Is hell exothermic or endothermic?

Any sufficiently advanced technology is indistinguishable from magic.

A thermodynamics professor gave his graduate students a take home exam. It had one question:


"Is hell exothermic or endothermic? Support your answer with a proof."

Most of the students wrote proofs of their beliefs using Boyle's Law or some variant to show either that hell was exothermic (generating heat faster than it is lost, resulting in a buildup of heat) or endothermic (generating heat slower than it is lost, resulting in a loss of heat).

One student, however, wrote the following:

First we must postulate that if souls exist, then they must have some mass.

So, at what rate are souls moving into hell and at what rate are souls leaving? i.e. what is the rate of change of mass of hell. I think that we can assume that once a soul gets to hell, it will not leave. Eternal damnation is pretty much final. Therefore, no souls are leaving. As for souls entering hell, let's look at the different religions that exist in the world today.

Many of these religions state that if you are not a member of their religion, you will go to hell. Since there are more than one of these religions, and people generally do not belong to more than one religion, we can project that everyone is damned by lack of adherence to one religion or another, and so all people and all souls go to hell.

With birth and death rates as they are, we can expect the number of souls in hell, and therefore its mass, to increase exponentially. Now, we look at the rate of change in volume in hell. 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 the volume needs to stay constant. We arrive therefore at two possible hypotheses:

    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.
    On the other hand, 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 postulate given to me by Therese Banyan during freshman year that:

"It'll be a cold night in hell before I sleep with you" ...

and take into account the fact that I still have not succeeded in having sexual relations with her, then Hypothesis 2. cannot be true.

Hence, hypothesis 1. must be correct: Hell is exothermic.