Kelvin–Planck statement of the Second law According to the Kelvin–Planck statement, a perpetual motion machine of which kind is impossible?

Introduction / Context:
The Second law of thermodynamics has several equivalent statements, including those of Kelvin–Planck and Clausius. Each rules out a class of perpetual motion machines (PMMs). Identifying which “kind” is prohibited by Kelvin–Planck clarifies what is fundamentally impossible for heat engines.

Given Data / Assumptions:

• Heat engines exchange heat with reservoirs and produce work cyclically.
• Thermal reservoirs are at fixed temperatures.
• Perpetual motion refers to devices violating energy or entropy principles.

Concept / Approach:

The Kelvin–Planck statement: It is impossible to construct a device that operates in a cycle and produces no effect other than the extraction of heat from a single reservoir and the performance of an equivalent amount of work. This forbids a PMM of the second kind (PMM2). A PMM of the first kind violates the First law by creating energy from nothing; Kelvin–Planck addresses the Second law (directionality and quality of energy), not the First.

Step-by-Step Solution:

Verification / Alternative check:

Equivalence with the Clausius statement can be shown by contradiction: if either were violated, one could violate the other, confirming both prohibit PMM2 and spontaneous heat flow from cold to hot without compensation.

Why Other Options Are Wrong:

PMM1 pertains to First law violation; not the Kelvin–Planck formulation.Other “kinds” are nonstandard or irrelevant nomenclature.

Common Pitfalls:

Thinking “100% efficient heat engine” is allowed if perfectly designed; the Second law forbids it regardless of ingenuity.

Final Answer:

second kind