A Phase change complexity of ammonium carbamate (AC) decomposition and recombination

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The discussion revolves around the complexities of understanding the energy dynamics involved in the decomposition of activated carbon (AC) into CO2 and NH3. The original hypothesis suggests that the energy required to break ionic bonds should equal the energy that can be extracted, yet calculations consistently yield negative Kelvin values, indicating an energy loss. This raises questions about the fundamental principles of energy conservation in this process. Additionally, the exothermic nature of the reaction implies that any temperature increase during recombination should correlate with the energy that must be lost to return to the initial state. The inquiry highlights a critical need for clearer definitions and explanations in existing research on this topic.
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Ive been researching AC and its properties for hundreds of horus and learnt a lot, however there are some things that have to have a more propper defenition to make sense. The public research that ive found have not satisfied the explanation. Here is the question:

The first philosophy i had was that regardless of input requirement for decomposition of AC it should equate to (Starting energy aka tempreature)+(energy required for breakign the ionic bond) = CO2 and NH3. if that is the case then it only makes sense that if we added x energy to break the bond we should be able to extract exactly x energy so that it returns to its initial state (starting energy aka tempreature). however every time ive asked and tried any calculations myself and via AI(over 200 or more hours ive lost count) ive always gotten a negative kelvin number, indicatign that somehow what we put in cannot be extracted. this doesent make sense as regardless if the x energy that we inputted was taken up by the gases as pressure,volume and tempreature it should only be an addition to what it started as and therefore extractable.

the other way to see it is that research indicates that when co2 adn nh3 are combined to form AC it releases a lot of heat (aka highly exothermic) with measurable rises in tempreature. this would mean that whatever the tempreature increase it has from recombination will also be equivalent to how mcuh it has to lose in order for it to recombine and reach initial tempreature. If it heats up by 1degC then we find out the kj of energy relevant to its specific heat capacity and that value becoems what the gases have to cool by to reach its inital state. FYI i avoided mentioning specific data as id rather you reaserch it yourself (AI is an easierr "research shotgun") incase the discrepency lies in my interpretatiosn of values. i know this is a pretty complex and strange question but here i am, desperate as my mind tears itself apart over the very critical but minor specifics. Thanks
 
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