Table 15.3 shows that the macrostate of 3 heads and 2 tails corresponds to 10 different microstates, while the macrostate of 5 heads and 0 tails corresponds to only 1 microstate. What does the source conclude from this about their relative probabilities?
AThe two macrostates are equally likely overall
B5 heads is 10 times more probable than 3 heads and 2 tails
C3 heads and 2 tails is slightly more probable than 5 heads
D3 heads and 2 tails is 10 times more probable than 5 heads
Answer & Solution
Correct answer: D. 3 heads and 2 tails is 10 times more probable than 5 heads
1. Every individual microstate is assumed equally likely, so the probability of a macrostate scales directly with how many microstates produce it.
2. The 3-heads-2-tails macrostate has 10 microstates, while the 5-heads macrostate has only 1.
3. Comparing these counts, 10 microstates versus 1, makes the 3-heads-2-tails macrostate 10 times more probable, exactly as given.
4. Option B reverses which macrostate is more probable, and option A wrongly claims they are equal despite the very different microstate counts.
5. Option C's "only slightly more probable" understates a genuine tenfold difference in likelihood.
_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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