Entropy: Thermodynamic Definition, Microstates, and Qualitative Trends

All flashcards

Entropy ($S$)

A thermodynamic state function whose change depends on the endpoints; it is also related to the number of possible microscopic arrangements.

Reversible process

An idealized process that proceeds through equilibrium states and can be reversed by an infinitesimally small change in conditions.

Boltzmann relation

$S = k\ln W$ relates entropy to the number of possible microstates, where $k$ is the Boltzmann constant.

Distribution

A grouping of microstates that share a general pattern without distinguishing every individual particle.

Entropy across phases

For a given substance, entropy generally follows $S_{\mathrm{gas}} > S_{\mathrm{liquid}} > S_{\mathrm{solid}}$.

Quiz questions

1. Which statement describes the Boltzmann relation between entropy and microstates?Answer: Entropy increases with the logarithm of the number of possible microstates.
2. Four distinguishable particles can each occupy either of two boxes. What is the probability of the two-in-each-box distribution?Answer: $6/16$, or $3/8$.
3. A gas expands into an evacuated container and gains access to more possible locations. What is the sign of its entropy change?Answer: Positive, because the number of accessible microstates increases.
4. What is the usual effect of raising the temperature of a substance on its entropy?Answer: Entropy generally increases as more energy arrangements become accessible.
5. As a qualitative guide to a chemical reaction, what does a net increase in gaseous particles often suggest about $\Delta S$?Answer: It often suggests a positive change, though other changes can also matter.