Identify the correct statement regarding a spontaneous process

The Second Law of Thermodynamics provides the fundamental criterion for spontaneity. It states that the total entropy of an isolated system always increases for a spontaneous (irreversible) process and remains constant for a reversible process.

Checking each statement:

Option A  For a spontaneous process in an isolated system, the change in entropy is positive.
In an isolated system there is no exchange of heat or matter with the surroundings, so the entropy change of the universe equals the entropy change of the system itself. According to the Second Law, $$\Delta S_{\text{isolated}} \gt 0$$ for every spontaneous process. Hence Option A is correct.

Option B  Endothermic processes are never spontaneous.
Spontaneity depends on Gibbs free energy $$\Delta G = \Delta H - T\Delta S$$, not on $$\Delta H$$ alone. An endothermic process ($$\Delta H \gt 0$$) can still be spontaneous if the $$T\Delta S$$ term is large and positive enough to make $$\Delta G \lt 0$$. Example: melting of ice at room temperature. Therefore Option B is wrong.

Option C  Exothermic processes are always spontaneous.
Although an exothermic process ($$\Delta H \lt 0$$) favours spontaneity, it is not a guarantee. If the accompanying entropy change is negative and large in magnitude, $$\Delta G$$ can be positive, rendering the process non-spontaneous. Hence Option C is wrong.

Option D  Lowering of energy in the reaction process is the only criterion for spontaneity.
Spontaneity is governed by both enthalpy change (energy) and entropy change. Gibbs free energy combines these two factors: $$\Delta G = \Delta H - T\Delta S$$. Thus energy lowering alone is not the sole criterion. Option D is incorrect.

Therefore, the correct statement is:

Option A which is: For a spontaneous process in an isolated system, the change in entropy is positive.