# Potential energy in nuclear energy

Where does the potential energy go if you carry uranium to a nuclear power plant on the top of a mountain and part of its mass becomes energy?

haruspex
Homework Helper
Gold Member
Energy generates, and is affected by, gravity. Einsteinian relativity treats mass and energy as equivalent in that respect.

Drakkith
Staff Emeritus
You have more than one type of potential energy here. First, you are performing work on the uranium by carrying up to the top of the mountain, so the whole thing will have greater gravitational potential energy. Second, you have your nuclear potential energy. This does NOT change when you move up or down the mountain, as nuclear energy does not come from gravity.

When the uranium undergoes fission part of the nuclear potential energy is converted into kinetic energy of the reaction products, eventually winding up as heat as the kinetic energy is transferred into the rest of the material. Now, the key here is to realize that the mass of the SYSTEM has not changed (Our system being the uranium) until that energy leaves and goes elsewhere. For example, you have an atom which splits through fission and converts part of the potential energy into kinetic energy and heat. If we were to measure the uranium right then and there the mass would be exactly the same. However, if we wait until the heat is removed and sent to the turbines to perform work and generate electricity, the uranium would now have less mass.

Meh, made the thread when I was tired, hoping for an answer in the morning =). Now the thread title is kind of misleading, and the example wasn't a very good one...

I was of course talking about gravitational potential energy. Say you create matter and anti-matter using E=mc^2 at sea level. Then you transport those into a higher gravitational potential and recombine. What happens to that potential energy?

Though now that I'm more awake... do photons also lose some energy (get redshifted) by moving "against" gravity? Would make sense if they can't escape black holes.

What if it creates new mass with kinetic energy (in effect, an object uses some of its mass to make the rest of the mass move)?
The mass still exists in a gravitational potential, but what about the kinetic energy?

Drakkith
Staff Emeritus
I was of course talking about gravitational potential energy. Say you create matter and anti-matter using E=mc^2 at sea level. Then you transport those into a higher gravitational potential and recombine. What happens to that potential energy?

What potential energy? You didn't have any.

Though now that I'm more awake... do photons also lose some energy (get redshifted) by moving "against" gravity? Would make sense if they can't escape black holes.

Absolutely, they are redshifted as they leave a gravity well and blue shifted as the enter one.

What if it creates new mass with kinetic energy? The mass still exists in a gravitational potential (as would photons if those were created), but what about the kinetic energy?

What if what did? What is creating these new particles?

mfb
Mentor
In theory, you should be able to produce 1GW of electric power in a mountain and use something like 1.000000000001 GW (arbitrary amount of "0", no calculation) in the valley. Of course, the effect is so tiny that you won't notice it in a real power grid. There is your energy. Electric power on a mountain is more valuable than power in a valley, similar to photons.

What potential energy? You didn't have any.
What? Moving mass against gravity.
What if what did? What is creating these new particles?
The recombination of the matter&antimatter that you created down in the gravity well. Or any other energy<->matter conversion example you like.

Drakkith
Staff Emeritus
What? Moving mass against gravity.

You moved from a lower area to a higher area. This required performing work on the material and added potential energy.

The recombination of the matter&antimatter that you created down in the gravity well. Or any other energy<->matter conversion example you like.

I still don't know what you are asking exactly.

mfb
Mentor
I still don't know what you are asking exactly.
Maybe I can rephrase his question. Consider two scenarios:

Scenario 1: Use 1kg of uranium in a valley as fission material and you get x kWh of electric and thermal energy plus 0.9999 kg (or whatever) of fission products.

Scenario 2: Take 1kg of uranium, lift it by 1km (needs g*1kg*1km energy). Use it as fission material to get x kWh of electric and thermal energy plus 0.9999 kg (or whatever) of fission products. Take those 0.9999kg down to the valley again, giving g*0.9999kg*1km. Compared to scenario 1, you "lost" energy.

However, at that level of precision, it matters where you produce your energy, so the "loss" of potential energy is compensated by the different location of your electric energy.

Remember that matter is just a form of energy. If you have an object that contains energy - it doesn't matter if it is heat or chemical energy or nuclear energy or matter(protons, neutrons, electrons) - that object will be affected by gravity. To lift the object to the top of a mountain you need to spend some energy. Either external or internal. Internal meaning that the object looses energy as it is lifted. That can happen if you have a box consisting of perfect mirrors filled with photons moving around inside. The photons inside will loose energy as you lift the box. Which by the way also means that the box weighs less than it's energy content suggests. If you convert matter into photons, send them up to the top of a mountain and convert them back to matter, you will end up with less matter than you started with. Part of the matter i.e. part of the energy was lost in the lifting process. Normally however matter doesn't loose energy when it is lifted. Instead external energy is used to do the job.

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Well I kind of figured out that the photon's energy does in fact depend on the gravitational field.
What about kinetic energy? If you store energy by making a sphere spin at high speed, what will happen to this spin if you move it into a different gravitational potential?

Drakkith
Staff Emeritus
Well I kind of figured out that the photon's energy does in fact depend on the gravitational field.
What about kinetic energy? If you store energy by making a sphere spin at high speed, what will happen to this spin if you move it into a different gravitational potential?

Nothing, it will remain the same. But that's ok, as the object still gains potential energy as you take it up or loses it as you bring it down.

What about kinetic energy? If you store energy by making a sphere spin at high speed, what will happen to this spin if you move it into a different gravitational potential?

You give the kinetic energy more potential energy. That sounds weird but an electron is a form of energy and it's ok to say you give an electron potential energy. So that means you could also talk about the potential energy of any other energy form. You could say you give the kinetic energy of a spinning sphere potential energy even if that terminology is usually not used in physics.
Or you could say you give the mass of the sphere potential energy and treat the kinetic energy as part of the spheres mass.