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Pressure and temperature have opposite effects on density. As temperature increases at constant pressure density decreases and as pressure increases at constant temperature the density increases (and vice versa). The change in density for liquids is smaller compared to gases.

But when we talk about the density change when both pressure and temperature increases, how can we say that the density of liquid decreases as we go towards critical point and the density of the gases increases as we go towards the critical point. Since pressure and temperature have opposite effects on density.

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For $a,b \gt 0$:

$$\frac{\Delta a}{a} \gt \frac{\Delta b}{b} \implies \Delta (\frac ab) \gt 0$$

$$\frac{\Delta a}{a} \lt \frac{\Delta b}{b} \implies \Delta (\frac ab) \lt 0$$


If there are 2 mutually opposite effects, the net outcome depends on what effect is stronger.


Imagine the phase diagram of the compound, figuratively going along both sides of the boiling curve toward the critical point.

For the liquid, the density decrease due thermal motion and formation of nano-cavities is much higher than the density increase due pressure compression. Therefore, the net density change is negative.

For the vapour, the density increase due pressure compression is much higher than the density decrease due gas thermal expansion. Therefore, the net density change is positive.

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  • $\begingroup$ Why is it that for vapour, the pressure compression results in higher density decrease than the increase caused by thermal expansion? I haven't heard about nanocavities and stuff will have a look into that. $\endgroup$ Commented Sep 29, 2022 at 11:39
  • $\begingroup$ Read carefully: For the vapour, the density increase due pressure compression is much higher than the density decrease due gas thermal expansion. $\endgroup$
    – Poutnik
    Commented Sep 29, 2022 at 11:48
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    $\begingroup$ Ah I meant the other way. Got it right in my head but wrong in typing. $\endgroup$ Commented Sep 29, 2022 at 11:49
  • $\begingroup$ I see....... Been there, done that. :-) // Nanocavities get significant when T is approaching Tc. If you think about it, liquid properties have to converge to gas properties somehow. $\endgroup$
    – Poutnik
    Commented Sep 29, 2022 at 11:50

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