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I've read about the Combined gas law which said:

The ratio between the pressure-volume product and the temperature of a system remains constant.

My question is: Does this law also works on solids? If not, Is there any kind of equivalent law?

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  • $\begingroup$ what is the pressure of a solid? $\endgroup$ – pentane Jul 7 '18 at 21:24
  • $\begingroup$ The pressure in a pressurised fluid tank in which the solid is immersed? $\endgroup$ – Philip Wood Jul 7 '18 at 22:18
  • $\begingroup$ @pentane, I suppose that pressure in a solid would be the amount of force you are producing on it in order to compress it. $\endgroup$ – Ender Look Jul 8 '18 at 2:22
  • $\begingroup$ @PhilipWood, I was not talking exactly about that but could also be. I'm not sure if my idea is correct, but wouldn't the pressure in a solid be the amount of force exerted on the solid (in order to compress it). $\endgroup$ – Ender Look Jul 8 '18 at 2:24
  • $\begingroup$ @Ender Look. If you exert "a force" on a solid you will cause the solid to accelerate! To exert a pressure requires a combination of forces pushing at right angles on the faces of the solid. $\endgroup$ – Philip Wood Jul 8 '18 at 7:30
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For small changes in the state of an ideal gas you can derive from $pV=nRT$ (by taking logs and then taking differentials) the relationship$$\text{d} \ln V=\frac{1}{T}\text{d}T-\frac{1}{p}\text{d}p.$$This has the same form as Chester Miller's relationship for a solid, so you can regard $\frac{1}{T}$ as his $\alpha$, and $\frac{1}{p}$ as his $\beta$ for a gas!

So, to answer the question, the $p, V, T$ relationship for gases does not work for solids, but in differential form the same law does apply to gases and solids. But note the comment of my2cts about relative magnitudes: $\alpha$ and $\beta$ are much smaller for a solid than for a gas. This implies that the magnitudes of small changes $\text{d}T$ and $\text{d}p$ over which $\alpha$ and $\beta$ are approximately constant is much smaller for a gas than for a solid.

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$$dlnV=\alpha dT-\beta dP$$ where $\alpha$ is the coefficient of volume thermal expansion and $\beta$ is the bulk compressibility (both functions of temperature and pressure).

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The product of pressure and volume divided by temperature equals the number of moles of an ideal gas time the universal gas constant. This relationship comes from the ideal gas law- it does not apply to solids

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No it does not apply. Solids have a much smaller thermal expansion coefficient than an ideal gas. An ideal gas at room temperature expands by 0.3% per degree. A solid typically expands by a 200 times smaller amount.

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  • $\begingroup$ 200 times less but it does, right? So... with an enormous pressure, should it work? $\endgroup$ – Ender Look Jul 7 '18 at 21:20

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