarily through the high-speed exhaust of combustion gases, the turboprop is designed to produce the majority of its thrust via the propeller.123

The process works as follows:
* Power Generation: The engine ingests and compresses air, which is then mixed with fuel and ignited in a combustion chamber. The resulting high-temperature, expanding gases pass through a multistage turbine.2
* Mechanical Transmission: This turbine extracts energy from the hot gas stream to rotate a shaft. In a turboprop, this shaft is connected to a reduction gearbox.2
* Propeller Drive: The gearbox reduces the high rotative speed of the turbine to a level suitable for the propeller. The propeller then turns to move large volumes of air, providing the primary propulsive force.12

While the propeller provides most of the thrust, additional thrust is often generated by the rearward discharge of the remaining hot exhaust gases.3