The connection between the number of microstates,W, and the entropy, S, of a sys
ID: 841236 • Letter: T
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, 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 0.440 times that of the initial number of microstates?
Explanation / Answer
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The connection between the number of microstates,W, and the entropy, S, of a system is expressed by the Boltzmann equation
S=k*ln*W
where k is the Boltzmann constant per molecule (particle)1.38*10^-23, . From this equation the entropy change,delta S , for a system can be related to the change in the number of microstates as
delta S=k*ln(W final/W initial)
where w final in the final number of microstates and w initial 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 0.458 times that of the initial number of microstates?
answer
We know that delta S = k * ln( W final / W initial )
where
k = Boltzmann constant per molecule = 1.38*10^-23
Given W final = 0.458* W initial
Plug the values we get delta S = 1.38*10^-23 * ln ( 0.458 )
= - 1.0776*10^-23 joules per kelvin per particle
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