Criteria for spontaneity – behavior of free energy and entropy For a spontaneous process under the usual thermodynamic criteria, how do free energy and entropy behave?

Introduction / Context:
Spontaneity indicates the natural direction of a process without external work input. Engineers use Gibbs free energy (for constant temperature and pressure) and Helmholtz free energy (for constant temperature and volume) to assess spontaneity in reactions and phase changes.

Given Data / Assumptions:

• Closed system in thermal contact with a large reservoir at constant temperature (and often constant pressure).
• Universe entropy criterion: ΔS_universe > 0 for spontaneous change.
• Gibbs free energy criterion: ΔG < 0 at constant T, P.

Concept / Approach:
Under constant T, P, the direction of spontaneity corresponds to a decrease in Gibbs free energy. Equivalently, the total entropy of the universe increases. This reconciles the system-level free energy change with the second law applied to system plus surroundings. Therefore, a concise, correct statement is that free energy decreases while entropy increases (considering the universe or, practically, the surroundings absorb heat and increase entropy).

Step-by-Step Solution:

Verification / Alternative check:
For a chemical reaction at fixed T, P, tabulated Gibbs energies predict direction; exergonic reactions have negative ΔG and proceed spontaneously toward equilibrium.

Why Other Options Are Wrong:

• Free energy is zero: Only at equilibrium, not for all spontaneous steps.
• Free energy increases: Opposite of the spontaneity criterion.
• Both decrease: Violates the second law.

Common Pitfalls:
Confusing system entropy with total entropy; the system's entropy can decrease if the surroundings’ entropy increases more.

Final Answer:
decreases whereas the entropy increases