[Bored chemist]

  In an expanding universe there isn't the time symmetry we want for Noether's theorem, 

I'm pretty sure there is except at the moment of the big bang.

[alancalverd]

That is still "hot" in comparison to absolute zero (0 k) specifically it should have thermal energy due to its temperature. 

Er, no. It has temperature because of its thermal energy.

[alancalverd]

 It isn't a conserved quantity

That is the only definition of energy. Quantities conserved in classical mechanics include energy and momentum.

[Eternal Student]

Hi.

I'm pretty sure there is except at the moment of the big bang.

   1.  Even that would technically be enough.   We need only one example for the original statement which was many posts ago.   Take your energy source back to that environment (the big bang) and it has a different ability to do useful work.
    2.   There actually isn't time symmetry at most times.   For example, electromagnetic waves drop to lower frequencies whenever they travel through expanding space.   What we thought was Energy E = hf   is just gone because f is lower. 
    This article gets a mention in the forum every now and again but it's been a while, so I'll put the link in here:
https://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/

That (...being a conserved quantity...) is the only definition of energy.

  Yes, I think that was the main thrust of the discussion.

Er, no. It has temperature because of its thermal energy.

   OK.   Cause and effect are a little arbitrary.   We can develop thermodynamics and state variables like Temperature and Pressure without needing to connect it to thermal energy or microscopic statistical mechanics.   When we do connect them, there is a  relationship but no reason why one must be the cause of the other rather than the other way round (as far as I can see anyway).   However, if you want it that way round, that's OK.

Best Wishes.

[paul cotter]

I think heat, or call it thermal energy is a poor choice for the original question, "what is energy". We know from thermodynamics that at most between zero and some fraction of the total may be converted to useful work. Electrical or mechanical energy can, in principle, be 100% converted.

[alancalverd]

Arbitrary? We can add or remove energy from a body, using e.g. electrical power, impact, friction, boiling, radiation, or chemistry. We do not have a source or sink of temperature. I think this distinguishes between cause and effect!

[Eternal Student]

Hi.

I think heat, or call it thermal energy is a poor choice for the original question, "what is energy". We know from thermodynamics that at most between zero and some fraction of the total may be converted to useful work.

    Yes.   Although I'd argue that's why it's a very good choice.

The original old school definition was something like this:
  Scientists define energy as the ability to do work....
     [Taken from US Energy Information Administration,   https://www.eia.gov/energyexplained/what-is-energy/   ]

..energy, in physics,  (is)  the capacity for doing work.
    [Encyclopedia Brittannica,  https://www.britannica.com/science/energy ]

By your statement, we can just throw that definition away or else teach them that thermal energy is NOT energy, it's something else.

Arbitrary?   (about thermal energy causing temperature)..

   OK.   It probably is more sensible that way round.  In the original sentence where the issue appeared, we only needed the idea that the temperature was above 0, so there is thermal energy there.

Best Wishes.   

[Halc]

We just need the universe to cool down until it is cooler.

You'd need an expanding universe to stand any chance of the temperature continuing to fall (things like molecules slow down in an expanding universe and settle to a static co-moving co-ordinate position).
   Before you say, "we'll allow an expanding universe because it is", if you allowed yourself an expanding universe then there are other examples we can find where something doesn't give the right ability to do work.

Been thinking about the bottle thing. I have a universe that is homogeneous, all equal temp and pressure. I have an insulated bottle full of gas at the same pressure as outside, and want to extract energy from it. I wait 20 billion years for the universe to cool and then extract energy from warmth of the bottle and from the pressure therein as well.  Where did that come from?

Well for one thing, energy is not conserved in any non-static metric, and an expanding metric isn't a static one. So thermal energy tends to cool, moving rocks tend to approach zero speed, light redshifts into oblivion.
The bottle seems to represent the energy needed. In an expanding metric, the bottle has kinetic energy due to the sides of the bottle moving towards each other relative to that metric. The rigidity also provides a steady force doing work on the bottle as it resists the expansion of its sides that it would do if it were just free bits. That force•distance is work, and we eventually harvest that work when we open the bottle billions of years from now.

The original old school definition was something like this:
  Scientists define energy as the ability to do work....
     [Taken from US Energy Information Administration,   https://www.eia.gov/energyexplained/what-is-energy/   ]

..energy, in physics,  (is)  the capacity for doing work.
    [Encyclopedia Brittannica,  https://www.britannica.com/science/energy ]

I don't think this is a well thought out definition. It certainly doesn't meet the definition of the kind of energy that is conserved in a closed system in a static metric like an inertial coordinate system. I have hot on one side, and cold on the other. I let them mix and the energy vanishes, violating said energy conservation laws.
It also directly contradicts the definition of entropy, which, if I google it, yields:

1. PHYSICS
a thermodynamic quantity representing the unavailability of a system's thermal energy for conversion into mechanical work, often interpreted as the degree of disorder or randomness in the system.

So if I substitute say Brittannica's funny definition, one gets "a thermodynamic quantity representing the unavailability of a system's thermal capacity for doing work for conversion into mechanical work", which, if you boil it down, says entropy is the portion of capacity for doing work that has no capacity to do work.

No, find a better definition than Brittannica please, one that they're talking about when they say that energy is conserved.

[alancalverd]

I have hot on one side, and cold on the other. I let them mix and the energy vanishes,

If I have a liter of water at 300K (room temperature) and another liter of water at 350K (from the hot tap) the total thermal energy is 650 kcal.

If I mix them I will end up with 2 liters of water at  325K (nice for shaving) with a total thermal energy of ....er....650 kcal.

Or does my handbasin not obey the laws of physics?

[paul cotter]

Halc, the energy in your bottle after 10 billion years was always there, but unavailable to do work due to the lack of a cold sink or pressure differential. That is the problem with heat energy, it may or may not be able to perform work, depending on it's environment.

[Eternal Student]

Hi.

   I like the idea of a force acting on the gas from the sides of the bottle as the universe expands.   You (Halc) have obviously been thinking about this  BUT  we're not going to let you explain away the extra useful work that easily...

Been thinking about the bottle thing. I have a universe that is homogeneous, all equal temp and pressure. I have an insulated bottle full of gas at the same pressure as outside, and want to extract energy from it. I wait 20 billion years for the universe to cool and then extract energy from warmth of the bottle and from the pressure therein as well.  Where did that come from?

     You're being very human or scientist and trying to cling to the idea that energy should have been conserved and so the ability to extract more useful work might have come from somewhere.    The walls of the container might be responsible for giving the energy we can extract from the presssure of the gas (compared to the external universe) but that is all.
     Do this:
     Assume the universe has increased in size by a factor k over the billion years or so.   So the bottle should really be k times bigger but it isn't.   OK... that shows the work available from the pressure MIGHT be due to work put in from the walls  BUT we don't have to allow that to contribute to the useful work we can extract.  Instead we can just waste that bit of work availability if we want.
    Perform a "Joule expansion" of the gas in the bottle.

   We have a gas in one small portion of a container as shown in the diagram.  We just pull out the wall between the two halves of the container.   The walls of the container are insulated so that no energy flows in or out.    What we have is an isothermal change but it's unlike any conventional isothermal expansion you can plot on a PV diagram.   There was no well defined pressure or volume until after a while when the gas particles fill the available space.  The thing just disappears off the PV diagram and re-appears later with a new Pressure and Volume.   This is the textbook example of an irreversible expansion.    This is expansion without extracting any useful work at all.
   Anyway, hopefully you can see where I'm going with this.   Perform a Joule expansion on your bottle of gas to get it to a volume that is the factor of k bigger,  i.e.  as if the bottle had expanded with the universe.  We've just undone all the extra work that was put into the bottle of stuff by the walls in one go.   However, the expanded gas hasn't lost all ability to give us useful work.  The temperature of the gas has not changed.   It is still hotter than the rest of the universe and you can still get useful work out of that.   
    So that's it...  you can't explain that the ability to get some useful work out of the bottle (a billion years later) was due to the force exerted by the walls of the bottle moved through a distance as the universe expanded.   At most, that gives you some extra useful work you could extract just due to the pressure,  it does nothing to explain away the temperature difference that would exist a billion years later and from which you can now extract useful work.

   The situation, I think is very much as you described later:

...energy is not conserved in any non-static metric, and an expanding metric isn't a static one.

   and we could easily say the same about "useful work".   The capacity of a thing (lets say an energy source) to provide useful work changes with time.

I don't think this is a well thought out definition.

   I agree.  In fairness, there are some GCSE physics syllabus' (syllabi ?) which are taught in UK schools which have been trying to move away from that old definition.   However, most of them are still advocating that energy is thought of as some quasi-material thing  rather than just being an abstract conserved quantity that appears in some models we use in physics.
    (I get the impression that most of the contributors to this post agree with that.  Energy is a complicated thing and a single sentence from encyclopedia Britannica isn't going to cover it).

@paul cotter,    your statement seems OK.  Except that there probably is some small portion of extra work available due to the pressure, which we can let Halc have.   The energy due to temperature, we're not letting him have that.  As you say, that was always in the stuff not given to the stuff by the walls of the bottle.

Or does my handbasin not obey the laws of physics?

   That's OK @alancalverd.  You might be a few posts behind.   Your handbasin obeys the laws of modern physics just not the old school stuff.  Unless it's an old school basin, they were great things with a tap that was cold and another that was also cold.  They realy knew how to conserve energy in the old days.

Best Wishes.

[alancalverd]

If you look at my wash basin (preferably before I've shaved) you can see that energy is always conserved but the efficiency of extracting it depends on the source temperature if the sink is not at absolute zero.

Remember Carnot: η = 1 - T_c/T_h

That is as "old school" as it gets - at least "O" level 1960, if not James Watt. If there is any inconsistency with whatever they teach in school today, someone needs to inform everyone who designs builds or uses engines today, or educate a few teachers: physics is about making mathematical models of what happens, not finding pointless ways of confusing students.

[paul cotter]

To return to the original question, I propose the following: energy is the capacity to do work with the limitation that in the case of thermal energy some or all( worst case ) will  not be able to do useful work. This is the reality because thermal energy manifests as random particle motion and hence has a degraded potential for work. 

[alancalverd]

Not according to Carnot or Watt. Kinetic energy is kinetic energy. If you have one last atom whizzing around at random in your elastic cylinder it will eventually collide with the piston and make the train move - as long as the temperature outside is lower!. Physics is relentless.

[paul cotter]

Ok, but to get full use of your thermal energy you would need an infinite 0°k sink.

[alancalverd]

Absolutely true!

[Halc]

If I have a liter of water at 300K (room temperature) and another liter of water at 350K (from the hot tap) the total thermal energy is 650 kcal.

If I mix them I will end up with 2 liters of water at  325K (nice for shaving) with a total thermal energy of ....er....650 kcal.

Or does my handbasin not obey the laws of physics?

That is the problem with heat energy, it may or may not be able to perform work, depending on it's environment.

You both make my point, which is that the laws of physics uses a different definition of energy than the one Britannica uses. The dictionary one isn't conserved in a closed inertial system. The energy you're both taking about is.

Ok, but to get full use of your thermal energy you would need an infinite 0°k sink.

Similarly, to get full use of something's kinetic energy, one requires an infinite mass against which to react.

Energy seems to be an abstract concept, not actually a thing.
What's the kinetic energy of a rock?  Well that's entirely a frame dependent question, so kinetic energy isn't something that just exists, it is simply a computed relation relative to an arbitrary frame. That kinetic energy can only be harvested for work if there is other mass with a relative velocity.

Potential energy has similar issues. What's the PE of the moon? I suppose again that it is a relation with another object. It has less PE in relation to the JWST and more in relation to the Earth.  What PE does it have in isolation? There's actually and answer to that as well but they can only be negative. Does an object having negative potential energy mean that work cannot be extraced from its PE? Of course not. There are all sorts of power generating stations harvesting useful work from the potential energy of say water by simply making it even more negative.

So again, what's the PE of the moon? The answer could be answered if there was a place to put it that was infinitely far from other masses, but of course there is no such place.

[alancalverd]

Please remind me again of the dictionary definition of energy and that defined by the laws of physics.

To the best of my knowledge mgh = ½mv² = msT in all classical physics texts, and the units of work (F.Δx) are the same as those of energy.

[alancalverd]

Similarly, to get full use of something's kinetic energy, one requires an infinite mass against which to react.

No. That would give you maximum transfer of kinetic energy from one object to another. Since the infinite object wouldn't move, you could hardly describe it as useful work!

Energy seems to be an abstract concept, not actually a thing.

Absolutely, which is why modern primary teaching is wrong. It is a conserved quantity in classical physics, and until you understand the notion of conservation, it is meaningless. It is no more a "thing" than speed.

[Eternal Student]

Hi.

  I don't know where to start and I'm sure I will miss some comments.  Sorry - but rest assured that I'm grateful for any time anyone has put in here.

It is a conserved quantity in classical physics, and until you understand the notion of conservation, it is meaningless. It is no more a "thing" than speed.

Energy seems to be an abstract concept, not actually a thing.

I propose the following: energy is the capacity to do work with the limitation that   ...(sometimes it isn't)....

So what is Energy?
 .....
2.    A quantity,  just some number which we might call E.   It just turns out that many physical systems have a quantity which is conserved...

    I think we're all in agreement that "Energy" is an abstract concept and not some quasi-material thing.

 - - - - - - - - - -

physics is about making mathematical models of what happens, not finding pointless ways of confusing students.

   OK but that doesn't have to hold for online science forums, surely.
Obviously the aim is not to confuse students, which is why many of the early posts had comments like this:

The remainder of this post is complicated and just for general interest.  Don't add it to your answers for school level physics....

    However, it can't be a bad thing to have a place where some people can discuss stuff and occasionally point out that some of the models or ideas that were taught in schools and presented as science aren't really all that simple.
   
Best Wishes.