There are several properties of gasses that are critical to the operation of Stirling engines:

• If you have a fixed amount of gas in a fixed volume of space and you raise the temperature of that gas, the pressure will increase.
• If you have a fixed amount of gas and you compress it (decrease the volume of its space), the temperature of that gas will increase.

There are four parts to the Stirling cycle. The two pistons in the animation above accomplish all of the parts of the cycle:

1. Heat is added to the gas inside the heated cylinder (left), causing pressure to build. This forces the piston to move down. This is the part of the Stirling cycle that does the work.
2. The left piston moves up while the right piston moves down. This pushes the hot gas into the cooled cylinder, which quickly cools the gas to the temperature of the cooling source, lowering its pressure. This makes it easier to compress the gas in the next part of the cycle.
3. The piston in the cooled cylinder (right) starts to compress the gas. Heat generated by this compression is removed by the cooling source.
4. The right piston moves up while the left piston moves down. This forces the gas into the heated cylinder, where it quickly heats up, building pressure, at which point the cycle repeats.

The diagram on the right is a PV-diagram of a typical small model Stirling engine.

This link from MIT (or a local copy) provides the explanation of the operation of the model shown in class.

A Wikipedia article on Stirling Engines

A Stirling engine running on the heat of a hand

A Stirling engine you can build at home

Swedish company retrofits submarines to use Stirling-engine-based Air-Independent Propulsion

Stirling engines for deep-space missions, a success story, spun off as Infinia Corporation (see "How Stirling engine works" describing the unusual NASA-originated design)