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My Chemistry book states that (talking about compressibility equation):

"A sample with Volume V is subjected to a pressure increase, delta P, and the resulting change in volume, change in V, is measured. The ratio is divided by V; thus, the tabulated value depends only on the substance being measured and not on the geometry of the sample."

I'm not sure exactly how they are drawing this conclusion. How does dividing by (-) volume cause the compressibility factor to not be dependent on the "geometry" of the sample?

Thanks.

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  • $\begingroup$ It doesn't. Generally speaking, this is not true. A solid may have different compressibility values along different directions. Though the book is not talking about solids, I guess. $\endgroup$ – Ivan Neretin Jan 19 '17 at 6:31
  • $\begingroup$ @IvanNeretin Is it true for gases? $\endgroup$ – Idiot Jan 19 '17 at 6:38
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    $\begingroup$ Yes. That's because gases (and liquids, for that matter) are isotropic. $\endgroup$ – Ivan Neretin Jan 19 '17 at 6:41
  • $\begingroup$ "(of an object or substance) having a physical property that has the same value when measured in different directions." $\endgroup$ – Idiot Jan 19 '17 at 6:42
  • $\begingroup$ Can you clarify what that means? What property of a solid is different when measured in "different directions"? $\endgroup$ – Idiot Jan 19 '17 at 6:42
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If you apply an external pressure on an object and analyze the deformational response of the object (say using Hooke's law in 3D), you find that the state of stress and strain within the object are completely uniform and independent of direction within the object (if the object has direction-independent properties to begin with), irrespective of the shape of the object. This is sort of the same kind of thing that happens in thermal expansion, where the object strains uniformly in all directions, and the strains are independent of the object shape.

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