Indicate whether each statement is true or false. (a) ΔS is a state function. (b) If a system undergoes a reversible change, the entropy of the universe increases. (c) If a system undergoes a reversible process, the change in entropy of the system is exactly matched by an equal and opposite change in the entropy of the surroundings. (d) If a system undergoes a reversible process, the entropy change of the system must be zero.

Verified step by step guidance

1. Identify the concept of a state function and recall that state functions depend only on the state of the system, not on how the system reached that state. Apply this to determine if ΔS (change in entropy) is a state function.
2. Understand the definition of entropy and the second law of thermodynamics, which states that the total entropy of an isolated system can never decrease over time. Use this to evaluate the statement about entropy change during a reversible change.
3. Recall the concept of reversible processes and how they relate to entropy. In a reversible process, the system is in thermodynamic equilibrium with its surroundings. Analyze how this affects the entropy changes in the system and its surroundings.
4. Understand the definition of a reversible process and its characteristics, particularly how it relates to changes in entropy. Consider whether the entropy change of the system must be zero for a process to be reversible.
5. Combine the knowledge of reversible processes and entropy to critically evaluate each statement and determine if it is true or false based on the principles of thermodynamics.

Key Concepts

State Functions

State functions are properties of a system that depend only on its current state, not on the path taken to reach that state. Examples include internal energy, enthalpy, and entropy (ΔS). Understanding that ΔS is a state function means recognizing that its value is determined solely by the initial and final states of the system, regardless of the process involved.

Entropy and the Second Law of Thermodynamics

The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. In a reversible process, the entropy of the universe (system plus surroundings) increases, indicating that while the system may return to its original state, the overall disorder or randomness increases, reflecting the natural tendency towards equilibrium.

Reversible Processes

A reversible process is an idealized process that occurs infinitely slowly, allowing the system to remain in equilibrium at all times. In such processes, the change in entropy of the system is equal in magnitude but opposite in sign to the change in entropy of the surroundings, leading to no net change in the total entropy of the universe. However, this does not imply that the entropy change of the system is zero.