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[Phys-l] Temp & Energy density

I am curious about the conditions for which energy density = temp of a gas.
For this question I have a small cylinder if gas with only a few gas particles.
Using work, if I squeeze a piston down when the few gas particles are at the bottom of the cylinder, then I have not given them any extra energy through a work process. Their temperature should remain constant.
Using energy density, this sneaky work can't be ignored. Energy density would show a temp difference regardless of how the piston was compressed.
This leads me to think the energy density solution includes some assumptions that I do not know.
I appreciate any help available.

Sent from my iPod so I can blame Apple for my typos.

Paul Lulai
St. Anthony Village Senior High
US First RoboHuskie Team 2574