At the left of the engine is the turbine section. In this figure there are two sets of turbines. The first set directly drives the compressor. The turbines, the shaft and the compressor all turn as a single unit:
At the far left is a final turbine stage, shown here with a single set of vanes. It drives the output shaft. This final turbine stage and the output shaft are a completely stand-alone, freewheeling unit. They spin freely without any connection to the rest of the engine. And that is the amazing part about a gas turbine engine -- there is enough energy in the hot gases blowing through the blades of that final output turbine to generate 1,500 horsepower and drive a 63-ton M-1 Tank! A gas turbine engine really is that simple.
In the case of the turbine used in a tank or a power plant, there really is nothing to do with the exhaust gases but vent them through an exhaust pipe, as shown. Sometimes the exhaust will run through some sort of heat exchanger either to extract the heat for some other purpose or to preheat air before it enters the combustion chamber.
The discussion here is obviously simplified a bit. For example, we have not discussed the areas of bearings, oiling systems, internal support structures of the engine, stator vanes and so on. All of these areas become major engineering problems because of the tremendous temperatures, pressures and spin rates inside the engine. But the basic principles described here govern all gas turbine engines and help you to understand the basic layout and operation of the engine.