Minimum Energy Input - is it delta G or Delta H?

[NsubRe]

Is it correct to state - Delta G is the work/energy that you must add to the system to have the chemical equation in equilibrium (an infinitesimal amount of energy over this will drive the reaction forward) , Delta H is the energy (Heat of Reaction, enthalpy) that the system will evolve and T Delta S is the entropy a measure of what the internal molecular level changes add or subtract to the process. In the cases the heat energy evolved is more than the work added to the system. i.e., The breaking of the Al2O3 bonds to form the elements Al and O2 provides the T delta S energy additional contribution to the delta H term. I'm working with two mechanical engineers (MIT) who insist the minimum is delta H not delta G. Please provide reference and examples if MIT is correct. Thank you

 

[rbcoulter]

Refer to Chap. 12 of "Chemical Principles" a typical freshman college chemistry textbook.
Basically, it says that a reaction will go to minimize the change in delta G (Gibbs Free Energy) . That is, the products would have lower G value than the reactants. At equilibrium the products and reactants have the same G value and that is why the reaction doesn't go further.

The delta H term is not necessarily minimized because of the entropy factor as you stated. A reaction or other process can proceed spontaneously and be endothermic. For example, many solids when dissolved in fluids will get cold. Most gases will get cold when allowed to expand. This is because there is a strong tendency for these processes to go to greater entropy levels that they take in energy from the surroundings.

Although your wording is a little confusing, you appear to be correct.