Can we make an analogy, in the narrow sense, between potential (gravitational) energy and a thermodynamic potential (eg: free energy or Gibbs potential)? Specifically, if an object of mass $m$ is at height $h$ and falls freely in a gravitational field, it tends towards the state of minimum potential energy. When the body is at height $h$, it has the maximum potential to produce (mechanical) work. By falling, it tends to the state of minimum potential (when there is no more potential to do mechanical work). In the same way, a thermodynamic potential tends to be minimized by spontaneous and irreversible processes, reaches equilibrium and the state of maximum entropy. What is different about the two scenarios and what are the cons in drawing this parallel?
1 Answers
"Minimization of a thermodynamic potential is just like a object of mass $m$ at height $h$ in a gravitational field; it tends toward a state of minimum potential energy."
But a buoyant mass would rise. And when I throw even a heavy object up to land on a shelf, say, it ends up in a state of maximum potential energy.
"I did specify 'falling' as part of the specifics; let's assume that the mass starts out motionless, with a density greater than air. The potential energy now ends up minimized, like a thermodynamic potential."
But if I release an initially motionless mass lying along the axis of a massive torus in space, the mass picks up speed, falls through the hole of the torus, and then begins to gain potential energy again.
"Look, I mean a uniform gravity field near the Earth's surface. The analogy is meant to refer to a familiar environment. The mass falls and loses potential energy. The potential energy goes down!"
Not if the mass lands on an ideal spring; ignoring friction of various types (air drag, mechanical hysteresis, etc.), the mass keeps bouncing as before, with no broad trend of potential energy minimization.
"The analogy assumes real materials! It reflects the kind of behavior we see every day, including the existence of friction and dissipative processes."
So the mass will bounce around for a while. Are you saying that thermodynamic potentials undergo damped oscillation?
"No! Look, consider the initial state and the state after a long time. The mass is now lower, things are warmer, and the potential energy has been minimized."
I think you could have just written $G^\star=U+PV-TS+mgh$, a modified Gibbs potential (differential form $dG^\star=-S\,dT+V\,dP+mg\,dh$) that incorporates a gravity field. You could then apply the Second Law—entropy maximization—to justify minimization of $G^\star$ and thus minimization of the height and the gravitational potential energy for slow movement at constant temperature, pressure, mass and gravity, for example.
"You've entirely missed the point of a simplifying analogy."
Etc., etc.
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