Can adiabatic compression increase pressure if no heat is exchanged?

[Farina]

I'm not asking about the specific questions contained in the attached document - I know all the answers. I'm wondering if this is even possible.

A to B: free expansion (which I take always means "adiabatic free expansion").

B to C: adiabatic compression.

Adiabatic means no heat is exchanged. So if system is returned to its original volume adiabatically, and no heat is exchanged, what -- physically -- could account for an increased pressure at C??

 

[phyzguy]

During the free expansion, no work is done by the gas and no heat is exchanged, so the internal energy of the gas is unchanged. During the adiabatic compression, however, while it is true that no heat is exchanged, work is done on the gas by the piston doing the compression. So the internal energy of the gas is increased.