Sign of entropy change – removing heat from a gas Consider a gas as a closed system. If heat is removed from the gas, what is the sign of the change in entropy of the gas?

Introduction / Context:
Entropy quantifies energy dispersal and the direction of thermal interactions. Determining the sign of entropy change for simple heating or cooling steps is a foundational skill for analyzing processes and assessing feasibility per the Second law of thermodynamics.

Given Data / Assumptions:

• Closed system containing a gas.
• Heat is removed from the system (net heat flow out).
• Reference to the system's entropy change, not the surroundings.

Concept / Approach:

For a reversible path, ds = δQ_rev / T. Removing heat corresponds to δQ_rev < 0, so ds < 0, i.e., entropy decreases. For irreversible cooling at the same end states, Δs is still negative because entropy is a state function; the sign is fixed by the end states. The entropy of the surroundings typically increases by at least the same magnitude divided by the appropriate temperature, ensuring total entropy production is nonnegative.

Step-by-Step Solution:

Verification / Alternative check:

Cooling an ideal gas at constant pressure: Δs = cp * ln(T2/T1) − R * ln(P2/P1). If T2 < T1 with modest pressure change, the dominant term is negative, confirming Δs < 0 for the gas.

Why Other Options Are Wrong:

“Yes/No” without context is ambiguous; the precise correct statement is that entropy decreases for the system when heat is removed.“Always increases” contradicts the Second law for the system under cooling.“Zero for all adiabatic” is false; only reversible adiabatic (isentropic) has Δs = 0.

Common Pitfalls:

Confusing the system's entropy change with total entropy production; the surroundings usually compensate so that ΔS_total ≥ 0.

Final Answer:

Entropy decreases (negative change) in general when heat is removed