| The author seems to mix up Gibbs free energy with entropy. The remark that thermal equilibrium equals maximum entropy is simply wrong. All examples can be explained with minimization of the free energy: dG = dH - TdS dH == internal energy (chemical bonds) + pV
dS == Entropy term
T == Temperature Where entropy is the number of different states the system can be in for a given internal energy.
A thermodynamic system in equilibrium will always tend to a state of lowest free energy. Example: a perfect crystal would be a totally ordered state (and with the lowest entropy), with the internal energy minimized due to the highest number of chemical bonds. For T -> 0, this would be the thermodynamically most stable configuration (however not always kinetically accessible, e.g. supercooled water). As Temperature goes up, the Gibbs free energy of a more disordered phase (e.g. crystal defects or a liquid/gas phase) becomes lower and will eventually lead to the melting of the crystal. For the oil/water example, the separated state minimizes the free energy since polar water molecules can form hydrogen bonds with themselves (lowering the internal energy), and push out the oil molecules, even though the entropy is lower than for a totally mixed state. At higher temperatures, this will change theoretically and the mixed-phase becomes favorable thermodynamically. From this point of view, seeing higher entropy as more disorder seems absolutely fine, where more disorder is "lower chance of guessing the exact configuration of all molecules in the system". |
If you put now the oil/water system into a isolated container the equilibrium state won't change substantially. It remains separated in two phases and that's now the maximum entropy state.