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Back in the day I learned that a few special thermodynamical processes have special names.

For example, if one keeps $P$ constant, the process is called isobaric, if one keeps $T, V$ or $S$ constant, one gets, correspondingly, isothermic, isochoric or isentropic processes. Similarly, if one keeps $\dfrac{\mathrm{d} \ln P}{\mathrm{d} \ln \rho}$ constant during the process, it is called polytropic, and if $\delta Q = 0$ at any time, the process is called adiabatic.

Now, the question: what is the process called, if one keeps internal energy $U$ constant?

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    $\begingroup$ @Danu, "isentropic" is typically used for hydrodynamical flows, rather than processes. Though I do agree that adiabatic is a bit more general (I add a specification). $\endgroup$ – Alexey Bobrick Nov 11 '13 at 18:42
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    $\begingroup$ When the energy is kept constant, the process is called isoenergetic (or, if you prefer, iso-energetic). $\endgroup$ – Georg Sievelson Nov 11 '13 at 19:16
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    $\begingroup$ Notice that if there is some subtlety and you keep a constant internal energy $U=\text{cte}$ but not a constant energy $E=U+E_{\text{m}}$, by modifying the mechanical energy $E_{\text{m}}$, you should refrain from using standard names like isoenergetic and explain precisely what happens. $\endgroup$ – Georg Sievelson Nov 11 '13 at 19:21
  • $\begingroup$ Dear @GeorgSievelson, thank you, this is exactly what I have been looking for! For completeness, would the term be suitable for flows, which keep specific internal energy constant (remembering your other comment, though)? $\endgroup$ – Alexey Bobrick Nov 11 '13 at 19:25
  • $\begingroup$ I would also gladly consider it as an answer, if you can apply a comment->answer transformation to your reply. $\endgroup$ – Alexey Bobrick Nov 11 '13 at 19:26
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A process where the energy is kept constant is called isoenergetic (or, if you prefer, iso-energetic). It also seems from the literature that a flow where the energy is constant when following a fluid particle is usually called an isoenergetic flow.

Similarly, when the enthalpy is kept constant, the process (or the flow) is said to be isenthalpic (or isoenthalpic). And so on.

Notice that if there is some subtlety and you keep a constant internal energy $U=\text{cte}$ but not a constant energy $E=U+E_{\text{m}}$, by modifying the mechanical energy $E_{\text{m}}$, you should refrain from using standard names like isoenergetic and explain precisely what happens.

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The process with constant internal energy is called free expansion.

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