Is ΔS equal to zero admissible?

Problem

A thermodynamic process produces $\Delta S=0$ for the system plus the surroundings. Discuss whether this is possible and what conditions it requires.

Solution

Yes, it is possible: it is the limiting case of the second law, which states $\Delta S_\text{tot}\ge 0$, with equality $\Delta S_\text{tot}=0$ reached only by REVERSIBLE processes. A reversible process requires: that it be quasi-static (passing through successive equilibrium states), that it be free of friction and dissipation, and that heat exchanges occur between bodies at infinitesimally close temperatures. This is an idealisation never exactly achieved in practice: every real process has friction, finite temperature gradients and irreversibility, so it always produces $\Delta S_\text{tot}>0$. $\ev{\Delta S_\text{tot}=0\Leftrightarrow\text{reversible process}}$

Links

Topics: Entropy and the second law Concepts: Entropy · Second law of thermodynamics · Thermodynamic processes Skills: Limiting-case and thought-experiment analysis