In what situation is a process considered spontaneous when both Delta H and Delta S are positive?

A process is considered spontaneous when it occurs without external influence, and thermodynamically, this is often evaluated using the Gibbs free energy equation: ( \Delta G = \Delta H - T \Delta S ). For a process to be spontaneous, the change in Gibbs free energy (( \Delta G )) must be negative.

When both enthalpy (( \Delta H )) and entropy (( \Delta S )) changes are positive, the spontaneity of the process depends significantly on temperature. A positive change in enthalpy indicates that the process is endothermic, which means it absorbs heat and may require energy input. A positive change in entropy means that the disorder of the system increases, which is thermodynamically favorable.

In this scenario, the temperature must be sufficiently high to make the term ( T \Delta S ) larger than ( \Delta H ) in the Gibbs free energy equation. This means that at high temperatures, the increase in entropy can offset the endothermic nature of the process, leading to a negative ( \Delta G ) and making the process spontaneous.

At low temperatures, the contribution of ( T \Delta S ) is not sufficient to outweigh ( \Delta H