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In this answer by Steeven on the meaning of Enthalpy, the following image is used to explain it:

enter image description here

In this comic, I don't understand two things:

  1. Why is the energy required to make space for the rabbit exactly given as $pV$? How would we prove that it is so from first principle?

  2. It is said that magician only has to expend the energy $G$ as work, this suggests that the creation of rabbit from thin air is positive entropy process... but how do we know that? To me, it should be a negative entropy process since the rabbit's whole body is a highly complex and highly ordered thing.


I have also seen this post which asks a similar question but I felt the answers were unsatisfactory.

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Why is the energy required to make space for the rabbit exactly given as pV? How would we prove that it is so from first principle?

Mechanical work is calculated as $dW=p\,dV$. The pressure is that of the atmosphere, which can be assumed to remain constant because it's much larger than the system. Integrate over the system volume $V$ to obtain $pV$. I'm a little confused because you yourself discuss this in this answer.

It is said that magician only has to expend the energy G as work, this suggests that the creation of rabbit from thin air is positive entropy process...

It does not suggest this; the comic's reasoning takes no position on entropy generation. The entropy $S$ here is transferred via heat transfer from the environment.

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  • $\begingroup$ Hmm how can you be so sure that external pressure would also be so high? Maybe there is a point in the process where they hit equilibrium and then the final work depends on processy ou take. $\endgroup$
    – Buraian
    Aug 22 at 2:34
  • $\begingroup$ In the comic , it is that TS can flow spontaneously as heat meaning that delta S is positive, no? $\endgroup$
    – Buraian
    Aug 22 at 2:34
  • $\begingroup$ (1) Earth's atmosphere is assumed. The pressure is 1 atm at sea level. (2) Yes. $\Delta S>0$ for the system. That's the entropy transferred to heat up the rabbit; it has nothing to do with whether the rabbit is "ordered." $\endgroup$ Aug 22 at 5:44
  • $\begingroup$ In my understand, if delta S is positive then the final state would be more disordered than the initial here. But rabbit is a highly oredered biological being, so delta S should be negative I think. $\endgroup$
    – Buraian
    Aug 22 at 6:36
  • $\begingroup$ Initially yes, 1 atm is much higher than 0 , but as it expands it may reach a point where the pressure becomes in equilibrium with the atmosphere. $\endgroup$
    – Buraian
    Aug 22 at 6:36

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