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I'm trying to figure out how to say this in a way that makes sense. If I have 5 Joules of energy stored in a capacitor, it seems like this is much more useful energy than say 5 Joules stored as the chemical energy in gasoline.

By this I mean, if you want to use the energy to do something useful, you can always get a higher efficiency using the electrical energy source than burning the gasoline and converting it to useful work either through an internal combustion engine or the Carnot cycle.

Of course if you just want to heat something up, they are identical. However it seems like the electrical energy source has lower entropy than the gasoline energy source. This might not be the correct usage of the word, but it seems like the energy of the electrical source is "less spread out" than that of the gasoline energy source.

Can someone help me understand this concept better, and let me know if this makes any sense at all?

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  • $\begingroup$ Heat engines cannot exceed the Carnot efficiency; other engines can. The reason is that heating transfers entropy but work doesn’t, and entropy can’t be destroyed; thus, the heat engine (which receives heat and outputs work, colloquially) uniquely needs to dump this entropy by heating something else, which sacrifices energy. Does this get at what you’re asking about? $\endgroup$ Nov 3, 2022 at 14:34
  • $\begingroup$ Of course, as you pull energy out of the capacitor the voltage drops as well. This impacts the real-life effectiveness of the energy storage. $\endgroup$
    – Jon Custer
    Nov 3, 2022 at 14:35
  • $\begingroup$ This paragraph almost answers my question: en.wikipedia.org/wiki/… It says "It is possible (in a thermal context) to regard lower entropy as a measure of the effectiveness or usefulness of a particular quantity of energy" So I think what I'm wondering is there a way to quantify how useful non-thermal energy sources are (like a capacitor) also using entropy? $\endgroup$
    – Hunter
    Nov 3, 2022 at 14:55
  • $\begingroup$ @Chemomechanics slight correction to "heating transfers entropy but work doesn’t" because moving any piece of matter transfers entropy from here to there without "loss"; instead it would be better to say "work obtained from entropy transfer via temperature differences increases entropy and reduces efficiency, work itself does not", see Carnot "Reflections on the Motive Power of Fire" $\endgroup$
    – hyportnex
    Nov 3, 2022 at 15:55

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Following Carnot who in his "Reflections on the Motive Power of Fire" demonstrated that in a heat engine the work is done by the "calorique", after Clausius we call entropy, as it drops from a higher temperature source to a lower temperature source. and only in that case, any cyclical engine's efficiency conversion from heat energy to anything else may never exceed the Carnot efficiency $1-\frac{T_{min}}{T_{max}}$ that depends only on the maximum and minimum temperatures at which entropy (calorique) transfer occurs.

A mechanical or electrical work source operating at the same temperature (isothermal) cyclically does not change either its own and its neighborhood's entropy upon work is done. Thus its heat conversion efficiency to work is zero for the two temperatures are the same, $T_{min}=T_{max}$ but it can convert one kind of nonthermal energy into another kind of nonthermal energy with 100% efficiency, for example, an electric motor converts electric energy $IV$ into mechanical kinetic energy, or an ideal capacitor can discharge into an ideal inductor and start oscillation without any dissipation, converting electrical energy to magnetic energy and back.

If, say, instead the electric motor has one temperature at which it generates the magnetic field because of its resistive windings and another at which its shaft is operating one could theoretically increase the overall motor efficiency by adding a reversible Carnot heat engine operating between the temperatures of the winding and the shaft but nobody does this for its obvious "Rube Goldberg" complexity.

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  • $\begingroup$ So one way of interpreting what you are saying is that the capacitor with 5 joules is more useful because the energy can be extracted with everything at room temperature (motor, wires, capacitor all at room temperature). But the gasoline only releases its energy at a high temperature (relative to the engine, car etc.)? $\endgroup$
    – Hunter
    Nov 4, 2022 at 14:27
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    $\begingroup$ yes that is a good and practical summary, but if you say this you must remember that almost all our large scale energy sources ultimately are "heat" sources (exception would be hydroelectric power plants), and we must first do a thermal energy conversion to something else and then use it as efficiently as possible. $\endgroup$
    – hyportnex
    Nov 4, 2022 at 14:35
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Entropy is associated with heat. Electrical work can be converted to mechanical work and back completely, assuming idealized machines. Heat on the other hand cannot be converted into mechanical work completely, even an ideal machine (Carnot cycle). Entropy in a sense is a measure of the energy in heat that cannot be converted to work. I would not use the term "low entropy" energy to characterize electricity, this implies that we can rank energies in terms of entropy. The only entropy associated with electricity is due to non idealities that dissipate some of that energy into heat, in principle, however, these non idealities can be reduced to zero

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    $\begingroup$ Entropy is not necessarily associated with heat. Entropy transfer is, but entropy generation can result from irreversible work with no heat transfer involved. $\endgroup$
    – Bob D
    Nov 3, 2022 at 15:19
  • $\begingroup$ Yes, but as I said, mechanical non-idealities can be reduced to zero. $\endgroup$
    – Themis
    Nov 3, 2022 at 15:22

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