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I am confused about the concept of conservation of energy in an isolated system.

1) Does an isolated system mean that it does not have any non conservative forces? If yes, then, is mechanical energy always conserved in an isolated system? If not, what does it mean?

2) Is internal energy conserved in an isolated system?

I looked up conservation of mechanical energy and it says that mechanical energy is conserved in an isolated system with only conservative forces. That seems to imply that there are other types of isolated systems. I am very confused, any help is appreciated. Thank you so much.

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The definition of an isolated system is: "A system that does not interact with its surroundings; that is, its total energy and mass stay constant."[source]

Does an isolated system mean that it does not have any non conservative forces?

No. If you imagine putting an electric circuit into a thermally insulating box, then the electric conservative forces will work just fine to make the currents flow. Isolated systems and conservative forces are two different things.

If yes, then, is mechanical energy always conserved in an isolated system? If not, what does it mean?

Mechanical energy (which would be one type of the internal energy in the system) is not necessarily conserved in an isolated system. The total energy is conserved. You could imagine some of the energy forms that we call mechanical (gravitational potential, kinetic...) being converted into e.g. thermal energy through heat inside the isolated system.

Is internal energy conserved in an isolated system?

Yes. That is half of the definition.

I looked up conservation of mechanical energy and it says that mechanical energy is conserved in an isolated system with only conservative forces.

Yes, this is correct. Conservative forces cause mechanical energy to be conserved generally (changing from potential energies to kinetic energies and opposite). Non-conservative forces are those that cause e.g. heat or so. They convert mechanical energy into something else, such as thermal.

If a system only contains conservative forces, so that it only can convert energy from one mechanical to another mechanical form, and if no energy is added or removed (isolated system), then it follows that the mechanical energy cannot change.

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  • $\begingroup$ Thank you so much! I don't understand your first answer though. In the thermally insulating box (which is an isolated system, I guess) what non conservative force is present that disproves that an isolated system doesn't necessarily only have conservative forces? $\endgroup$
    – laksheya
    Aug 27 '19 at 13:49
  • $\begingroup$ @laksheya You are welcome. You use quite a lot of double negatives here... Your original question was: "Does an isolated system mean that it does not have any non conservative forces?". And I answered that no, is does not mean that. An isolated system can certainly contain conservative forces, such as those within an electric device. But it can also certainly contain non-conservative forces, such as if you put a spinning wheel in the box, and that wheel is slowed down by the non-conservative friction force. $\endgroup$
    – Steeven
    Aug 27 '19 at 13:53
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    $\begingroup$ Thank you! (And sorry for the weird wording of the question.) $\endgroup$
    – laksheya
    Aug 27 '19 at 13:58

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