Second law of thermodynamics – Kelvin–Planck statement Which of the following correctly expresses the Kelvin–Planck statement of the second law of thermodynamics for heat engines operating in a cycle?
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AIt is impossible to construct an engine operating in a cycle whose sole effect is to convert heat completely into work.
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BIt is possible to construct an engine that converts all absorbed heat into work if it is perfectly insulated.
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CIt is impossible to construct a cyclic device that produces no effect other than transfer of heat from a cold body to a hot body.
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DNone of the above.
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EIt is possible to reach absolute zero by a finite number of steps.
Answer
Correct Answer: It is impossible to construct an engine operating in a cycle whose sole effect is to convert heat completely into work.
Explanation
Introduction / Context:The second law imposes fundamental limits on energy conversion. The Kelvin–Planck statement focuses on cyclic heat engines and forbids 100% conversion of heat from a single reservoir into work with no other effect.
Given Data / Assumptions:
- Heat engine operates on a cycle between thermal reservoirs.
- “Sole effect” means no other changes in the universe (no heat rejected elsewhere).
- Classical macroscopic thermodynamics context.
Concept / Approach:The Kelvin–Planck statement: No heat engine, operating in a cycle, can produce net work while exchanging heat with only one reservoir. Some heat must be rejected to a lower-temperature sink. This is equivalent to saying that thermal efficiency cannot reach unity for a cyclic engine.
Step-by-Step Solution:1) Consider a hypothetical engine that absorbs Q from a single reservoir and delivers W = Q with no rejection.2) Such an engine would violate the Kelvin–Planck statement.3) Real engines must reject heat Q_out so that W = Q_in − Q_out.4) Therefore option (a) correctly states the prohibition.
Verification / Alternative check:The Kelvin–Planck and Clausius statements are equivalent; option (c) paraphrases the Clausius statement (no device can cause heat to flow from cold to hot without external work), not Kelvin–Planck.
Why Other Options Are Wrong:
- (b) contradicts the second law regardless of insulation.
- (c) is the Clausius statement, not Kelvin–Planck.
- (d) incorrect because (a) is correct.
- (e) relates to the unattainability of absolute zero (third law concept), not Kelvin–Planck.
Common Pitfalls:Assuming perfect insulation permits perfect conversion; second law limitations are not removed by insulation alone.
Final Answer:It is impossible to construct an engine operating in a cycle whose sole effect is to convert heat completely into work.