How the hell are you on your way to a PhD? You're describing a motor, not the law of physics that combusting something causes it to expand, causing pressure against its container. If somebody patented "The combustion of fuel causing the resulting pressure to push against an object, therefore causing motion", it might be analogous to a patent on an algorithm.

That would be why they couldn't patent physical principle of fuel-air mixture burning. Instead, they had to patent an engine that used it.

No. Algorithms are the maths. An implementation of the algorithm is the application. However, we already have a system for protecting implementations of algorithms, we call it copyright.