Quantitative relationship between entropy and number of microstates The connecti

Question

Quantitative relationship between entropy and number of microstates 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 x 10^-23 J/(K .particle). From this equation the entropy change, delta S, for a system can be related to the change in the number of microstates as AS= kin W1 Initial: where Wfinal in the final number of microstates and is the initial number of microstates. Part B 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 0,558 times that of the initial number of microstates? Express your answer numerically in joules per kelvin per particle.

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 = 0.558

now

change in entropy = k ln (Wfinal / Winitial )

using the obtained values

we get

change in entropy = 1.38 x 10-23 x ln 0.558

change in entropy = -8.051 x 10-24

so

the change in entropy is -8.051 x 10-24 J/K.particle

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