## Ramani K. Raman

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A physics professor gave his graduate students in a thermodynamics course a take home exam. It had only one question, albeit a strange one:

"Show by means of rigorous proof whether Hell Exothermic or Endothermic? What does this mean?

Most of the students wrote proofs of their beliefs using Boyle's Law or some variant. One student, however, turned in the following truly witty answer:

First, we postulate that if souls exist, then they must have some mass. If they do, then a mole of souls will also have a mass. So, at what rate are souls moving into hell and at what rate are souls leaving? This will determine whether hell is indeed exothermic or endothermic.

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.

Having established that, what is the rate at which these souls are entering 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.

Thus, there are two possibilities:

• 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.
• Alternately, if Hell is expanding at a rate faster than the increase of souls in hell, than the temperature and pressure will drop until hell freezes over.

If we accept the postulate given to me by a young lady during my first year, "It will be a cold night in Hell before I sleep with you", and given the fact that as of now, all my attempts to sleep with her have failed, clearly number 1 above must be true, in which case, Hell is exothermic. However, I continue to nurture the hope that hell shall turn endothermic in the near future.

Exothermic / Endothermic?

• Any system which is hotter than its surroundings and hence gives out heat is termed Exothermic
• Any system which is cooler than its surrounding and hence absorbs heat is termed Endothermic

This above story is found floating around the net, often attributed to  certain Dr. Schambaugh, Professor at the School of Chemical Engineering at University of Oklahoma. I decided to check the veracity of this story and to my surprise found that the professor is not fictional and does indeed exist. So I wrote to him to check the veracity of this claim. He was kind enough to reply back, and this is what he had to say:

Mr. Raman,

I receive numerous e-mails about this urban legend.  My name is misspelled more than 20 different ways in the various versions of the story, and usually the story involves an actual class that I teach (CHE 3123 – Heat, Mass, and Momentum Transfer II).  Yes, I am notorious for giving unusual problems.  However, I never gave this problem about hell.

Regards,

Robert L. Shambaugh

Professor