Sample “proof by contradiction”

received via e-mail:

Subject: Thermodynamics of Hell

The following is an actual question on a University of Washington chemistry mid-term:

Bonus Question: Is Hell exothermic or endothermic?

Everyone defined exothermic and endothermic correctly: exothermic=gives off heat (is “hot”), endothermic=absorbs heat (is “cold”). Then, most students wrote proofs using Boyle's Law: gas cools as it expands and heats when it is compressed. The answer by one student was so "profound" that the professor shared it with colleagues via the Internet, which is, of course, why we have the pleasure of seeing it as well.

"First, we need to know how the mass of Hell is changing in time. So we need to know the rate that souls are moving into Hell and the rate they are 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 how many souls are entering Hell, let's look at the different religions that exist in the world today. Most of these religions state that if you are not a member of their religion, you will go to Hell. Since there is more than one of these religions and since people do not belong to more than one religion, we can project that 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 of the volume in Hell because Boyle's Law states that in order for the temperature and pressure in Hell to stay the same, the volume of Hell has to expand proportionately as souls are added. This gives two possibilities:

1) If the volume of 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 the volume of Hell is expanding at a rate faster than the increase of souls in Hell, then the temperature and pressure drops and Hell freezes over.

So which is it? If we accept the postulate presented to me by Teresa in my Freshman year, "...it will be a cold day in Hell before I sleep with you," and observe the evidence that in fact I still have not succeeded in having an affair with her, then #2 above cannot be true, and thus I am sure that Hell is exothermic."