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

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 x IO-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 Delta S = k ln Wfinal/Winitial where in the final number of microstates and 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. 680 times that of the initial number of microstates? Express your answer numerically in joules per kelvin per particle.

Explanation / Answer

S = k ln(Omega) on Boltzmann's tombstone!!! Sinitial = k lnw S final = k ln (w*0.680) delta S = k ( ln(w*0.408) - lnw ) by quality of logs..... delta S = k ln(0.680) = 1.38x10^-23 * ln(0.680) = 0.532x10^-23= 5.32x10^-24 J/(K*particle) To get this in terms of molar entropy, multiply by Avogadro's number: ?S = - 0.532x10^-23 J/(K*particle) * (7.022*10^23 particles/mol) = -3.73 J/(mol*K)

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