A question about performance of a turbojet. Why are compression ratio and thrust are not in linear but increase exponentially with RPM?
Because the compression in a turbojet is an aerodynamic effect caused by the rotating compressor blades.
Lift and drag forces on an object moving through a fluid are proportional to the square of its relative velocity:
$$F \propto v^2$$
and that velocity is linear with the rpm of the shaft because:
$$v = \omega \cdot r$$
hence, since work done is also linear with the applied force:
$$W \propto F \propto \omega^2$$
Thrust is not linear with the compression ratio, however, and also depends on an array of other factors. Thrust is the net effect of the Brayton cycle in the engine, and that cycle develops along an adiabatic line during the compression step.