Is Hell endothermic or exothermic?
Is Hell hotter than Heaven?

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A delightful story has been circulating around the Internet for years. It concerns an imaginative answer to a mid-term chemistry exam at a U.S. university. The student's answer -- the only one in his class that got an "A" -- is so brilliant that we want to share it with you. Unfortunately, we were originally unable to trace the copyright author, so we can only paraphrase the story. We had a hunch that this was an urban folk tale that may not have actually happened.

However, Snopes.com determined that the original author was Paul Darwin Foote who worked for Taylor Instrument Company as a high temperature measurement specialist back in the 1920s. He wrote it for Taylor's internal newsletter. ₁

University of Washington exam question:

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

"Exothermic" means that the system gives off heat; "endothermic" means that it adsorbs heat.

About Boyle's law:

Most of the students' answers made reference to Boyle's law. This is a fundamental law in chemistry that describes how the temperature of a gas varies with its pressure. When a gas expands, it cools off. This can be observed when you open the valve on a compressed air pipe; the air released will cool down the the surroundings. When a gas is compressed, it heats up. This is why, when you pump up a tire with a hand pump, the gas is compressed and heats up the pump barrel. 

Air conditioners work by first compressing a gas, causing it to heat up. Then the gas is allowed to cool. Finally, it is permitted to expand, thus cooling its surroundings.

The answer:

The student who received an "A" started his calculations by considering whether the total mass of Hell was increasing or decreasing with time. For this, he had to first calculate whether there was a net increase in the number of souls in Hell with time, or a reduction.

From basic theological assumptions, no souls ever leave Hell. Hell is conceived of as a place of punishment where its inmates are tortured for all eternity. On the other hand, souls are continually entering Hell. The student observed that many religions teach that anyone who is not a member of their particular faith will go to Hell. Historically, Christians have taught that all non-Christians will go to Hell. And many non-Christians have believed that all Christians will go there as well. One might therefore assume that all souls will end up in Hell. Thus with souls continually entering Hell and no souls exiting, the total mass of Hell is increasing.

There are two possibilities:

1. If the volume of Hell is expanding at a slower rate than souls are entering, then the temperature and pressure in Hell will "clearly increase until all Hell breaks loose." 
   
   
2. On the other hand, if hell is expanding faster than this rate, then the temperature and pressure will "drop until Hell freezes over."

The student recalled a postulate given to him by a certain coed during his freshman year. She said that "it will be a cold night in Hell before I sleep with you." He noted that he had still not been able to engage in sexual relationships with her. He concluded that Hell is in no danger of freezing over. Thus Option 2 is invalid, the temperature of Hell is increasing, and thus Hell is exothermic.

Which location is hotter: Heaven or Hell?

The temperatures of Heaven and of Hell are not given specifically in the Bible. That may be because the various temperature scales (Fahrenheit, Celsius, Rankin and Kelvin) were not created by the 1^st century CE. However, there is sufficient data available to estimate the temperature of Heaven, and to know at least the maximum temperature of Hell.

Heaven's temperature: Isaiah 30:26 states: "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." One individual interpreted this passage as meaning that the radiation received by Heaven from the sun is 7 times 7 or 49 times as much as the earth does today. ₁ Added to that is the contribution of the moon which would equal the present amount that the earth receives from the sun. Thus Heaven would receive (49 + 1) or 50 times the radiation as the earth does today. The Stefan-Boltzmann law for radiation links the temperature of an object with the amount of radiation received. It would predict that the temperature of heaven would be 498 degrees Celsius hotter than the earth is currently. Thus heaven would be about 525 ºC or 977 ºF. 

However, this temperature would only be the "steady-state" temperature. Presumably Heaven was created shortly after Earth so that it would be ready for its first inhabitants: Abel, Adam and Eve. Revelation 21:17 says that the walls of New Jerusalem are 144 cubits thick. This is about 66 meters or 216 feet. Such a thick wall would be an effective insulator. Heaven would thus have taken a very long time to reach its equilibrium temperature. However, it has presumably reached equilibrium at about 525 ºC  by today -- after the passage of a little over 6,000 years assuming that the earth was created in 4004 BCE as many conservative Christians believe.

Hell's Temperature:  Revelation 21:8 states "But the fearful, and unbelieving ... shall have their part in the lake which burneth with fire and brimstone." Brimstone is sulphur. In order for sulphur to be molten, and form a lake, its temperature must be:

• Above its melting point, which is 115.2 °C or 239.4 °F and
  
  
• Be at or below its boiling point, which is 444.6 ºC or 832 ºF. 

Thus heaven is at least 80 ºC or 145 ºF hotter than Hell. Assuming that the glorified bodies that the inhabitants have in Heaven are as sensitive to heat as our present earthly bodies, then they would suffer greatly. Heaven would be hotter than Hell. Since that cannot happen, due to theological considerations, Heaven must have some very effective methods of air conditioning to handle the excess incoming radiation.

Reference:

1. "Hellfire," Snopes, at: http://www.snopes.com/
2. "Applied Optics" Vol. 11, (1972), Page A14. Quoted by Adrian Gilbert in http://www.sandelman.ottawa.on.ca/People/

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