Temperature of Dragon's breath weapon (fire) or I guess cold too

[Yogibear41]

Does it say anywhere what the exact temperature of a fire breathing (or ice breathing) dragons breath weapon is? I know that red dragons and their like tend to get hotter with age, (body temp) and I'm sure this would effect their breath attacks, but is it specifically listed anywhere?

[TuggyNE]

Does it say anywhere what the exact temperature of a fire breathing (or ice breathing) dragons breath weapon is? I know that red dragons and their like tend to get hotter with age, (body temp) and I'm sure this would effect their breath attacks, but is it specifically listed anywhere?

What is this "temperature" of which you speak? D&D+physics — a strange game; the only winning move is not to play.

[Psyren]

Given that Endure Elements doesn't protect against cold or fire damage, it's safe to assume that fire damage is hotter than 140F and cold damage is colder than -50F. (Note that under Environment, lethal fire damage from your surroundings is at the same threshold - 140F - but lethal cold damage is only at -20.)

That gives you minimum thresholds to work with. Obviously more fire damage would be hotter, but how much hotter is difficult to say.

[Emperor Tippy]

Does it say anywhere what the exact temperature of a fire breathing (or ice breathing) dragons breath weapon is? I know that red dragons and their like tend to get hotter with age, (body temp) and I'm sure this would effect their breath attacks, but is it specifically listed anywhere?

Well a Great Wyrm Red breathes hot enough to theoretically liquify 4 inches of solid iron across an 80 foot or so line. So an 80 foot wall of iron 4 inches thick could be liquified by a single attack by a Great Wyrm Red.

[Diarmuid]

ET - what is this theory based on?

[Emperor Tippy]

ET - what is this theory based on?

A pure iron wall has 30 HP per inch of thickness and Hardness 10. A Great Wyrm Red has a breath weapon that does 24d10 Fire Damage in a 70 ft. cone. Maximum damage is 240, which is halved against objects for 120, which is then dropped by 10 because of Hardness. So it's technically a little less than 4 inches thick that can be liquified. A 70 ft. cone has a maximum straight horizontal line in it of something like 80 ft., and everything in the AOE takes full damage.

[supermonkeyjoe]

ET - what is this theory based on?

4 inch thick Iron has 120HP and hardness 10, and a Great wyrm breath weapon does 24d10 damage in a 70' cone which averages at 132 damage.

However fire would do half damage to objects (I personally wouldn't say that iron walls are particularly vulnerable to fire) which after hardness would be 56 damage so a basic MM great wyrm red dragon would probably heat the metal thoroughly but not completely destroy it.

[RFLS]

Well a Great Wyrm Red breathes hot enough to theoretically liquify 4 inches of solid iron across an 80 foot or so line. So an 80 foot wall of iron 4 inches thick could be liquified by a single attack by a Great Wyrm Red.

I'm going to murder some catgirls about now.

Starting assumptions:


The heat from the breath is distributed evenly across and throughout the iron.
The iron is elementally pure.
Spherical dragon.
Frictionless Plane.


First thing first - how much iron are we talking about here? Let's see -

5 feet * 80 feet * 1/3 foot * (magical-cubic-feet-to-cubic-meters-number) = ~4.5 cubic meters of iron.

Cool. We've got 4.5 cubic meters of iron. I've truncated the second decimal, but it's largely irrelevant. What's the next step? Well, it actually looks like we've got to make another assumption - that the iron is currently at room temperature, or, as far as I'm concerned, 20 degrees Celsius, or 293 degrees Kelvin. Next step!

We have to figure out how much energy it takes to move the iron from room temperature, to melting, to melted. Cool. According to my sources (Wikipedia), it takes ~25 Joules to make 1 mole of iron 1 degree Kelvin warmer. Cool. Or hot. Whatever. So, we've got to figure out how many moles of iron we've got. Here're the numbers:



4.5m3 * (magic number) = 4,500,000cm3
4,500,000cm3 * (Density of Iron) = 35,415,000 grams
35,415,000 * (magic number) = 634166 moles of iron


The next step is to figure out what that means in terms of energy. We're taking 634166 moles of iron and making it (1811-293) degrees Kelvin hotter, or 1518 degrees. More math!



Molar Heat Capacity (J/mol*K) * moles * degrees Kelvin = energy used!
25.1 (J/mol*K) * 634166 mol * 1518 K = 24162866098.8 Joules


Wow. That's a lot of energy. However, we're not quite done - the iron is hot enough to melt, but has not yet melted. The energy required for that is as follows:



Heat of Fusion (J/mol) * moles = energy used!
13.81 (J/mol*K) * 634166 mol = 8757832.46 Joules


Adding them together, we get 24171623931.26 Joules to melt that block of iron. How hot, exactly, is that? Well, here's another set of assumptions:


The air heated is only within that line - the volume is 5 feet by 5 feet by 80 feet, minus the volume of the iron.
The air needs to have roughly double the amount of energy required to melt the iron. This isn't strictly true, but because the molar heat capacity of iron and air are fairly similar, I feel comfortable making this assumption; at least, for a first, rough pass at the problem.


I'll handwaive through a lot of the arithmetic; you've seen it all once. We've got 51 cubic meters of air with 48343247862.52 Joules of energy contained within it. It takes .0013 Joules to heat 1 milliliter of air 1 degree Kelvin. We have 5.1e+7 milliliters of air, meaning that we have heated this air to ~950 degrees Kelvin.

That number is very, very low - and it's wrong. The heat is also bleeding off into the surrounding space at a much faster rate than it's bleeding into the iron. The surrounding space has almost twice as much area that the energy is distributed across to warm it. It's also taking about .8 as much energy to warm the same volume, meaning we've got a final multiplier of around 1.6 times as much energy consumed by the surrounding squares as by the wall of iron. I can go through all of the arithmetic again, but the end result is that the air breathed out by the dragon is 1520 degrees Kelvin, 1246 degrees Celcius, or 2276 degrees Fahrenheit.

DISCLAIMER: The math presented here was done very roughly. Many numbers are rounded or handwaived, and the physical assumptions of the situation are rough. The author is not to be held responsible if you are incinerated by an angry red dragon after buying Fireproof (Up to 2500 degrees!) armor and taunting it.

EDIT: Upon reflection, I realized that I've counted air and iron as having the same heat capacity in one place, but accounted for the difference in another. In light of that realization, the actual values are as follows:

1187.5 Joules
1900 degrees Kelvin
1557.5 degrees Celcius
2845 degrees Fahrenheit.

[Diarmuid]

Your numbers look good, but I think you're imposing your own version of how that would be represented. I think my issue was with how you verbalized "hot enough to theoretically liquify 4 inches of solid iron across an 80 foot or so line".

The breath weapon is dealing damage and how that damage is dealt and represented is not something specifically defined. The iron could be reduced to ash, simply scorched to the point where its structural integrity is completely compromised, etc.

My concern is that someone very well versed in science could see your post, actually know what kind of temperature that would require and then arbitrarily assign that temperature to the dragon's breath and assume/imply other impacts/effects based on it.

[Ortesk]

Well a Great Wyrm Red breathes hot enough to theoretically liquify 4 inches of solid iron across an 80 foot or so line. So an 80 foot wall of iron 4 inches thick could be liquified by a single attack by a Great Wyrm Red.

621 degrees to melt lead down, given that it melts it in roughly 3 seconds and can melt huge amounts of lead at once, we can safely say it would need to be far g\higher than that actually. So roughly speaking, a full grown red dragon breathes at about 2400 degrees, which means non magical armor would melt beneath his breath

[Spore]

You do realise that is actually just about the peak temperature of a bunsen burner and that welding torches are hotter?

[Ortesk]

You do realise that is actually just about the peak temperature of a bunsen burner and that welding torches are hotter?

And Steel melts at roughly 2500 degrees, which means a dragons breath would have the power to melt steel unless tippy was underestimating its heat. Welding torch is hotter than whats needed to melt steel by a good deal

[RFLS]

You do realise that is actually just about the peak temperature of a bunsen burner and that welding torches are hotter?

No; I just do molar arithmetic for fun in my spare time. Never actually taken a chemistry course.

[Ortesk]

Although if we go off the fact dnd dragons are based off tolkien dragons, we can easily figure the temperature of a red dragon.

[PraxisVetli]

No; I just do molar arithmetic for fun in my spare time. Never actually taken a chemistry course.

I lol'd

so, how then would one calculate a White's?
And hey, lets cross the line from mass murderer to genocide (catgirls are totally infinite).
Whats the wattage / pH of a green/black /blue?

[hamishspence]

"Standard" D&D lightning bolts, created by natural storms, do d10xd8 damage according to the SRD:

http://www.d20srd.org/srd/weather.htm#thunderstorm

Maybe this could be correlated to energy in joules of a normal lightning bolt- with the high figure being close to the highest recorded example?

[lsfreak]

Whats the wattage / pH of a green/black /blue?

Despite being listed as "acid," with a disclaimer that I haven't studied chem except a high school class, I'd be tempted to stat up the acid attacks as some of the more terrifying oxidizers.

For the sake of keeping the numbers (relatively) sane, I'd also say whoever does the electric attack should assume that the (1d10)d8 done by lightning ignores the existence of positive lightning.

[hamishspence]

I recall "1.21 gigawatts" being given as a ballpark figure for a typical lightning bolt in Back to The Future, at least. :smallamused:

[Spore]

No; I just do molar arithmetic for fun in my spare time. Never actually taken a chemistry course.

Bah. I thought you were one of those - those - physicists. Who calculate the surface temperature of the sun but can't hold a beaker the right way. :D


I recall "1.21 gigawatts" being given as a ballpark figure for a typical lightning bolt in Back to The Future, at least. :smallamused:

I thought the unit is jiggawats (http://global3.memecdn.com/1-21-giga-wat_fb_2053971.jpg).

[RFLS]

"Standard" D&D lightning bolts, created by natural storms, do d10xd8 damage according to the SRD:

http://www.d20srd.org/srd/weather.htm#thunderstorm

Maybe this could be correlated to energy in joules of a normal lightning bolt- with the high figure being close to the highest recorded example?

Sure. No problem. Here we go:

1d10(d8) dice gives, on average, 24.75 damage. Let's pretend that that's an average cloud-to-ground lightning bolt. 24.75 damage correlates to 500 megajoules[1] (http://en.wikipedia.org/wiki/Lightning#Cloud_to_ground_.28CG.29), or 500,000,000 joules. The most powerful lightning bolt that could naturally occur would be ~3.2 times as powerful (80/24.75), or 1,600,000,000 joules.

Fun fact: This means that electricity is 18 times more energy efficient than fire for dealing damage in D&D.


I lol'd

so, how then would one calculate a White's?
And hey, lets cross the line from mass murderer to genocide (catgirls are totally infinite).
Whats the wattage / pH of a green/black /blue?

Cold would be much more difficult to calculate - you'd have to find the brittle transition temperature for iron, and then see if you can find the point where it simply falls apart due to any vibration whatsoever.

I'll come back later tonight with the pH of acid breath.