Under what conditions does an increase in temperature turn a nonspontaneous process into a spontaneous process?

This, is an incomplete question, here is a complete question.

Under what conditions does an increase in temperature turn a nonspontaneous process into a spontaneous process?

Choose one or more:

ΔH < 0, ΔS > 0

ΔH > 0, ΔS > 0

ΔH > 0, ΔS < 0

ΔH < 0, ΔS < 0

(What I'm trying to figure out is if you need to consider T being negative OR positive to start)

Answer :  The correct option is, ΔH > 0, ΔS > 0

Explanation :

According to Gibb's equation:

= Gibbs free energy  

= enthalpy change

= entropy change  

T = temperature in Kelvin

As we know that:

= +ve, reaction is non spontaneous

= -ve, reaction is spontaneous

= 0, reaction is in equilibrium

As there are 4 conditions:

(A) ΔH is positive or (ΔH>0) and ΔS is negative or (ΔS<0).

The reaction is non-spontaneous at all temperatures or spontaneous in reverse at all temperatures.

(B) ΔH is positive or (ΔH>0) and ΔS is positive or (ΔS>0).

 (at low temperature) (non-spontaneous)

 (at high temperature) (spontaneous)

The reaction is spontaneous as written above a certain temperature.

(C) ΔH is negative or (ΔH<0) and ΔS is positive or (ΔS>0).

The reaction is spontaneous as written at all temperatures

(D) ΔH is negative or (ΔH<0) and ΔS is negative or (ΔS<0).

 (at high temperature) (non-spontaneous)

 (at low temperature) (spontaneous)

The reaction is spontaneous as written below a certain temperature.

From this we conclude that, the condition ΔH is positive or (ΔH>0) and ΔS is positive or (ΔS>0) at increase in temperature turn a nonspontaneous process into a spontaneous process.

Hence, the correct option is, ΔH > 0, ΔS > 0