Final Exam

A retiring Phys Chem professor was setting his last exam, for a graduate course in statistical thermodynamics. Being a bit bored with it all, and with a well-kept and wry sense of humor, he set a single question on the sheet: "Is Hell endothermic or exothermic? Support your answer with proof."
He had little idea what to expect, or how to grade the results, but decided to reward any student who was able to come up with a reasonable and consistent reply to his query. One A was awarded. Most of the students wrote proofs of their beliefs using Boyle's Law or some variant. The top student however wrote the following:


First, we postulate that if souls exist, then they must have some mass. If they do, then a mole of souls can also have a mass. So, at what rate are souls moving into hell and at what rate are souls leaving? I think that we can safely assume that once a soul gets to hell, it will not leave. Therefore, no souls are leaving. As for souls entering hell, lets look at the different religions that exist in the world today. Some 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 do not belong to more than one religion, we can project that 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 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 volume needs to stay constant. There are two possible conditions:


Condition One: 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 exponentially until all hell breaks loose.
Conversely, Condition Two: 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.


We can solve this with the 1990 postulation of Theresa LeClair, the girl who lived across the hall from me during my first year residence. Since I have still not been successful in obtaining sexual relations with her, condition two above has not been met, and thus it can be concluded that condition one is true, and hell is exothermic.