Is it experimentally possible that the heat absorbed by the cylinder could be greater than that work performed on it?

Yes, it is experimentally possible for the heat absorbed by the cylinder to be greater than the work performed on it, particularly in systems where heat transfer is significant. For example, in a heat engine or a thermodynamic cycle, the heat absorbed from a heat source can exceed the mechanical work done on the system, especially if the system undergoes processes such as expansion or phase changes that allow it to absorb additional heat. This scenario often occurs in processes that are not perfectly efficient, where internal energy changes and external energy inputs lead to greater heat absorption.