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Are the following statements, line of reasoning all correct? I'm particularly interested in the last bullet.

  • For a closed system energy is conserved and constant.

  • For an open system energy is not necessarily conserved but is
    constant. In other words if we account for the work done on the
    system, the work done by the system (energy losses and gains due to
    work) and the energy stored in the system, then the net energy is
    constant.

  • The power is the time rate of change of energy.

  • Therefore the net power (over any interval of time) for an open system is equal to zero.

Any caveats?

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    $\begingroup$ Would it be better to say "isolated" instead of "closed" system? In thermodynamic lingo, closed usually just means no mass transfer; but doesn't restrict energy. $\endgroup$ – JMac Aug 21 '18 at 19:12
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    $\begingroup$ what is the difference between conserved and constant? $\endgroup$ – Adam Aug 21 '18 at 20:13
  • $\begingroup$ If by net power you mean mechanical power (turning a turbine for example) then it is not necessarily zero for an open system. $\endgroup$ – Deep Aug 22 '18 at 6:25
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The first example that comes to mind is a hydrogen molecule, which can be viewed as an open system that, when excited (by cosmic rays, for example) into two hydrogen atoms can irreversibly dissociate in such a way that the natural 'internal energy' of the original molecule would increase. So it might be necessary to add a confinement condition. The result would then require showing that, for any 'reasonable' environment, the rate at which the system is compressed is eventually offset by radiation. Naively, it would seem that black holes contradict this statement; if Hawking radiation exists, however, the question would then boil down to whether you associate radiation with an object itself, or its state at a previous time (i.e. do you imagine Hawking radiation as a kind of dissipation, or as dissociating q-'bits' of the original system.)

[Additional caveat: this presumes that an open system has a well defined notion of 'energy'.]

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