The connection between the number of microstates, W , and the entropy, S , of a

Question

The connection between the number of microstates,W, and the entropy, S, of a system is expressed by the Boltzmann equation

S=klnW

where k is the Boltzmann constant per molecule (particle), 1.38×1023 J/(Kparticle). From this equation the entropy change, S, for a system can be related to the change in the number of microstates as

S=klnWfinalWinitial

where Wfinal in the final number of microstates and Winitial is the initial number of microstates.

A gaseous system undergoes a change in temperature and volume. What is the entropy change for a particle in this system if the final number of microstates is 0.418 times that of the initial number of microstates?

Explanation / Answer

According to the given equation

S=k ln WfinalWinitial

let W initial =X

Wfinal = 0.418 X W initial =X

on putting values in the equation

S = 1.38×1023 ln (0.418 X/X)

=  1.38×1023 ln (0.418)

=1.38×1023 x - 0.8722

S = -1.20 x1023

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