THEOLOGICAL THERMODYNAMICSThis document reproduces two classics of science parody/humor. The first appeared in Applied Optics [11(8) A14 (1972), August]. It applies the physics of thermodynamics to conclude that Heaven is hotter than Hell. The second is a response that combines Biblical evidence with thermodynamics to argue that, while heaven is devilishly hot, Hell is hotter still. It appeared in the Journal of Irreproducible Results in 1979.
While the first paper is well known, and available many places on the web, the follow-up isn't as well known. It is included here, for the first time on the net, in the interest of fairly presenting both sides of this burning debate on a hot issue.
Cartoon © 1988 by John C. Holden*
HEAVEN IS HOTTER THAN HELLThe temperature of heaven can be rather accurately computed. Our authority is the Bible, Isaiah 30:26 reads,
Moreover, the light of the moon shall be as the light of the sun and the light of the sun shall be sevenfold as the light of seven days.Thus, heaven receives from the moon as much radiation as the earth does from the sun, and in addition seven times seven (forty nine) times as much as the earth does from the sun, or fifty times in all. The light we receive from the moon is one ten-thousandth of the light we receive from the sun, so we can ignore that. With these data we can compute the temperature of heaven: The radiation falling on heaven will heat it to the point where the heat lost by radiation is just equal to the heat received by radiation. In other words, heaven loses fifty times as much heat as the earth by radiation. Using the Stefan-Boltzmann fourth power law for radiation
where E is the absolute temperature of the earth, 300°K (273+27). This gives H the absolute temperature of heaven, as 798° absolute (525°C).
The exact temperature of hell cannot be computed but it must be less than 444.6°C, the temperature at which brimstone or sulfur changes from a liquid to a gas. Revelations 21:8: But the fearful and unbelieving... shall have their part in the lake which burneth with fire and brimstone." A lake of molten brimstone [sulfur] means that its temperature must be at or below the boiling point, which is 444.6°C. (Above that point, it would be a vapor, not a lake.)
We have then, temperature of heaven, 525°C. Temperature of hell, less than 445°C. Therefore heaven is hotter than hell.
This version differs from some on the net, and has been faithfully copied from the version in Applied Optics. The misprint in the exponent of the equation has been corrected, and one insertion added, in square brackets. The author of this piece is probably Paul Darwin Foote, published anonymously in a 1920 publication of the Taylor Instrument Company. The Applied Optics version was prefaced by "The following reached your Managing Editor via John Howard (from) H. William Koch (from) Alan Bromley (from) an unnamed environmental physicist of several decades back."
A REFUTATION OF THE PROOF THAT HEAVEN IS HOTTER THAN HELLDr. Tim Healey, F. R. C. R.; M. I. Nuc. E.
In Applied Optics (1972, 11 A14) there appeared a calculation of the respective temperatures of Heaven and Hell. That of Heaven was computed by substituting the values given in Isaiah 30 26  in the Stefan-Boltzman radiation law, so that (H/E)4 = 50, where E, the absolute temperature of the Earth, is 300ºK, whence the temperature of Heaven, H, is 798ºK or 525ºC. This is hard to find fault with.
The assessment of the temperature of Hell stands, I suggest, on less firm ground. As authority we use the data provided in Revelations 21 8 , so that the temperature of Hell seems to be 444.6ºCthe temperature at which liquid sulfur is in equilibrium with its vapoura temperature indeed which is sufficiently reliable to be used in the secondary calibration of pyrometers.
Now this last reckoning fails to follow the argument through. 444.6ºC is the temperature at which liquid sulfur is in equilibrium with its vapour at normal atmospheric pressure. Have we any data as to the pressure likely to be found in Hell?
The answer is "Yes". A nineteenth century mathematician has already provided the groundwork for us  and we may feel confident that by the year 2000 the total number of the damned will be at least 29,422,641,251,519,917,000 souls. Yet the area of the valley of Gehinnom  is only 7,000,000 square meters.
We can now apply these figures in the Ideal Gas Equation to calculate what the pressure will be in the valley of Gehinnom. Since surely some souls must have been damned since 1877 , the pressure can only have increased since these calculations were made and the equilibrium point on the phase diagram of sulfur must have shifted still further, so that if we can show that at a temperature of 525ºC sulfur would still be liquid at the pressure calculated (which is a minimum value, remember), Hell (Gehinnom) is now cooler than Heaven.
Certain corrections must be applied first, however.
1. Neiht based his calculation on a date of creation of 1658 + 2326 - 1877 = 2107 BC (minimum). Counting generations in the Bible gives a date for the Creation of 4004 BC. However, atomic dating has shown that Olduvai man is at least 2 × 106 years old .
2. We should use a Fibonacci series for the expansion, not a simple doubling series.  The ancient Jewish laws against inbreeding also act in the same direction. 
3. By a fortunate coincidence, the effects of 1 and 2 cancel each other exactly. 
4. The human body is not an ideal gas, but
5. A good deal of it is gaseous at 525ºC, and in any case,
6. It could well be that at very great pressures the external pressure may well exceed the pressure of electromagnetic repulsion, when different "gas" laws would apply. This merely explains how the Lord works in fitting so large a number of damned souls into so small a space  and it need not be quantitative.
In the calculation the following assumptions are made:
1. The average height can be taken as one meter. This seems a fair figure between the newborn babe and the fullgrown man.
2. The average space needed is about 30 cm × 20 cm. It seems unlikely that any closer packing could be achieved. Neiht uses a figure of 1/20 cubic meters per person, which is nearly identical with my independent assessment. Mine allows a neat cancellation, later.
3. I have assumed that not more than two layers of damned persons can be accommodated, since otherwise those in the middle layers would escape the full rigours of Hell.
The volume available in Gehenna is 60 × 106 × 2 m3 and
The original volume of the damned is 0.06 × 29.422641 × 1018m3
Then, at constant temperature (which we assume, taking equilibrium)
P1V1 = P2V2 or P2 = P1V1/V2
Now let us see what pressure is needed to liquefy sulfur vapour at 525ºC.
We have, using the Clausius-Cleypeyron equation in its integrated form,
Log P = 7.43287 - 3268.2 / T
where P = pressure in mm Hg
and T = the elevated boiling point in ºK,
Log P = 7.43287 - (3268.2/798) = 3.3373813
(1) is so much greater than (2) that Revelations 21 8 indicates a temperature very considerably higher than 525ºC.
Thus, Hell is hotter than Heaven (which remains deucedly hot).
REFERENCES1. "The light of the moon shall be as the light of the sun and the light of the sun shall be sevenfold as the light of seven days..." The light of the moon is negligible in comparison with that of the sun.
2. "...the lake which burneth with fire and brimstone: which is the second death".
3. A Mathematical Proof of the Non-Existence of Hell from the writings of the free-thinker Neiht, born in Brussels, 1877. "The area of the valley of Jehoshaphat is 60,000,000 sq. ms. ... Supposing that each race originated with one couple only, one has five couples or ten people, and applying to them the principle of compound interest, up to the Flood there were 9,289,000 births in 1,658 years. Since the Flood up to our epoch 2,326 years have passed, during which, if only five couples survived, they would have produced 2,213,867,610,000 children. If these calculations are extended up to the year 2000, the resulting number is 34,326,414,259,675,172,000 which, together with the 9,289,000, makes 34,326,414,259,684,461,000 offspring. If one concedes, charitably, that all papists are saved, their number today being 1/7th of the population of the earth, that of the damned would be made up of those born before the Flood plus those born since the Flood up to the year 2000 minus the 1/7th of those born since the year 44, that of the birth of Christ: this number is 4,903,773,008,164,544,000, and the total of damned would be 29,422,641,251,519,917,000.
"The mean cubic area between a new-born infant and an adult is about 1/20th metre; the bulk of the damned above is equal to the mass of a sphere of radius 705,504 metres; that of the earth is 6,366,200 metres.
"If one puts back the origin of man, following certain German naturalists, to 80,000 years, the number of damned would form a cube three times the size of the earth.
"Now, how does one assemble the 34,326,414,260 millions risen on a surface of 60,000,000 sq. metres to judge them and how does one sink this mass of damned, through all manner of rock, to a depth of 5,660,660 metres?"
 The valley of Jehoshaphat is the Gehenna of the Jews (Jehennam in the Koran)the place of eternal torment. The word is derived from Gehinnom = the valley of Hinnom where sacrifices were offered to Moloch (2 Corinthians 33 6) (= Adremmelechthe God of Sepharvaim). In later times, all manner of refuse was dumped there and fires were constantly maintained to consume it. The sulfurous stench and the fire was the original of the Christian concept of Hell. (The estimate of Nieht of Gehenna's area 60 × 106 sq. m. is wrong, according to measurements taken on the spot by the Editors).
 e.g. Dzhugashvili, Losif and DeSalvo, Albert H.
 Curtis G. H. and Evemden, J. F. in Nuclear Clocks USAEC Pp 40-41.
 Leonardo da Pisa Liber Abaci 1202 (Out of print).
 Leviticus 18 6 et seq.
 Westfall, R. S. Newton and the Fudge Factor. Science 1973 751 -758.
 "In my father's house are many mansions: If it were not so I would have told you. I go to prepare a place for you." John 14 2. Also, "Those things which are impossible with men, are possible with God" - Luke 18 27, and "...with God all things are possible." Matthew 19 26.
This paper appeared in The Journal of Irreproducible Results, Vol 25, No.4:17-18 Copyright © 1979 by The Journal of Irreproducible Results, Inc.
IS HEAVEN EXOTHERMIC OR ENDOTHERMIC?
I've received a number of requests to include one more scientific/theological parody using thermodynamics. This one showed up in a humor post to the newsgroup rec.humor in 1997. It has been "going around" ever since as a "true story" in several variants. But that's surely bogus. See snopes.com for a discussion.A true story. A thermodynamics professor had written a take home exam for his graduate students. 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. One 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. So, 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. Of course, 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.
It was not revealed what grade the student got.
Notes from snopes.com:
Notes by D. E. S.
These unattributed distributions with false claims of "a true story" are simply annoying, and also unfair to the original authors. The roots of this joke have been traced back to about 1920, to a piece written by Paul Darwin Foote in a house publication of the Taylor Instrument Company. If anyone knows of an earlier appearance, please let me know. Also, if anyone has the original version, I'd like to see it.
I haven't yet seen the original version. This piece does not compare temperatures of Heaven and Hell. It begins with the "assumption that souls have mass". Mass is never an issue in the other two. It also assumes souls have volume. The "logic" is completely different in these various parodies.
It seems to me far-fetched to connect the later parodies with the Foote parody. Nor am I convinced that Foote's piece "inspired" the others. I see no case that could be made for plagiarism.
A good rule is "Whenever a story begins with 'This is a true story...' you can be sure it isn't so." I encountered a lot of this sort of thing when I was compiling a book of science humor, "Science Askew". People suggested to me innumerable anecdotes attributed to famous scientists and mathematicians, all purporting to be "true". The trouble was that the same stories were often attributed to different persons and from different places. I have come to assume that they are all inventions, or at least heavily embellished, unless some serious documentation is provided. The same is true for "quotes". The "If I have seen further than others..." quote widely attributed to Isaac Newton has been traced back to a Roman Poet Lucan (39-65 CE). So another rule is "If something is catchy enough to be attributed to someone famous, it really had its origin much earlier, probably with someone less famous." You can quote me on that.
Finally, some readers quibbled about a misprint in the temperature of Hell that I had in the final line of the parody from Applied Optics, which I think is now corrected, though I still don't have access to the original printed copy. If anyone still doubts the result for the temperature of Hell, we suggest they apply the experimental method and go to the source carrying an accurate thermometer. But if anyone has access to the paper copy in Applied Optics I'd be happy to receive a scan of it.
No one has (yet) faulted the calculation of the temperature of Heaven. Perhaps none are expecting to go there.
* The cartoon, which was not associated with either of these documents, is by John C. Holden, from No Dinosaurs on the Ark by Sol Omon (Harris B. Stewart). It was published by THE BOOKMAKER, Star Route 38, Winthrop, WA 98862 (509) 996-2576.
Last edited May 2014.