Is this a counterexample for the idea that reversible and quasi-static processes must infinitely slow?

Question

Many people say that a reversible process must be quasi-static and infinitely slow. I (think I) understand the examples involving gases inside pistons to demonstrate the point, but I don't understand why people say this has to be true for all possible processes.

Consider a simple situation: a lossless spring launches a tennis ball vertically upward, the ball reaches the peak, and falls back on the spring. Are the classifications below by me correct?

• It is quasi-static because all relevant variables are always well-defined (spring extension, spring extension velocity, ball position, ball velocity all take definite values).
• It is reversible, because the motion of the spring and the ball adhere to Newtonian mechanics when run forward and backward.
• The process does not take an infinite time to carry out.

If the above is true, then doesn't this serve as a counterexample to the idea that reversible processes must be infinitely slow? What am I misunderstanding?

Answer 1

The quasistatic/indefinitely slow condition is relevant for thermal contact exchange only and is used to define equilibrium thermodynamics.

In order exchange heat by a heat flow between to systems in thermal contact, there must be a temperature difference.

But if the two temperatures of two reservoirs in contact are different by a small amount $dT$, by the basics, an exchange of $dQ$ of heat energy increases the entropy by $$-\frac{dQ}{T+dT}+\frac{dQ}{T}=\frac{dQ}{T} \frac{dT}{T}.$$

So all equations concerning entropy bilances are valid only in the limit $dT\to 0$. Time simply must not play a role in the ideal Carnot processes.