(b) In a particular spontaneous process the entropy of the system decreases. What can you conclude about the sign and magnitude of ΔS_surr?

Verified step by step guidance

1. Identify the given information: The entropy of the system (ΔS_sys) decreases, which means ΔS_sys is negative.
2. Recall the second law of thermodynamics, which states that for a spontaneous process, the total entropy change of the universe (ΔS_univ) must be positive, i.e., ΔS_univ = ΔS_sys + ΔS_surr > 0.
3. Since ΔS_sys is negative, ΔS_surr must be positive to ensure that the sum (ΔS_univ) is positive for the process to be spontaneous.
4. Determine that the magnitude of ΔS_surr must be greater than the magnitude of ΔS_sys to compensate for the negative ΔS_sys and still achieve a positive ΔS_univ.
5. Conclude that ΔS_surr is positive and its magnitude is greater than the magnitude of the negative ΔS_sys.

Key Concepts

Entropy (S)

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it quantifies the number of ways a system can be arranged, with higher entropy indicating greater disorder. For spontaneous processes, the second law of thermodynamics states that the total entropy of an isolated system must increase over time, which is crucial for understanding the behavior of systems in nature.

Second Law of Thermodynamics

The second law of thermodynamics states that in any spontaneous process, the total entropy of the universe (system plus surroundings) must increase. This principle implies that if the entropy of a system decreases, the entropy of the surroundings must increase by a greater amount to ensure that the overall entropy change is positive, thus driving the spontaneity of the process.

Gibbs Free Energy (ΔG)

Gibbs free energy is a thermodynamic potential that measures the maximum reversible work obtainable from a system at constant temperature and pressure. It is defined as ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy. A negative ΔG indicates a spontaneous process, linking the concepts of entropy and energy changes in chemical reactions.