‘Til hell freezes over…

A thermodynamics professor presented an exam to his graduate students. It had one question:   “Is Hell exothermic or endothermic? Support your answer with proof.”
Most of the students wrote proofs of their beliefs using Boyle’s Law or some variant. One student, however, wrote the following:
First, we postulate that if souls exist, then they have mass. If they do, then a mole of souls must have mass. So, at what rate are souls moving into Hell and at what rate are souls leaving? Judeo-Christian tradition holds that once a soul gets to Hell, it will not leave.
No souls are leaving, therefore. As for souls entering Hell, let’s look at the different religions that exist in the world today. Some religions state that if you are not a member, then you will go to Hell. Since there is more than one religion with this perspective, and — typically — people do not belong to more than one religion, if we presume that each such religion is internally consistent, then we can project that all people and souls go to Hell. With current birth and death rates, we can expect the number of souls in hell to increase exponentially.
Now, we look at the rate-of-change in Hell’s volume. Boyle’s Law states that in order for the temperature and pressure in Hell to stay the same, the ratio of the mass of souls and volume needs to stay constant. Two options exist:
    1. If Hell is expanding at a slower rate than the rate at which souls enter Hell, then the temperature and pressure in Hell will increase until all hell breaks loose.
    2. If Hell is expanding at a rate faster than the increase of souls in Hell, then the temperature and pressure will drop until Hell freezes over.
So which is it? If we accept the quote given to me by Theresa Banyan during Freshman year, “that it will be a cold night in Hell before I sleep with you,” and take into account the fact that I still have NOT succeeded in sleeping with her, then Option 2 cannot be true.
Consequently, Hell is exothermic.

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