Question

The entropy of the most probable macropartition for a system of Einstein solids is 6025.3 k​B​, while the entropy of an extreme macropartition is only 5755 k​B​. What is the probability of finding the system at a given time in the extreme macropartition compared to that of finding it in the most probable macropartition?

a) The probability of the extreme macropartition is higher.
b) The probability of the most probable macropartition is higher.
c) Both probabilities are equal.
d) The relationship cannot be determined from the information provided.

Answer 1

The most probable macropartition with higher entropy (6025.3 kB) is more likely than the extreme macropartition with lower entropy (5755 kB), following the principle that greater entropy implies higher probability.

Step-by-step explanation:

When comparing the probability of finding a system in an extreme macropartition versus the most probable macropartition, we must consider the relationship between the number of microstates and entropy. Since entropy increases logarithmically with the number of microstates, the macropartition with the higher entropy will be more probable. In this case, the most probable macropartition has an entropy of 6025.3 kB, which is greater than that of the extreme macropartition at 5755 kB. Therefore, the most probable macropartition is more likely to occur than the extreme one.