Can you get this USNCO question?

ThermodynamicsNational 2019

A system confined in a rigid, well-insulated container undergoes a spontaneous change. What statement about the system must be true?

23% of national qualifiers got this right

Explanation

draft

A rigid, well-insulated container means the system is isolated: no heat, work, or matter crosses its boundary ( $q = 0$ , $w = 0$ , $\Delta U = 0$ ).

The second law of thermodynamics states that for any spontaneous process in an isolated system, the total entropy of the system must increase: $\Delta S_{sys} > 0$ .
Gibbs free energy, $G = H - TS$ , is only a useful spontaneity criterion at constant temperature and pressure, not for an isolated (constant $U$ , constant $V$ ) system. Since $T$ and $P$ are not controlled here, $\Delta G$ has no defined meaning as a spontaneity criterion for this system.
Therefore the only statement that must be true is that entropy increases.

Answer: (C)

Incorrectly assumes $\Delta G$ governs spontaneity even in an isolated system; $\Delta G$ only applies at constant $T$ and $P$ , which are not fixed in a rigid, insulated container.

Confuses the isolated-system criterion with the constant $T,P$ criterion; a student recalls 'spontaneous means $\Delta G$ decreases' without checking that this only holds at constant temperature and pressure.

Correctly applies the second law: for an isolated system, spontaneous change requires $\Delta S_{sys} > 0$ .

Misremembers the direction of the entropy criterion, thinking spontaneous processes decrease entropy, perhaps confusing system entropy with surroundings entropy in a non-isolated case.

Concept · Second law of thermodynamics and entropy criterion for isolated systems