Question & Answer: The connection between the number of microstates,W, and the entropy, S, of a system is…..

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, ΔS, for a system can be related to the change in the number of microstates as ΔS=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 0.501 times that of the initial number of microstates?