# How can I interpolate between two densities at different temperatures?

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?

• 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. – Weijun Zhou Jan 29 '18 at 19:58 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 $40.000\ \mathrm{^\circ C}$.