Which type of supercharger does NOT have a volumetric capacity proportional to engine speed?

The exhaust gas turbocharger is unique among the options listed because its operation relies on exhaust gases rather than being directly driven by the engine's crankshaft. This means that its volumetric capacity is not directly proportional to engine speed like mechanical superchargers. Instead, it generates boost based on the amount of exhaust flow created by the engine, which can vary depending on engine load, speed, and exhaust conditions.

In contrast, mechanical superchargers such as Roots blowers, Lysholm compressors, and centrifugal superchargers draw power directly from the engine, meaning their output is closely tied to engine speed. As the engine RPM increases, so does the capacity of these superchargers to compress air, resulting in a more direct correlation between the two. This is fundamentally what sets the exhaust gas turbocharger apart; while it may increase boost pressure at higher engine speeds due to increased exhaust flow, it does not have a linear relationship with engine speed like the other types of superchargers do.