Entropy change when heat is removed from a gas Consider a closed system of an ideal (perfect) gas. If heat is removed from the gas (i.e., the system rejects heat), is the change in the system's entropy necessarily positive?
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AYes, entropy change is always positive when heat is removed
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BNo, entropy change is generally negative when heat is removed at a given temperature
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CIt is always zero regardless of process details
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DIt depends only on pressure, not on the process path
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EIt depends on reversibility; entropy may decrease despite heat removal if generation is small
Answer
Correct Answer: No, entropy change is generally negative when heat is removed at a given temperature
Explanation
Introduction / Context:Entropy quantifies the energy dispersal per unit temperature and sets limits on heat-to-work conversion. This question examines the sign of entropy change when a gas rejects heat. Understanding the distinction between entropy transfer with heat and entropy generation due to irreversibility is crucial for thermodynamics and refrigeration problems.
Given Data / Assumptions:
- Closed system containing a fixed mass of ideal gas.
- Heat is removed from the system (Q < 0 for the process considered).
- Temperature is measured on the Kelvin scale.
- Process may be reversible or irreversible unless otherwise specified.
Concept / Approach:The entropy change of a system over any process can be written as ΔS_system = ∫(δQ_rev/T) + S_gen, where S_gen ≥ 0 accounts for irreversibilities. For a reversible path at temperature T, rejecting heat (δQ_rev < 0) gives a negative contribution to ΔS. Only if irreversibilities are present and large enough can the positive S_gen outweigh the negative heat-term and make ΔS nonnegative.
Step-by-Step Solution:State the relation: ΔS_system = ∫(δQ_rev/T) + S_gen.For heat removal at representative temperature T: ∫(δQ_rev/T) is negative.For a reversible cooling step: S_gen = 0, hence ΔS_system < 0.For an irreversible cooling step: ΔS_system = negative quantity + S_gen; sign depends on magnitude of S_gen.Therefore, the blanket statement “entropy change is positive when heat is removed” is incorrect.
Verification / Alternative check:Cooling water or gas in a reversible heat exchanger reduces the fluid’s entropy, while the surroundings gain entropy by |Q|/T_surroundings. The total entropy of the universe increases or stays the same, but the system’s entropy typically decreases upon heat removal.
Why Other Options Are Wrong:Option A claims always positive—contradicted by reversible cooling. Option C claims always zero—false except for special contrived paths. Option D ignores the path dependence of heat and the role of T. Option E is partially insightful but still does not make the original unconditional statement true; the correct evaluation of the stem is “No”.
Common Pitfalls:Confusing system entropy change with total entropy generation; assuming “heat out” must increase entropy due to the second law (it does not for the system; it does for the surroundings or the total).
Final Answer:No, entropy change is generally negative when heat is removed at a given temperature