(a) What is the difference between a state and a microstate of a system? (b) As a system goes from state A to state \(B,\) its entropy decreases. What can you say about the number of microstates corresponding to each state? (c) In a particular spontaneous process, the number of microstates available to the system decreases. What can you conclude about the sign of \(\Delta S_{\text { surr }}\) ?

(a) A state is a set of macroscopic properties defining a system's condition (e.g., temperature, pressure, volume), while a microstate is a specific microscopic configuration of particles associated with a particular state, having the same macroscopic properties but varying positions and velocities of particles. (b) If entropy decreases when going from state A to state B, the number of microstates for state B is less than for state A, as entropy is related to microstates through \(S = k_{B} \ln{W}\). (c) If microstates decrease in a spontaneous process, \(\Delta S_{\text{sys}}\) is negative, and for the process to be spontaneous, \(\Delta S_{\text{surr}}\) must be positive, indicating an increase in the entropy of the surroundings.