Does the gravitational potential energy affect the burning of two logs?

Homework Statement

Let's consider two wooden logs. We burn the first one at the base of the mountain and the second one on the peak. Which one is releasing more energy? Do they release the same amount of energy?
Does the potential energy affect the burning

Homework Equations

$\Delta H =$ Sum of bond energies broken - Sum of bond energies formed

$E=mc^2$

$Potential \ Energy = mgh$

$v_T=\sqrt{\frac{3kT}{\mu m_H}}$

The Attempt at a Solution

I know that the reaction enthalpy depends on temperature so they must release different amounts of energy. So I guess the answer will be the log located on the peak of the mountain.

Another approach I tried is to apply the Einstein equation, $E=mc^2$. Supposing that the two logs have the same mass the answer will be simple: both release the same amount of energy.

Also I was thinking about the oxygen levels for this two altitudes. The log at the lower altitude has more oxygen so it should release more energy. But if the two logs have equal masses, the oxygen level should not matter. Am I wrong?

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This problem seems misguided. It asks if the potential energy affects the quantity of energy released in burning a log. I have to ask, “which potential energy?” Since the problem is about burning you would like to think they are referring to some sort of chemical potential energy, but since they are comparing the bottom of a mountain to the peak I have to believe they mean gravitational potential energy.

I am guessing they are trying to illustrate the connection or lack thereof between different kinds of energy. (I guess ?!??). The problem with that is you can think of a lot of reasons that different amounts of energy will be released (as you have) which have nothing to do with gravity.

Perhaps I am missing something, but the best way I can interpret this question is: assume the log oxidizes completely (I.e. don’t worry about unmentioned things like the amount of oxygen, how long it takes, or how thoroughly it burns) does the chemical energy released depend on whether you are at the bottom or top of the mountain?

Well that’s my best guess of what they are getting at, anyway.

This problem seems misguided. It asks if the potential energy affects the quantity of energy released in burning a log. I have to ask, “which potential energy?” Since the problem is about burning you would like to think they are referring to some sort of chemical potential energy, but since they are comparing the bottom of a mountain to the peak I have to believe they mean gravitational potential energy.
Yes, they mean gravitational potential energy. Sorry for the confusion.