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?

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.