A negative change in entropy, $\Delta S<0$, indicates that which of the following is true for the system?

• A. The process must be spontaneous under all conditions.
• B. The system becomes more ordered and has fewer accessible microstates.
• C. The system becomes more disordered and has more accessible microstates.
• D. The temperature of the system must increase during the process.

Answer: (B)

Verified step by step guidance

1. Understand that entropy (S) is a measure of the disorder or randomness in a system, and it is related to the number of accessible microstates (W) by the Boltzmann equation: \(\Delta S = k_B \ln \frac{W_{final}}{W_{initial}}\), where \(k_B\) is the Boltzmann constant.
2. Recognize that a negative change in entropy, \(\Delta S < 0\), means that the entropy of the system decreases during the process.
3. Since entropy is related to disorder, a decrease in entropy implies that the system becomes more ordered.
4. Because entropy is connected to the number of accessible microstates, a decrease in entropy means the system has fewer accessible microstates after the change.
5. Note that a negative \(\Delta S\) does not necessarily mean the process is spontaneous under all conditions, nor does it directly imply a change in temperature; spontaneity depends on the Gibbs free energy, which includes enthalpy and temperature effects.