Defining reversibility without resorting to entropy

Question

Is it possible to define the concept of reversible process without using any mention to entropy?

The Wikipedia definition of reversible process seems to accomplish this by stating that:

In thermodynamics, a reversible process is a process, involving a system and its surroundings, whose direction can be reversed by infinitesimal changes in some properties of the surroundings, such as pressure or temperature.

But what exactly is meant here by "whose direction can be reversed by infinitesimal changes in some properties of the surroundings"?

Thanks in advance

Answer 1

Reversible process means that given the outside controllable mechanical, electrical, magnetic, chemical, etc., macroscopic parameters $\hat x_1,\hat x_1,\hat x_2,...,\hat x_n$ of the surroundings and its temperature $\hat T$ at which heat exchange can also take place any and all internal thermodynamic properties (parameters), say $z$, of the system at any time instant during the process can be written as a function of said external parameters: $z(t) = f(\hat T(t), \hat x_1(t),\hat x_2(t),...,\hat x_n(t))$. Notice the function depends only on the instantaneous values and not on the time rates of the external parameters. The $t$ in the function is just a process index by which the various consecutive stages of the thermodynamic process is marked, i.e., time.

If the function $f$ is differentiable then a linearized approximation over a short time interval $\delta t$ will give $\delta z= \frac {\partial f}{\partial T}\delta \hat T + \sum_k \frac {\partial f}{\partial \hat x_k}\delta \hat x_k$. If all $\delta \hat T$ and $\delta \hat x_k$ are small enough steps, then flipping their signs will get you back where you started from. This is the change of direction in the process you are asking about.

Answer 2

But what exactly is meant here by "whose direction can be reversed by infinitesimal changes in some properties of the surroundings"?

It means that the process is conducted under infinitesimal gradients of temperature, pressure and chemical potential. Equivalently, $T$, $P$ and $\mu$ remain uniform throughout the process. For example, to exchange heat reversibly is to bring the system, presumed at $T$, into contact with another system at $T+dT$. By reversing the sign of $dT$ the state retraces its path. This is possible only of $dT$ is a true differential, not a finite $\Delta T$.