Selena states that $S _ { f } - S _ { i } = n R \ln \left( \frac { V _ { f } } { V _ { i } } \right)$ proves that entropy has a definite value at the beginning and end of an adiabatic free expansion.Ron says $S _ { f } - S _ { i } = k _ { B } \ln \left( \frac { W _ { f } } { W _ { i } } \right)$ ,where W is the number of microstates of a given macrostate.Which one,if either,is correct?
A)Only Selena,because entropy can depend only on macroscopic variables.
B)Only Ron,because entropy can depend only on microscopic variables.
C)Only Selena,because $\left( \frac { V _ { f } } { V _ { i } } \right) = \left( \frac { T _ { f } } { T _ { i } } \right)$ in an adiabatic free expansion.
D)Neither,because we cannot calculate changes in entropy in an adiabatic free expansion.
E)Both,because entropy,which is macroscopic is a function of microscopic disorder.

Question

Quizplus · Accepted Answer

Both Selena and Ron are correct. Selena's equation relates to the macroscopic view of entropy change in terms of volume change, while Ron's equation relates to the microscopic view of entropy change in terms of the number of microstates. Entropy is a macroscopic property that arises from microscopic disorder.

Selena States That Sf−Si=nRln⁡(VfVi)S _ { f } - S _ { i } = n R \ln \left( \frac { V _ { f } } { V _ { i } } \right)Sf​−Si​=nRln(Vi​Vf​​)

Selena States That $S _ { f } - S _ { i } = n R \ln \left( \frac { V _ { f } } { V _ { i } } \right)$