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

S=klnW

where k is the Boltzmann constant permolecule (particle), 1.38×10?23 J/(K?particle). From thisequation the entropy change, ?S, for a system can berelated to the change in the number of microstates as

?S=klnWfinalWinitial

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

A gaseous system undergoes a change in temperature and volume.What is the entropy change for a particle in this system if thefinal number of microstates is 0.424 times that of the initialnumber of microstates?