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 0.652 times that of the initial number of microstates?

Explanation / Answer

given

change in entropy = k ln (Wfinal / Winitial )

given

boltzmann constant (k) = 1.38 x 10-23

also

given

the final number of microstates is 0.558 times that of the intial number of microstates

so

Wfinal = 0.558 x Winitial

so

Wfinal / Winitial = 0.652

now

change in entropy = k ln (Wfinal / Winitial )

using the obtained values

we get

change in entropy = 1.38 x 10-23 x ln 0.652

change in entropy = -5.902 x 10-24

so

the change in entropy is -5.902 x 10-24 J/K.particle

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