Second law of thermodynamics – Clausius statement (direction of heat flow) Which of the following correctly reflects the Clausius statement of the second law? Select the statement that captures the impossibility without external aid.

Introduction / Context:
The Clausius statement of the second law formalizes the natural direction of spontaneous heat flow and the requirement of external work to move heat against this direction.

Given Data / Assumptions:

• Macroscopic, classical thermodynamics.
• External source means an external agency supplying work or equivalent high-grade energy.
• Refrigerators and heat pumps are practical embodiments.

Concept / Approach:
Clausius statement: No process is possible whose sole result is the transfer of heat from a cooler body to a hotter body. Equivalently, cold-to-hot transfer requires external aid (work input). The question asks for the statement that emphasizes the impossibility without aid.

Step-by-Step Solution:
Identify the spontaneous direction: hot → cold.Recognize that reversing this requires external work.Choose the option that forbids cold → hot without aid.Hence, select the impossibility statement (option b).

Verification / Alternative check:
Refrigeration cycles explicitly consume work to move heat from low to high temperature, satisfying the Clausius statement while achieving the transfer with external aid.

Why Other Options Are Wrong:

• (a) Omits the “external aid” requirement and is false as a general spontaneous statement.
• (c) True in practice but not the Clausius prohibition; it describes an application, not the principle.
• (d) Incorrect because (b) is correct.
• (e) Misstates spontaneity; spontaneous flow is hot → cold without work.

Common Pitfalls:
Confusing the descriptive statement (refrigeration is possible with work) with the normative prohibition (impossible without work).

Final Answer:
It is impossible to transfer heat from a lower-temperature body to a higher-temperature body without the aid of an external source.