1. The problem asks to identify the correct representation of the second law of thermodynamics from the given options. 2. The second law of thermodynamics states that the total entropy of an isolated system (the universe) always increases or remains constant in a reversible process. Mathematically, this is expressed as: $$\Delta S_{univ} \geq 0$$ where $\Delta S_{univ}$ is the change in entropy of the universe. 3. Let's analyze each option: - a) $(\Delta S_{sys} + \Delta S_{univ}) = 0$ is incorrect because it mixes system entropy change with universe entropy change incorrectly. - b) $(\Delta S_{sys} + \Delta S_{surr}) = 0$ is the condition for a reversible process where the system and surroundings entropy changes sum to zero. - c) $\Delta S_{univ} = 0$ is true only for a reversible process, but the second law allows $\Delta S_{univ} > 0$ for irreversible processes. - d) $\Delta S_{univ} < 0$ contradicts the second law since entropy of the universe cannot decrease. 4. Therefore, the second law of thermodynamics is best represented by option b) $(\Delta S_{sys} + \Delta S_{surr}) = 0$ for reversible processes, and more generally by $\Delta S_{univ} \geq 0$. Final answer: b) $(\Delta S_{sys} + \Delta S_{surr}) = 0$