A gaseous system undergoes a change in temperature and volum

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 0.819 times that of the initial number of microstates?

Solution

If all the microstates have equal probability of occurring, then Boltzmann\'s equation tells you that the entropy of the system is given by: k = 1.38 x 10-23 J/K S = k*ln(W) where W is the number of microstates available to the system. In this case, we have a change in the number of microstates, and the question is asking for teh change in entropy: S_final - S_initial = k*[ln(W_final) - ln(W_initial)] ?S = k*ln(W_final/W_initial) We are told that in this case, W_final = 0.819*W_initial, so: ?S = k*ln(0.819) = -.2755*10^-23 J/(K*particle) To get this in terms of molar entropy, multiply by Avogadro\'s number: ?S = -.2755*10^-23 J/(K*particle) * (7.022*10^23 particles/mol) = -1.93J/(mol*K)