# Energy Conservation and the Dragons (Game of Thrones)

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## Summary:

I want to calculate how many goats the dragon would have had to eat to make the sack of King's Landing compliant with energy conservation.
I thought I'd calculate how much heat was required to melt the Iron Throne, and then multiply that by the number of flame-gushes during the sack of Kings Landing, to get a total amount of energy expended. Then I'd convert that to calories and use the average number of calories per goat to determine how many goats the dragon would have had to eat to spew that much flame. I'm not sure I have the science right.

Formula: Heat = mass of iron throne * specific heat of iron * melting temperature of iron.

I found the mass of the iron throne using m=v*d.Based on visual assessment of people sitting on the Iron Throne, I let it equal 3 times the volume of small person, notably Geoffrey or Daenerys. That gives it a volume of 1.5 * 105 cm3. Density of iron is 8 g/cm3. So, the Iron Throne has a mass of 1.2*103 kg. That passes the common-sense check, since it is roughly half the mass of a car, which seems about right.

The specific heat of iron (C) is 460 J/(kg*K) and the melting point of iron is 1770 K

Heat = 1.2 103 * 460 * 1770 = 9.8 * 108 Joules. So, I was going to convert that to calories and multiply by goats/calorie to determine diet and whether, as I suspect, energy conservation was violated.

The problem I'm having is that this doesn't take into account the size of the flame gush. I wonder if I need to then calculate the temperature of the air needed to raise iron to the melting point, and multiply that by the volume of the flame-gush (about 40 times the volume of Daenerys) to find the energy in a gush of dragon flame.

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Nugatory
Mentor
You are overthinking this problem.
Ignore all the concerns about the size of the blast of flames, just assume that all the energy goes into melting the throne. That will give you a substantial underestimate of the number of goats required... and if even with that underestimate you find that dragons are impossible you have your answer.

I wil resist pointing out that Robert Heinlein proposes in "Glory Road" a different mechanism for producing dragonfire.

Joe591
kuruman
Homework Helper
Gold Member
First a conceptual correction that will not make much difference. The equation is ##Q=mc\Delta T##. We assume that the throne room is at room temperature and not at absolute zero, so ##\Delta T =1470 K## or so.

Secondly, what do you know about dragon metabolism? Let's agree on the number of ##E=9\times 10^9## Joules required for melting the throne. I claim that the dragon has a relativistic metabolism (magic is involved after all, isn't it?), in which case the mass of goat required is $$m = \frac{E}{c^2}= \frac{9 \times 10^9~\mathrm{kg \cdot m^2/s^2}}{9\times 10^{16}~\mathrm{~m^2/s^2}}=10^{-7}~\mathrm{kg}=100 ~\mathrm{ng}.$$In this case no goats need be involved; just by licking his chops the relativistic dragon will have much more input mass than needed to do the job.

My point here is that when you do a calculation and suspend disbelief for part of the calculation while expecting to use the existing laws of physics in another part, you can get any answer you want. Just shift the line between reality and fake reality. Arguably, where you draw the line is no better than where someone else draws the line. I personally prefer to draw no lines and stick to reality.

Hi, thanks for the replies. Dragons do eat. In the premier of Season 8, we hear that they are hardly eating, because they've only eaten "18 goats and 11 sheep" that day. They are known for a fondness for goats, sheep, and the occasional shepherd. So a nuclear reactor as an internal organ seems out.
https://www.eater.com/2019/4/24/18512398/what-do-the-game-of-thrones-dragons-eat

I think Nugatory is saying my original calculation was reasonable.

phinds
Gold Member
2019 Award
I wil resist pointing out that Robert Heinlein proposes in "Glory Road" a different mechanism for producing dragonfire.
And ... you resisted that quite well.

Nugatory
Mentor
And ... you resisted that quite well.
That move was perfected by Cicero centuries ago.

They are known for a fondness for goats, sheep, and the occasional shepherd. So a nuclear reactor as an internal organ seems out.
I cannot see how eating goats, sheeps and every now and then a human rules out a nuclear reactor. Can explain that in detail?

sophiecentaur
Gold Member
I always have a problem with the way 'Aliens', in general handle their available energy. Their food supply is always a concern; how did the dragons survive before there were suitable humans to provide 'meat'? In the wild it would have been the dynamically fluctuating "foxes and rabbits' situation. Bearing in mind that all dragons (except the hatchlings) are ancient (take Smaug as an example), you have to ask where their natural fool supply would have come from

In the Alien films, the creatures seem to be constantly dribbling highly reactive saliva, which must need a fair bit of energy. Wetness in general seems to be a horror trope but our friendly neighbourhood molluscs like slugs and snails have a serious water conservation problem. If a typically dribbling alien shows up in my garden I will just wait until it dries out.

If a typically dribbling alien shows up in my garden I will just wait until it dries out.
But the alien wouldn't wait and an average human body consits of around 60 % water.

sophiecentaur
Summary:: I want to calculate how many goats the dragon would have had to eat to make the sack of King's Landing compliant with energy conservation.

Heat = 1.2 103 * 460 * 1770 = 9.8 * 108 Joules. So, I was going to convert that to calories and multiply by goats/calorie to determine diet and whether, as I suspect, energy conservation was violated.
I think you forgot a factor of a 1000 with kilo-calories.
Combustion enthalpy of fat is 3.8*10^7 J/kg. protein/carbohydrate is 1.7*10^7 J/kg. A lean goat might be 10*10^7 J/kg, so you'd need about 100 kg. Less if it's a really fat goat.

kuruman
Homework Helper
Gold Member
##\dots## ask where their natural fool supply would have come from ##\dots##
Is "fool supply" a typo or intentional?

Hi, thanks for the replies. Dragons do eat. In the premier of Season 8, we hear that they are hardly eating, because they've only eaten "18 goats and 11 sheep" that day. They are known for a fondness for goats, sheep, and the occasional shepherd. So a nuclear reactor as an internal organ seems out.
https://www.eater.com/2019/4/24/18512398/what-do-the-game-of-thrones-dragons-eat
I will ask one more time, how does dragon metabolism fit in all this? Regular digestion of a goat produces energy at a rate limited by enzyme kinetics. From what I have seen in GOT, a burst of dragon fire lasts no more than 5 seconds. This means that to release 109 Joules in 5 s, the power output would have to be 500 MW, a typical output of a power plant. So all the energy from the goat cannot be released as it is generated at the rate of digestion but must be stored somewhere to be released all at once. This in turn raises the issue of where all this energy is stored and how? You might wiggle out of this and say that the dragon spews out some kind of liquid that spontaneously combusts in air, something like Greek fire. OK, but then you have to do another back-of-the-envelope calculation to show that this combustible material can raise the temperature high enough to melt iron. And so on. Once you start a calculation of this sort, you have to cover all the bases to make it plausible otherwise it's just numerology.

anorlunda
Staff Emeritus
Why are you concerned with conservation of energy in a magic world? Just conjure up more magic.

Magic doesn't erase rules.

sophiecentaur
sophiecentaur
Gold Member
Magic doesn't erase rules.
Surely that's what Magic is all about????
Only nerds like PF actually try to reconcile the two.

There is one thing you are leaving out. The iron thrown isnt simply being heated, it is melting. This means that a phase change is occurring and you should add the latent heat of melting of iron to the mix. You will need even more goats to make this work. Goats are going towards extinction. Its a bad time to be one...

The iron thrown isnt simply being heated, it is melting.
That adds another 0.27 MJ/kg resulting in 1 MJ/kg for heating and melting. With 1200 kg/throne that makes 1.2 GJ/throne.

I just checked if heat loss by radiation needs to be considered: A fireball with 1770 K and 3 m in diameter within a 300 K environment would lose around 8 MJ/s by radiation out of the upper hemisphere. This could be neglected if the throne melts within some seconds. However, in order to melt the throne that fast, the fireball would need to be much hotter and would therefore lose more energy. As I'm currently to lazy to agonise over heat transfer into and inside the throne I just add another 1000 K. That results in around 47 MJ/s wasted energy. Thus it makes sense to assume that half the energy gets lost as a rough estimation.

If I go with 2.4 GJ/throne, a heat of combustion of 10 MJ/kg meat and 18 kg meat/goat I get 13 goats/throne. Assuming that there is just a single iron throne this is not a problem for goatkind.

Gremlins in a dragon's stomach harvest enery from the 13th dimension and convert it to napalm which is ejected from the thorax via a T-shirt cannon.

sophiecentaur