Help Needed With My Thermal Design Project - Designing a Turbo System for the Slant!

Not to be argumentative but it is the piston moving upward in the cylinder that forces the exhaust gas to exit the cylinder and begin its journey through the exhaust system. The heat still has nothing to do with it. Force is always strongest at its point of origin that is why turbos are connected to the exhaust manifold. Its like standing in front of a fan. The fan speed doesn't change but the farther away you move from it the less air you feel moving.
~Michael

Force is not always strongest at its point of origin, that is the whole concept behind a lever.

The piston moving is also because of the volumetric expansion and heat generated when the air/fuel mixture is ignited in the combustion chamber during the power stroke. Some of this force is retained in the flywheel and used to force the piston up the bore during the exhaust stroke. So, in the end it is thermal energy that does all of the work. It is absolutely thermal energy that provides the power to spin the turbine.

Without getting into the thermodynamic properties or calculus proofs, consider the ideal gas law. PV = mRT If you increase the temperature you are also increasing the pressure and volume of the exhaust gas. More heat = more volume and pressure = more power to the turbine. I know that we are not exactly dealing with an ideal gas but the same concept applies.