Ludwig Boltzmann connected entropy to the probability of a macrostate occurring, using the number of microstates W that correspond to it. According to the source, how does the entropy of a more probable state compare with that of a less probable one?
AA more probable state has greater entropy
BA more probable state has smaller entropy
CProbability and entropy are entirely unrelated
DOnly the least probable state has any entropy at all
Answer & Solution
Correct answer: A. A more probable state has greater entropy
1. Boltzmann's statistical picture ties a macrostate's entropy to how many microstates, W, can produce it, and more probable macrostates correspond to larger W.
2. The source draws the direct conclusion from this connection: the more likely the state, the greater its entropy.
3. This rules out option B, which reverses the relationship, and option C, which denies any relationship exists at all.
4. Every macrostate, even a highly ordered and improbable one like 100 heads, still corresponds to at least one microstate and therefore still has a defined, nonzero entropy, ruling out option D.
_Source: OpenStax College Physics (CC BY 4.0), Ch 15 "Thermodynamics", section 15.7 Statistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying Explanation_
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