Entropy Criteria for Spontaneity and Absolute Entropy

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What is the entropy change of the universe?

It is the sum of the entropy changes of the system and surroundings: $\Delta S_{\text{univ}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}}$.

State the second law of thermodynamics in terms of entropy.

Every spontaneous change increases the entropy of the universe, so a spontaneous direction has $\Delta S_{\text{univ}} > 0$.

What does a negative $\Delta S_{\text{univ}}$ mean?

The process is nonspontaneous in the direction considered; the opposite direction is spontaneous.

Why does heat flow spontaneously from hot to cold?

The entropy gained by the cooler surroundings exceeds the entropy lost by the hotter system, making $\Delta S_{\text{univ}}$ positive.

What is the entropy criterion for equilibrium?

At equilibrium, $\Delta S_{\text{univ}} = 0$; for objects at the same temperature, their entropy changes from heat exchange balance.

Quiz questions

1. What entropy value does the third law assign to a pure, perfect crystal at $0\ \text{K}$?Answer: Zero, because the crystal has one possible microstate.
2. How is standard reaction entropy calculated from tabulated molar entropies?Answer: $\sum \nu S^\circ(\text{products}) - \sum \nu S^\circ(\text{reactants})$
3. Melting has $\Delta S_{\text{sys}} = +22.1\ \text{J/K}$ and $q_{\text{surr}} = -6000\ \text{J}$. At $263.15\ \text{K}$, what is the approximate result for melting?Answer: $\Delta S_{\text{univ}} \approx -0.7\ \text{J/K}$; melting is nonspontaneous.
4. For condensation, use $S^\circ(\mathrm{H_2O(g)}) = 188.8\ \text{J mol}^{-1}\text{K}^{-1}$ and $S^\circ(\mathrm{H_2O(l)}) = 70.0\ \text{J mol}^{-1}\text{K}^{-1}$. What is $\Delta S^\circ$?Answer: $-118.8\ \text{J mol}^{-1}\text{K}^{-1}$