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I have always used adiabatic process to be fast, so that the system doesn't get enough time to exchange energy in the form of heat. But as I was reviewing adiabatic process from the Resnick, Halliday, & Krane book, the authors claim that:

we assume the process to be carried out slowly, so that the pressure is always well defined.

Now this is completely out of sync what I already know and most web searches also agreeing with adiabatic process being fast.

Which one is right?

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    $\begingroup$ You are correct that in thermodynamics, adiabatic process means a process without transfer of heat. In quantum mechanics though, the term "adiabatic" usually means isentropic or quasi-static. Your example also seems to use to word "adiabatic" in the sense of isentropic process (reversible process). $\endgroup$
    – wcc
    Commented Jul 31, 2018 at 7:46
  • $\begingroup$ @sammygerbil : I don't think that "Possible duplicate question" is same as mine and the answers there are tuned to that particular question. $\endgroup$
    – Global
    Commented Jul 31, 2018 at 8:12
  • $\begingroup$ Of course they are turned to that particular question since they could not have predicted your question. But the issue is the same : whether the speed of the process (kinetics) is tied to its thermodynamics. $\endgroup$
    – sammy gerbil
    Commented Jul 31, 2018 at 8:28
  • $\begingroup$ You are reading far too much into your text's lead-up to the Carnot cycle. Unless the quality of Halliday & Resnick has declined drastically over the last 50 years, your edition certainly addresses the concept of the free expansion of a gas. This is an adiabatic process that is the antithesis of a quasi-static process. An adiabatic process can be fast or slow. All that adiabatic means is that the system in question is not exchanging heat with its external environment. $\endgroup$
    – David Hammen
    Commented Jul 31, 2018 at 11:18

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In Thermodynamics parlance, an adiabatic process is one in which there is no exchange of heat between the system and its surroundings. One way of accomplishing this is to have perfect insulation between the system and surroundings (zero thermal conductivity). In this case, it doesn't matter how rapidly the process is carried out; the heat transfer between the surroundings and the system Q is zero. Another way of accomplishing this in a system that is not perfectly insulated is to first carry out whatever deformation (expansion/compression) occurs during the process very rapidly, so there is not adequate time for a significant amount of heat to be transferred. However, in this case, if the final state of the system is supposed to be a thermodynamic equilibrium state, one must slap on insulation after the deformation is complete, and then allow the system to thermodynamically equilibrate with no further heat transfer.

In summary, the term adiabatic process has nothing to do with whether the process is reversible or irreversible, or fast or slow. It just means that, during the process, there is negligible heat transferred either to or from the system.

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Maybe in practice (approximate) adiabatic processes are carried out fast in order to make them as adiabatic as possible, but in theory one could have an isolated system where energy is preserved, which is useful when you want the pressure to be well defined at all times.

You can however assume that any process in a theoretical book is carried out slowly, because most of them are assumed to be reversible.

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Usually the definition of adiabatic process is that there is no heat or matter transfer between the system and surroundings. This definition is not entirely correct.

Let's take a cylinder divided by a piston. There is a gas in one half of it. Now you move the piston very-very fast, so that the gas can fill all the cilinder's volume. You have moved the piston almost instantly, much faster than the speed of gas molecules. Although there was no mass or heat exchange with surroundings this is not an adiabatic process. F.e. as the molecules of gas spread around all the available volume the total energy of the molecules would not change, so the temperature of gas would not change, etc.

The usual formula of adiabatic process is derived assuming that the parameters of the system are changing very slowly compared to the speed of molecules in the system.

In practice when you deal with actual gases this assumption usually holds. Speed of molecules is about kilometers per second, no pistons moves that fast. But there are some heat leaks. And the slower the process, the greater is the influence of the heat leaks.

So, the adiabatic process is a process slow enough (compared to the speed of particles in the system), and fast enough, so that the influence of heat leaks is not significant.

Theoretical physicists usually have to care about the first part of this definition ("isn't it said that the system is isolated?")

Experimental physicists usually have to care only about the second part.

UPDATE to avoid (or add) some confusion.

Looks like there are different definitions of "adiabatic" process. According to one of them the above-described gas expansion IS called adiabatic.

But neither of definitions says the adiabatic process has to be fast. Making the process fast is only an experimental trick required to reduce the influence of heat leaks.

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  • $\begingroup$ Would it be right to say that an adiabatic process is "fast" enough such that there is no heat exchanged with the environment and "slow" enough such that the internal pressure change is smooth and well defined? $\endgroup$
    – Global
    Commented Jul 31, 2018 at 9:13
  • $\begingroup$ @Global I think that's correct. One more note: I think that "slow" part of definition is much more important for understanding adiabatic process. The "fast" part is only required if/when the system is isolated not good enough. $\endgroup$
    – lesnik
    Commented Jul 31, 2018 at 9:24
  • $\begingroup$ Re Although there was no mass or heat exchange with surroundings this is not an adiabatic process. This is completely incorrect. In the limit of replacing your piston with a valve that is opened quickly, the process you described represents the free expansion of a gas. This is the canonical example of an irreversible adiabatic process. $\endgroup$
    – David Hammen
    Commented Jul 31, 2018 at 11:25
  • $\begingroup$ @DavidHammen I understand your point. Apparently there are different definitions of "adiabatic", or at least different practices to use this term. When they say "formula of adiabatic process" they mean reversible process. Than again, there are "adiabatic invariants". Looks like we read different books. But may be you are right and my answer requires amendment. $\endgroup$
    – lesnik
    Commented Jul 31, 2018 at 11:54
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    $\begingroup$ @DavidHammen This answer is completely correct, you're simply using a different definition of adiabatic. An adiabatic process can also be defined as one where $\Delta S = 0$, which is more restrictive than just $\Delta Q = 0$. This is the proper definition, as it matches how it's used in the adiabatic theorem, adiabatic invariants, etc. $\endgroup$
    – knzhou
    Commented Jul 31, 2018 at 11:58

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