A process will be spontaneous at all temperatures if:

🧠 For spontaneity at ALL temperatures, both the enthalpy and entropy terms must push in the same direction $\Delta G = \Delta H - T\Delta S$. For $\Delta G < 0$ at every temperature $T > 0$, you need $\Delta H$ to be negative AND $T\Delta S$ to add to that (not fight it).

🗺️ Checking each case (a) $\Delta H < 0$, $\Delta S < 0$: $\Delta G = \Delta H - T\Delta S$ = negative − (negative) = negative + positive. At high $T$, $\Delta G$ becomes positive — not spontaneous at all temperatures. ✗

(b) $\Delta H < 0$, $\Delta S > 0$: $\Delta G$ = negative − (positive) = always negative regardless of $T$. ✓

(c) $\Delta H > 0$, $\Delta S > 0$: spontaneous only at high $T$. ✗

(d) $\Delta H > 0$, $\Delta S < 0$: $\Delta G$ always positive — never spontaneous. ✗

⚠️ Trap: Option (a) is spontaneous at low temperatures — students confuse "spontaneous at low T" with "spontaneous at all T."

$\boxed{\text{Answer: (b)}}$