Kelvin–Planck statement of the second law: Is it possible to construct a cyclic heat engine whose sole effect is to convert all absorbed heat into work?

Introduction / Context:
This question targets the Kelvin–Planck statement of the second law of thermodynamics, which places a fundamental limit on the performance of heat engines operating in cycles.

Given Data / Assumptions:

• A cyclic device exchanging heat and work with surroundings.
• Sole purpose: convert heat into work with no other effect.
• No allowance for additional reservoirs or changes elsewhere.

Concept / Approach:
The Kelvin–Planck statement asserts that it is impossible to devise a cyclic engine that converts all heat received from a single thermal reservoir entirely into work. Some heat must be rejected to a lower-temperature reservoir. Thus, 100% conversion in a cycle violates the second law.

Step-by-Step Solution:

Verification / Alternative check:
Carnot's theorem: Even the ideal reversible engine (Carnot) has efficiency η = 1 − T_c/T_h < 1 for finite temperatures, requiring Q_out > 0 unless T_c = 0 K (unattainable).

Why Other Options Are Wrong:

• Possible / possible with an ideal gas / possible at absolute zero: Each contradicts the second law or invokes unattainable conditions.

Common Pitfalls:
Confusing one-shot energy conversion (non-cyclic) with cyclic operation; misinterpreting the role of multiple reservoirs.

Final Answer:
impossible