Four particles are in the insulated box of Fig. 20-17. What...

Four particles are in the insulated box of Fig. $20-17$. What are (a) the least multiplicity, (b) the greatest multiplicity, (c) the least entropy, and (d) the greatest entropy of the four-particle system?

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Key Concepts

Multiplicity

Multiplicity in statistical mechanics is the number of ways a system’s particles can be arranged without changing its macroscopic state. It expresses the count of microstates associated with a given macrostate and is key to determining the probability of that state’s occurrence.

Entropy

Entropy is a measure of the disorder or randomness in a system, reflecting the number of microstates that correspond to a macroscopic state. It is quantitatively defined by Boltzmann's formula (S = k ln ?), where an increase in multiplicity corresponds to an increase in entropy.

Microstates and Macrostates

In statistical thermodynamics, a microstate is a specific detailed arrangement of the system's particles, while a macrostate is defined by macroscopic properties such as energy, volume, and particle number. The multiplicity of a macrostate is the total number of microstates that result in the same macroscopic configuration.

Isolated System

An isolated system is one that does not exchange energy or matter with its surroundings, meaning its total energy and particle number remain fixed. This condition is crucial when analyzing multiplicity and entropy because it confines the system to a set of microstates that obey conservation laws.

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