Gibbs paradox
E517576
The Gibbs paradox is a concept in thermodynamics and statistical mechanics highlighting an apparent contradiction in the entropy change when mixing identical versus distinct gases, which helped clarify the role of particle indistinguishability.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Gibbs paradox canonical | 1 |
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
concept in statistical mechanics
ⓘ
entropy paradox ⓘ thermodynamics paradox ⓘ |
| appearsIn | discussions of thermodynamic extensivity ⓘ |
| category |
paradoxes in physics
ⓘ
thermodynamic entropy ⓘ |
| concerns |
mixing of distinct gases
ⓘ
mixing of identical gases ⓘ |
| concernsProperty | extensivity of entropy ⓘ |
| describes | apparent contradiction in entropy change ⓘ |
| discussedIn |
foundations of thermodynamics literature
ⓘ
textbooks on statistical mechanics ⓘ |
| field |
statistical mechanics
ⓘ
thermodynamics ⓘ |
| hasConsequence |
corrects overcounting of microstates
ⓘ
ensures continuity of entropy as gases become identical ⓘ |
| highlights |
difference between classical and quantum descriptions of particles
ⓘ
need for indistinguishability postulate in statistical mechanics ⓘ role of labeling in counting microstates ⓘ |
| historicalImpact |
clarified foundations of statistical mechanics
ⓘ
motivated adoption of indistinguishability in quantum theory ⓘ |
| implies | entropy of mixing for identical gases should be zero ⓘ |
| involvesConcept |
classical statistics
ⓘ
entropy of mixing ⓘ ideal gas ⓘ particle indistinguishability ⓘ quantum statistics ⓘ |
| involvesProcess | mixing of gases ⓘ |
| involvesQuantity | entropy ⓘ |
| namedAfter | Josiah Willard Gibbs NERFINISHED ⓘ |
| occursWhen |
classical particles are treated as distinguishable
ⓘ
two gas samples have same macroscopic properties ⓘ |
| relatedTo |
Boltzmann entropy formula
NERFINISHED
ⓘ
S = k_B ln W ⓘ Sackur–Tetrode equation NERFINISHED ⓘ Shannon entropy NERFINISHED ⓘ ideal gas entropy ⓘ information-theoretic entropy ⓘ mixing entropy ⓘ |
| resolutionInvolves |
division by N! in counting microstates
ⓘ
indistinguishability of identical particles ⓘ quantum mechanical treatment of identical particles ⓘ use of correct combinatorial factors in statistical mechanics ⓘ |
| resolvedBy |
treating identical particles as indistinguishable
ⓘ
using quantum statistics for identical particles ⓘ |
| states | entropy of mixing appears nonzero for identical gases in classical treatment ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.