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 0.651 times that of the initial number of microstates?

1.38*10^-23ln (0.65/1)

=-5.7*10^-24

Explanation:

If all the microstates have equal probability of occurring, then Boltzmann's equation tells you that the entropy of the system is given by:

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) ]

ΔS = k*ln (W_final/W_initial)

We are told that in this case, W_final = 0.651*W_initial, so:

S = k*ln (0.651) = - 10.00*10^-23 J / (K*particle)

To get this in terms of molar entropy, multiply by Avogadro's number:

ΔS = - 10.00*10^-23 J / (K*particle) * (7.22*10^23 particles/mol) = - 5.7*10^-24