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I'm trying to find the temperature of methanol ($\ce{CH3OH}$) when its density is equal to $\pu{780 kg m-3}$.

I know that when $T = \pu{30^\circ C}$ the density is equal to $\pu{783 kg m-3}$, and when $T = \pu{40^\circ C}$ the density is equal to $\pu{774 kg m-3}$.

Is there any formula or a trick to find the temperature corresponding to an intermediate density? Likewise is it possible to find the density at a temperature intermediate between the two?

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    $\begingroup$ There are no simple relation, but if you assume the expansion coefficient does not change with temperature you can use a linear relation for the volume given the same mass. $\endgroup$ – Weijun Zhou Jan 29 '18 at 19:58
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You could use tabulated literature data and then interpolate between the data points. For example, the following plot was created using data from NIST Reference Fluid Thermodynamic and Transport Properties Database (REFPROP) – NIST Standard Reference Database 23, Version 9. It shows the liquid saturation line as well as the vapour saturation line.

Density of methanol

In this case, interpolation for a liquid density of $780.00\ \mathrm{kg/m^3}$ yields a temperature of $31.643\ \mathrm{^\circ C}$.

By way of comparison, the calculated liquid density is $781.55\ \mathrm{kg/m^3}$ for a temperature of $30.000\ \mathrm{^\circ C}$, and $772.10\ \mathrm{kg/m^3}$ for a temperature of $40.000\ \mathrm{^\circ C}$.

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    $\begingroup$ Hello and thank you for your answer , would you mind providing a link for this database? Because I would like to be informed about the liquid saturation line as well as the vapour saturation line not just for the methanol but for most popular liquide $\endgroup$ – napi15 Jan 29 '18 at 22:25

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