Which of the following is a proper statement of the second law of thermodynamics?

The second law of thermodynamics can be succinctly summarized through several useful concepts and equivalent statements, one of which is that it is impossible for a system operating in a complete cycle to transfer heat from a cooler body to a hotter body without additional work being done on the system. This principle is encapsulated in the correct choice, which stresses that the only effect of such a cycle would be the heat transfer from a given temperature to a higher temperature, without any work interaction.

The essence of this statement highlights the directionality of natural processes—heat naturally flows from hot to cold, and to induce a reversal of this process, some form of energy input is necessary. This is a foundational concept in thermodynamics and is crucial for understanding processes like refrigeration, where work must be performed to move heat against its natural gradient.

The other statements touch upon elements of the second law but don't capture the importance of performing work to achieve specific heat transfer outcomes clearly as the correct choice does. For example, one of the options incorrectly implies that heat can only be exchanged with bodies at lower temperatures for work, which contradicts the established principles of heat engines and thermodynamic cycles. Each of these nuances contributes to a comprehensive understanding of how energy transfer and transformations are governed by the laws