Introduction
Every so often I, like everyone else, reminisce about all the things I have experience in my life. The happy moments, the sad moments and especially the goofy ones. So today I bring you a blast from the past, if you grew up around the same time as I did of course, with a blog post related to Cloudy with a chance of meatballs.
This is a somewhat wackier movie where the main character, Flint Lockwood, invents a machine with an obtuse acronym which can turn water and a lot of power into food. Ah just how mama used to make it when I was a child.
While his invention leads to all sorts of entertaining shenanigans, I will be focussing on just how this machine, The FLDSMDFR (pronounced fludsh-muh-duh-fur), would work. However, as you’ll soon see, this process isn’t as simple as described here. So I want you to keep the next image in mind as we go about explaining each part of this wonderful apparatus.
The structures before and after
To start, we will have to know what we’re starting with and what we are trying to make. We all know the composition of water, in this case we’re going to assume its pure, because the other stuff inside of there is safe for consumption so it’ll also be in the food. So H2O is the easy part, but what are we going to be turning it into?
For this I’m mostly gonna take the average composition of organic compounds, like glucose/sugar and fats. Glucose is the easiest to work with so that’s what you’re getting; pure sugar. Jokes aside it the main compound we use for energy production in the powerhouses of our cells (can I get a yeah! for mitochondria?), so it’s a good starting point, and besides, other compounds only differ in ratios and not in anything else we’ll be doing.
The ratio very roughly corresponds to 2:1:1 for Hydrogen, carbon and oxygen respectively, but this isn’t the entire part of our delicious puzzle. This is because it also costs energy to break and forge the chemical bonds between the atoms in these molecules, so this has to be taken into account. We are going to rely on the fact that the mass before and after stays the same, including the byproduct of course.
Those who know a little chemistry might immediately see the problem and might even call it impossible, because how do we get those carbon atoms exactly? Normally we can’t make carbon with oxygen, but if you introduce a very very large amount of energy you could break the atom in two with fission. This is the same principle as with splitting radioactive materials, but with smaller nuclei it needs a lot of energy instead of releasing it.
Fission
It is important to see if our little reaction cost or releases energy. An intuitive way to do this is with a very useful diagram called the curve of binding energy, which can be found on wikipedia, where we also took this image from.
An important note before I get lost in the sauce you must remember that the binding energy is per nucleon, not per atom. This is where a common misconception comes from that the fusion of hydrogen generates more energy than the fission of uranium. While true per nucleon, the uranium nucleus has a way way higher amount of them so the total energy will be higher.
We can see that iron (Fe) is at the top, with a steep drop-off at the left side and a subtle decline on the right side. This graph represents the energy held within the bond of an atom, if this number is higher it takes more energy to separate it.
The origin of the binding energies is mostly the aptly named strong nuclear force, who is responsible for overcoming the repulsion between the protons in the nucleus because of their equal charge. So if there are more nucleons (protons and neutrons) in the atom this force becomes stronger and that causes it to be harder to break apart.
However, where does the slow decline on the right side come from then? While the strong nuclear force is fittingly strong over short ranges it becomes exponentially weaker as the distance between the building blocks of these, less appetizing, atoms get further away from each other.
On a little side tangent, this is also how many stars come to die. A star is held up from gravity because it fusion (the opposite of fission) keeps happening in the core and releasing a huge amount of energy. First light elements fuse, heavier elements keep forming. The core slowly approaches iron, which has the optimal size for the strong nuclear force.
At that point fusion doesn’t release any more energy and the balance between gravity which forces it to implode and the core ceases to exist.
Now we can take a look at our food (I know I kept you waiting), where we see that that the superior, more handsome oxygen atom has a larger binding energy than that of our product; carbon. This would mean that it cost energy to make its glorious transformation for not just food for thought but also our belly.
Turning water into food
With this knowledge firmly in our mental digestive tracks we can now look at what the reactions would be for making food out of water. I’ll be taking it one step at a time to explain what happens.
Firstly, we need to overcome the binding energy between the atoms in a water molecule, to go from H2O to its loose components. Normally two H2O molecules would break down creating O2 gas, but in this case we are acting like the oxygen splits before that can happen.
After this, the oxygen splits into a helium atom and the desired carbon. This happens to the required half of all oxygen so we end up with the right ratio (2:1:1). This also means that for every carbon/oxygen we have four hydrogen left over because of the previous step. This would release H2, a flammable gas. No worries, I’m sure Flint has an incredibly fool proof solution for this (I hope). There will also be one escaping helium atom escaping per carbon atom produced, but this is a nobel gas so nothing would happen except the atoms saying “let them eat cake” when our food is being made.
There are a couple of ways to force an atom to undergo fission, but in this case the most plausible and easiest one is to fire an electron at the nucleus with a high enough kinetic energy for the bonds within it to break. This is also how fission is achieved in uranium within a nuclear bomb for example, because they each send out a neutron which can then cause another uranium atom to undergo fission etc.
Then these loose atoms will be bonded into our desired food, in this case glucose.
What is our food yield?
Let’s say we start with 1kg of water when we put it into the FLDSMDFR, where would this mass go? To do this we must first start with translating the mass of water to moles, not the digging kind but the Avagrado kind.
Moles are used to quantify the amount of molecules in a given thing, such as water. We know what all the ratios are between the amount of atoms, so once I calculate that we’ll have the masses in a jiffy.
<Frantic calculations ensue>
While it is possible to calculate the mass of glucose with the hydrogen, carbon and oxygen, I wouldn’t do it that way. It would be way easier to calculate the mass lost as gases and use the fact that mass is conserved. The mass of helium and hydrogen gas is a total of 0,167kg. Because the total mass is an easy, nice and round 1kg we know this to be 16,7% of the total mass, leaving 0,833kg or 83,3% of the original mass as glucose. This means that our theoretical maximum yield is a steady 83,3%, way to go Flint!
We know the mass of the start and finish is the same (we’ll almost), however the energy in bonds between the atoms and even the protons and neutrons isn’t. We know that mass as well as energy must be conserved so it must be added somehow. In the movie it is displayed that he causes a town wide power outage because he needs to use so much, but I wonder; would this be accurate?
What would the electric bill be?
This brings us to the final section so we can finally get the full picture. For this are going to take the energy consumed by the reactions (or held within the bonds), not the total energy it would cost. There is a good chance some energy escapes our system, or is needed to heat the system up enough past the energy actually needed for the atoms are be able to undergo fission.
The first bonds that are going to be broken up are those of the H2O molecules. To do this we won’t only need to break the bonds between hydrogen and oxygen, but also the hydrogen bonds between the water molecules. These (2 per molecule) also hold the entire structure of molecules together (causing it to be in a less energy costly state) and they cease to exist if we force a very sad divorce between the atoms in water.
The required energy for this is normally in the order of 10^5 Joules per mol, which is why we don’t actually have to calculate it. We will soon find that the energy needed for the next step outweighs it by such a landslide that we can just ignore it.
Next we’re going to look at how much energy it takes to break up oxygen into carbon and helium. This is a whole lot easier because we only have to compare the nuclear binding energies of the nuclei and the amount of nuclei in the atoms..
This gives us an energy deficit of 3,24 MeV per atom, which luckily for us, and Flints bank account, isn’t a lot. This is per atom though so if we want to see how much total energy it is we first have to translate it to energy per moles (using Avagrado’s number) and then to the actual energy. This equals to a whopping 5,191 • 10^-13 J, which is even less. Now if we multiply by the amount of atoms we have we get a different picture: 8,643 • 10^12 J of required energy.
Because the formation of glucose has the same order of magnitude as that of water we can also easily ignore it. This also means that we are done with our little calculation, now that wasn’t so hard was it? Our total power of 2,4 GWh (Giga Watt hours), which while being a little easier to comprehend is still a quite astonishing amount though.
This puts into perspective how much energy is held in the smalles things, but to put it into more perspective I will compare it to a couple goofy things. Hold on let me think of a good think for scale….. ah yes a banana.
This would be the equivalent energy of groveling up about thirteen and a half billion bananas (b in billion is for banana), so about three meals or so.
If we look at how much energy Flint’s town we halve we get a more interesting result (less delicious though). The amount of energy is coincidentally also enough for 135 thousands homes for one day. This being easily more than what the small town under the A in Atlantic Ocean has, making the power outage the most accurate part of the movie. Which is the answer to the question that got this entire thing started.
So now, I take you back to the figure where it all started, understanding the importance and (totally worth it) cost of how his first cheeseburger was made.
Final remarks
This was it for another one of my famous fiction physics posts (definitely not my second one or anything), but make sure to check out the other one(s) while you’re at it! Sending Cape Canaveral into space with C-moon. I hope you enjoyed reading at as much as I did wirting it, and that you also took some new knowledge away from it. Later on in the movie the machine gets sent up into the atmosphere where it gobbles up the clouds in the sky, let’s just not think about where it’s getting its energy from in that scenario.
Anyway I’m going to enjoy my perfectly made, definitely not total waste of energy, glucose that just plopped out of my FLDSMDFR at home.
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