Second law (Clausius statement) – feasibility of heat transfer from cold to hot Evaluate the statement: “It is impossible to transfer heat from a body at a lower temperature to a body at a higher temperature without the aid of an external source.”

Introduction / Context:
This is the Clausius statement of the second law of thermodynamics. It expresses the directionality of spontaneous heat flow and the necessity of external work (or equivalent agency) to move heat from cold to hot.

Given Data / Assumptions:

• Thermal reservoirs at different temperatures.
• No external work or effect unless stated.
• Macroscopic, classical thermodynamic setting.

Concept / Approach:
Clausius statement: No process is possible whose sole result is the transfer of heat from a cooler to a hotter body. Refrigerators and heat pumps perform cold-to-hot transfer only by consuming external work, fully consistent with the statement.

Step-by-Step Solution:
Identify spontaneous direction: hot → cold.Recognize that reversing this direction requires an external agency doing work.Therefore the statement as written is correct.

Verification / Alternative check:
Coefficient-of-performance formulas for refrigerators explicitly include input work to move heat against the natural gradient, demonstrating compliance with the second law.

Why Other Options Are Wrong:

• “Incorrect” and conditional variants contradict the second-law principle.
• “Happens spontaneously” is false; spontaneous heat flow is from hot to cold.

Common Pitfalls:
Confusing the descriptive possibility (refrigeration exists) with the prohibition (not without external aid).

Final Answer:
Correct