# Are Quasi-static Processes in Thermodynamics Theoretically Unattainable under the Framework of Gas Dynamics?

According to Wikipedia:

"In thermodynamics, a quasi-static process is a thermodynamic process that happens slowly enough for the system to remain in internal equilibrium."

But if we look at things more closely, I do not think that the statement above is physically attainable. To illustrate that point, suppose that we have the classic thermodynamic system of a container with some sort of gas inside. The system is thermally isolated and at equilibrium $$(P,V,T)$$. We further assume that there is no gravity and no friction between the piston shown and the walls. A schematic of the system can be seen in the following figure.

The red rectangular shape represents the piston. At this stage, the pressure at the outer side of the piston equals $$P$$ to keep the piston at equilibrium. We now change the state of the system to $$(P',V',T')$$ by going to a volume $$V'$$ with $$V' < V$$ via a quasi-static process. We do that by exerting a force $$\vec{F}$$ with $$|\vec{F}| \rightarrow 0 \$$as shown:

And consequently, in the beginning, the piston accelerates a little$$^{1}$$ to gain some velocity which is then held constant and small in magnitude. During this phenomenon, the pressure changes near the piston, and the new pressure gets propagated through the entire gas$$^{2}$$. This happens until the process stops.

• $$^{1}$$My first point is that, because of that initial acceleration that needs to happen to get the piston going, there is a point in time where the function of pressure $$P(\vec{r},t)$$ is not homogeneous.

• $$^{2}$$ Even when the velocity of the piston is constant, the new pressure are propagated throughout the gas and thus there are times (after the first step of accelerating the piston) where $$P(\vec{r},t)$$ is again not homogeneous.

In conclusion, however slow a process might be, I think that it is not capable of preserving the system at internal equilibrium at all times. The time intervals of pressure propagation might be really small, but they are not zero. Is then the concept of a quasistatic process an complete and total idealization? It seems to me that such a process, unlike other 'idealized' cases like the free particle in Classical Mechanics and QM, is not even theoretically achievable (at least under the framework of fluid/gas dynamics). If I am wrong on this, where exactly is my reasoning incorrect?

• You're correct that it's an idealization the is exact only in the limit. The same goes for perfect geometric objects like squares and circles. However, many processes in real life come pretty close to being reversible. Mar 14, 2019 at 2:00

The important point to note is that if you change the pressure $$\delta P$$ , the entropy created is second-order in $$\delta P$$.