What is the formula that relates ΔS of a system to heat and temperature?

The correct formula that relates the change in entropy (ΔS) of a system to heat transferred and temperature is ΔS = q_rev/T. This formula is specifically applicable to reversible processes, where q_rev represents the reversible heat transfer.

In thermodynamics, entropy is a measure of the dispersal of energy within a system and how that energy can be used to do work. The relationship indicates that as heat is added to a system at a constant temperature, the change in entropy is directly proportional to this heat divided by the temperature. This relationship emphasizes the importance of the process being reversible, as the entropy change for irreversible processes would not yield the same relation due to the additional factors that come into play such as irreversibilities.

This formulation aligns with the second law of thermodynamics, which stipulates that the change in entropy for a reversible process can be precisely calculated using this equation. Hence, the inclusion of "rev" in the formula affirms that only for reversible heat exchanges can we directly apply this relationship to determine entropy changes.