Final answer:
The assertion that it is impossible for a system unaided by an external agency to transfer heat from a cooler to a warmer body is true, and the reason that it would violate the Second Law of Thermodynamics is also correct, making option A the correct answer.
Step-by-step explanation:
The question pertains to the Second Law of Thermodynamics and whether heat can spontaneously transfer from a body at a lower temperature to one at a higher temperature without external work. The assertion correctly states that such a transfer is not possible without an external agency. The reason provided, which claims it is due to the impossibility of violating the second law of thermodynamics, is also correct. The second law dictates that heat transfer occurs spontaneously from higher- to lower-temperature bodies and not the reverse unless external work is applied.
The second law is fundamentally based on the concept of entropy, which tends to increase in a spontaneous process. If heat were to transfer from a colder body to a hotter one spontaneously, the entropy of the system would decrease, which contradicts the second law.
Therefore, when considering heat engines, refrigeration, or any thermodynamic cycle, work is necessary to achieve such a non-spontaneous transfer of heat.
Given these considerations, we can confirm that the assertion and reason are correct, and the reason is indeed the correct explanation for the assertion. Hence, the correct option answering the question is A. Both assertion and reason are correct, and the reason is the explanation for the assertion.