I have seen the argument that one cannot reach absolute zero in a finite number of steps. For instance on Wikipedia, it states

It is impossible by any procedure, no matter how idealized, to reduce the temperature of any closed system to zero temperature in a finite number of finite operations.

This is explained using a diagram which shows that a series of entropy and temperature lowering steps cannot get to zero temperature: enter image description here

But what about if I used a different experimental technique that amounted to taking steps in the $T, S$ plane at a certain slope? Could I not then reach zero temperature in finite steps? As in enter image description here

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    $\begingroup$ Does this answer your question? Why is $0K$ impossible to reach if the heat capacity goes to $0$ as $T$ approaches $0 K$? $\endgroup$ May 1, 2022 at 8:46
  • $\begingroup$ @StephenG-HelpUkraine I don't think so? How does this answer rule out the third diagram I provided? $\endgroup$
    – Kris
    May 1, 2022 at 9:09
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    $\begingroup$ You have drawn an arbitrary diagram and it does not represent any actual process you can make. Just drawing a diagram does not make something possible. $\endgroup$ May 1, 2022 at 9:21
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    $\begingroup$ @StephenG-HelpUkraine Yes but I have no reason to expect a priori that such a thing can't be done and so the argument doesn't seem complete $\endgroup$
    – Kris
    May 1, 2022 at 9:26


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