Sign of entropy change: For a gas (system) that absorbs heat, what is the sign of the system's entropy change?

Introduction / Context:
Entropy indicates the degree of energy dispersion and is central to the Second law. Determining the sign of entropy change for heating or cooling helps assess feasibility and direction of processes in both closed and open systems.

Given Data / Assumptions:

• System is a gas receiving heat.
• Reference is the system's entropy change, not the surroundings.
• Temperature is positive on an absolute scale.

Concept / Approach:

For a reversible path, ds = δQ_rev / T. If the system absorbs heat, δQ_rev > 0, and with T > 0, ds > 0. For irreversible heating, entropy change is evaluated via any reversible path between the same states; it remains positive because entropy is a state function determined by end states only.

Step-by-Step Solution:

Verification / Alternative check:

For ideal gases at constant pressure: Δs = cp * ln(T2/T1) − R * ln(P2/P1). With heating at modest pressure change, ln(T2/T1) > 0 dominates, giving Δs > 0.

Why Other Options Are Wrong:

Negative: corresponds to net heat rejection by the system.Positive or negative: sign is not ambiguous when net heat is absorbed.Zero for any adiabatic: only reversible adiabatic has Δs = 0; general adiabatic may increase entropy.Undefined: entropy change is well-defined for state changes.

Common Pitfalls:

Mixing up system and surroundings; surroundings often lose heat and may have a negative local Δs while total entropy change remains nonnegative.

Final Answer:

positive