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

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*10^-23 J/(K*particle). From this equation the entropy change, change in S, for a system can be related to the change in the number of microstates as change in S=klnWfinal/Winitial 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 0.440 times that of the initial number of microstates?

Explanation / Answer

S = kln(w)

delta S = kln(Wfinal)/(Winitial)...(i)

Wfinal = 0.440 * Winitial

Plugging this in equation (i), we get;

delta S = 1.38 * 10^(-23) * ln(0.440)

delta S = -1.132 * 10^(-23) J

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