On Friday, June 12, 2015 9:24 PM, John Denker <jsd@av8n.com> wrote:
"If we look at the classical microscopic physics of an ideal
gas, 100% of the energy is kinetic energy.
OTOH if we put the gas in a cylinder, and take the macroscopic
position of the piston as the only coordinate of interest,
then the gas acts like a spring, giving rise to a potential
energy."
At this stage, the analogy with a spring is incomplete. An elastic spring has a relaxed state, and once in such state, it resists any displacement, be it compression or stretch. In the described system, gas behaves as a compressed spring, always pushing the piston outward, without relaxed state. The analogy will be stronger with gas filling the whole cylinder, and the piston inside. If gas on both sides of the piston has the same pressure and temperature, the piston will be in equilibrium, and the whole system will be analogous to a relaxed spring with zero potential energy (or, for that matter, to a mass between two identical relaxed springs, each having its opposite end fixed). In this case, any displacement from the initial position will increase the effective potential energy of the system at the cost of work necessary to do it. The gas in the expending volume will do positive work on the piston, the gas in the contracting volume will do negative work, but the latter will be larger in magnitude due to the increased pressure, so an external source of work is needed for finite displacement. Moreover, such effective spring will also obey the Hooke law at sufficiently small displacements, as does a real spring. Thus, kinetic energy alone can, indeed, model potential energy even in the absence of any interactions.