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Bipolarity

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I've been doing some chemistry, and come up with a confusing problem that I can't seem to solve. It's a problem I made up while trying to understand the Gibbs Free Energy, but I will try to phrase it solely as a calculus question.

It is known that

[itex] \Delta G + \epsilon \Delta S < 0 [/itex] and that [itex]\epsilon[/itex] is an infinitely small positive quantity. Nothing is known about the sign of [itex] \Delta S [/itex].

Both [itex] \Delta G [/itex] and [itex] \Delta S [/itex] are finite.

Can I prove that [itex] \Delta G ≤ 0 [/itex] ?

I appreciate all help on this matter. Thanks!

BiP

It is known that

[itex] \Delta G + \epsilon \Delta S < 0 [/itex] and that [itex]\epsilon[/itex] is an infinitely small positive quantity. Nothing is known about the sign of [itex] \Delta S [/itex].

Both [itex] \Delta G [/itex] and [itex] \Delta S [/itex] are finite.

Can I prove that [itex] \Delta G ≤ 0 [/itex] ?

I appreciate all help on this matter. Thanks!

BiP

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