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Is resistance an intensive quantity or an extensive one? And why? Let me present 2 scenarios.

  1. Resistance of a wire: The resistance of a wire depends on area and length. This implies it depends on the "quantity" of the wire taken. Does this mean it is extensive?

  2. Resistance of a cell: As we know, resistance of a cell is $R = \dot G/\sigma$, where $\dot G$ is the cell constant and the property of the cell, and $\sigma$ is the conductivity. Now, this won't depend on the amount of electrolyte taken in the cell. Does this imply resistance is an intensive quantity?

So, my final question is, whether the resistance is an intensive or an extensive quantity and why?

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  • $\begingroup$ Welcome to Chem.SE -- thanks for posting your question here! Can you link to the reference where that cell constant $\dot G$ is defined? It would help to understand your argument in point (2). Thanks! $\endgroup$ – hBy2Py Mar 30 at 16:14
  • $\begingroup$ Ah, nevermind, found a reference. $\endgroup$ – hBy2Py Mar 30 at 16:27
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    $\begingroup$ There's already a good answer, so supplementing it. Consider resistance and resistivity. Resistance is extensive while resistivity is intensive. The resistance of a cell or a wire is a function of its geometry and its resistivity. $\endgroup$ – Eashaan Godbole Mar 30 at 18:47
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To the extent that it's appropriate to treat it as a thermodynamic quantity, given that it's generally a description of a specific, macroscopic system (and thus violates the statistical-mechanical large-numbers assumption of thermo), resistance is extensive, always.

  1. Resistance of a wire: The resistance of a wire depends on area and length. This implies it depends on the "quantity" of the wire taken. Does this mean it is extensive?

Yep! You're spot on on this.

  1. Resistance of a cell: As we know, Resistance of a cell is $R=\dot G/\sigma$ where $\dot G$ is the cell constant and the property of the cell, and $\sigma$ is the conductivity. Now, this won't depend on the amount of electrolyte taken in the cell. Does this imply resistance is an intensive quantity?

Actually, this resistance measure will depend on the amount of electrolyte in the cell. Per here, $\dot G$ is a function of the dimensions of the active portion of the cell, in particular the sizes and shapes of the electrodes, and how far they are from one another. These geometrical characteristics then affect how much electrolyte must be used in order to fill the cell. Thus, the resistance $R=\dot G/\sigma$ is still extensive.

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  • $\begingroup$ But one thing, suppose now i have a cell which is completely immersed in the electrolyte. If i add more electrolyte, of the same concentration, this won't change the resistance of the cell, right? Because the resistance still remains Ġ/σ and the cell constant won't change since the area and the separation between the plates doesn't change. $\endgroup$ – user226375 Mar 30 at 16:45
  • $\begingroup$ @user226375 See my edit, first. Then: <nod>, this a situation where the assumption that resistance can be treated as a thermodynamic quantity can start to break down. However, I would argue that that extra electrolyte you're adding in this situation isn't actually part of the electrochemical cell--it's "spectating", in a certain sense, because little to no current will be passing through it, since it's being added in a region of the apparatus where it's not a functional part of the system. $\endgroup$ – hBy2Py Mar 30 at 17:35

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