Second law (Clausius statement) – heat transfer from cold to hot with external aid Identify the scientist associated with the statement: “Heat can flow from a colder body to a hotter body, but only with the aid of an external agency (input).”

Introduction / Context:
The second law of thermodynamics has several equivalent formulations. The Clausius statement focuses on the direction of spontaneous heat transfer and the need for external work to move heat from cold to hot.

Given Data / Assumptions:

• Macroscopic thermodynamics framework.
• Understanding of “external agency” as work input (e.g., refrigeration cycles).
• Equivalence between Clausius and Kelvin–Planck statements.

Concept / Approach:
The Clausius statement asserts: “It is impossible for a self-acting machine, unaided by any external agency, to transfer heat from a cooler body to a hotter body.” With external work input, such transfer is possible (as in refrigerators and heat pumps). Hence the attribution is to Rudolf Clausius.

Step-by-Step Solution:
Recognize the quoted idea: cold-to-hot requires external aid.Associate this with the Clausius formulation of the second law.Select “Clausius” as the correct scientist.Note: Kelvin–Planck version instead prohibits 100% conversion of heat to work in a cyclic heat engine.

Verification / Alternative check:
All refrigeration devices (vapour compression, absorption) consume work or high-grade energy specifically to move heat from a low-temperature region to a higher-temperature region, exemplifying the Clausius statement.

Why Other Options Are Wrong:

• Kelvin: authored the Kelvin–Planck statement (heat engines), not the cold-to-hot transfer statement.
• Joule: established the mechanical equivalent of heat (first law), not directionality.
• Gay-Lussac: known for gas laws, not the second law statements.
• Carnot: analyzed ideal engine efficiency; did not state this form.

Common Pitfalls:
Mixing the two second-law statements; remember Clausius → refrigerators/heat pumps, Kelvin–Planck → heat engines.

Final Answer:
Clausius