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Mass/energy equivalence question


Prometheus

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I understand energy is defined as the potential to do work, and is a property of a system depending on the systems configuration.

I have also heard that E=mc^2 implies that energy and matter are equivalent. Would this equivalence not then imply that mass is also a property of a system dependent upon its configuration? I'm not sure what that really means. 

 

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3 hours ago, Prometheus said:

I understand energy is defined as the potential to do work, and is a property of a system depending on the systems configuration.

Certain types of energy, such as potential energy, are dependent on the configuration.  

Quote

I have also heard that E=mc^2 implies that energy and matter are equivalent. Would this equivalence not then imply that mass is also a property of a system dependent upon its configuration? I'm not sure what that really means. 

Energy and mass, not matter. Mass is a form of energy.

Yes, mass will be a property of the configuration. If you have an electron and a proton, separated and with no KE, you will have a certain mass. If you combine them into a hydrogen atom, it must release energy (the PE goes down by 27.2 eV, and the KE goes up by half that amount). The Hydrogen has less mass in the amount of 13.6eV/c^2

If you absorb a photon with energy E and excite the atom, the mass will increase by E/c^2

These effects have been experimentally confirmed.

 

 

 

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3 minutes ago, swansont said:

Certain types of energy, such as potential energy, are dependent on the configuration.  

What types of energy are not dependent on configuration. I came across the idea of internal energy, but that seems to refer to an entire system.

 

28 minutes ago, swansont said:

Energy and mass, not matter. Mass is a form of energy.

A distinction i had not appreciated. So we may say that the mass of a system is dependent upon its configuration. And just to clarify, i take configuration to mean the relations in forces acting between objects (usually dependent on distance).

 

34 minutes ago, swansont said:

If you combine them into a hydrogen atom, it must release energy (the PE goes down by 27.2 eV, and the KE goes up by half that amount)

So when we talk about the conservation of energy we should more properly speak of mass/energy conservation?

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26 minutes ago, Prometheus said:

And just to clarify, i take configuration to mean the relations in forces acting between objects (usually dependent on distance).

Not really forces, no, although they may be present and indirectly contributory.

consider a (small) tank containing a hydrogen and oxygen mixture.

This has potential energy you can release by igniting the hydrogen, but there are no forces between the particles whilst the tank sits there.

29 minutes ago, Prometheus said:

What types of energy are not dependent on configuration. I came across the idea of internal energy, but that seems to refer to an entire system.

Well there's translational energy (often called kinetic energy)

vibrational energy

rotational energy

Heat energy (which is really a mixture of the above three)

Then there's nuclear binding energy and some more esoteric types.

41 minutes ago, Prometheus said:

So when we talk about the conservation of energy we should more properly speak of mass/energy conservation?

Sort of but it get very complicated very quicky when you start talking about the tensors in general relativity that contribute to this.

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13 hours ago, Prometheus said:

What types of energy are not dependent on configuration. I came across the idea of internal energy, but that seems to refer to an entire system.

A distinction i had not appreciated. So we may say that the mass of a system is dependent upon its configuration. And just to clarify, i take configuration to mean the relations in forces acting between objects (usually dependent on distance).

Anything that is present due to an interaction with another particle or otherwise depends explicitly on position is configuration-dependent, as you note. If it doesn't, then it's not.

Kinetic energy would be an example of an energy that is not (necessarily) configuration-dependent. In a system of particles that don't have long-range interactions, such as an ideal gas.

 

13 hours ago, Prometheus said:

So when we talk about the conservation of energy we should more properly speak of mass/energy conservation?

It's more that conservation of energy includes mass energy, and mass is not a conserved quantity (though it's a reasonable approximation to say it's conserved at the macroscopic scale, in most cases) 

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7 hours ago, MigL said:

I would go even further, as you can make the argument that all energy could be associated with the configuration of the system.
My citation for this, would be AJB.

Consider an ideal billiard-like system  (no frictional losses, and elastic collisions) The total energy is not dependent on the configuration. (and a proper citation would be a link, because I'm pretty sure there would be a context to such a claim)

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On 3/18/2019 at 9:32 PM, studiot said:

This has potential energy you can release by igniting the hydrogen, but there are no forces between the particles whilst the tank sits there.

Would the force here not be the electromagnetic force responsible for the oxidation? And would that process not be dependent upon the configuration of the electrons in the hydrogen and oxygen atoms?

Still thinking about kinetic energy examples, but one thing at a time.

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47 minutes ago, Prometheus said:

Would the force here not be the electromagnetic force responsible for the oxidation? And would that process not be dependent upon the configuration of the electrons in the hydrogen and oxygen atoms?

Still thinking about kinetic energy examples, but one thing at a time.

 

To be honest you are overthinking this.

 

Configuration is a geometrical term which (in this case) means the disposition in space of all the parts of a system.

Potential energy is that energy which will (in general) change when you change the disposition i.e. move the parts of a sytem to new locations relative to each other.

The exceptions are systems such as a body orbiting the Earth at constant distance from the centre, and multipart systems where some parts gain PE in the reconfiguration, and some loose PE with a net overall zero change to PE.

The concept was introduced in connection with Mechanical Energy, and is best understood this way.

The principle of conservation of Mechanical energy states

The total mechanical energy of an isolated mechanical system is constant.

Mechanical energy can be divided into Potential Energy and Kinetic Energy, so this means that their sum is constant.

Consider a heavy pendulum swinging from a fixed point above the Earth in the Earth's gravitational field.

At the bottom of its swing it has some KE as it sweeps past the low point and some PE due to its height above the centre of the Earth.

At the top of its swing it stops completely so has zero KE.

So what has happened to that KE?

Well once the bob has passed its low point it rises to a greater and greater distance from the centre of the Earth so its PE increases and, in fact at the high point, all its energy is now PE.

Once it has passed the high point it falls again and gains KE at the expense of PE.

Does this help?

 

 

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2 hours ago, studiot said:

To be honest you are overthinking this.

Quite likely. 

So i'm happy with KE + PE = TE, where TE is constant. The PE in this set-up is dependent on the configuration of the system. Does it not then follow that KE is similarly dependent upon the configuration (i.e. where the pendulum is its swing)? However, the TE is not dependent on the configuration - something external would need to be gained or lost for that.

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I think we are all overthinking it, Studiot.

the two definitions of energy I like are AJB's ...
'a property of the configuration of the system'
and Mordred's …
'a property that defines the ability to do work'.

In the case of the idealized system described by Swansont, we can't really talk about the ( global ) system's ability to do work, as you need a temperature difference to achieve that. IE you can only have energy compared to another system ( altering configuration ).
You can however talk about the energy of the individual ( billiard balls ? ) constituents of that same system, and their translational/vibrational energy ( kinetic ). But then again we are back to configuration of the individual constituent particles.

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