# Relationship between density of water and temperature

How can I find the different temperatures of the water with the same density?

E.g., at approximately what other temperature does water have the same density as at 1°C?

As usual, you can go to Wiki and find this:

The density is seen to be nonmonotonic around 4°C.

I assuming you are referring to the density at 1 deg C and 1 atmosphere of pressure.

The open-source thermodynamic property programs CoolProp and Cantera can help you (Cantera does a lot more than this, but for this discussion, this description should be adequate). These both implement recent multiparameter equations of state for water.

The density can be evaluated from the equation of state with pressure-temperature inputs specifying the thermodynamic state. You can then use density-pressure inputs (state variables) to determine other temperatures that give the same density.

Thermodynamic properties for metastable water (ie. liquid water that is superheated) can be evaluated in the proprietary thermodynamic property program RefProp; they can also be evaluated in CoolProp (with some non-trivial work on the part of the user).

I'm not sure where you would obtain thermodynamic data for ice, so this probably only helps for the liquid phase.

• Would there be a scenario where different temperature share the same density for liquid state? Commented Aug 25, 2020 at 12:03
• As shown in the other answer, the density shows non-monotonic behaviour near the freezing point; I was unaware of this, but assuming this plot is along an isobar, then pressure-density inputs don't result in a unique thermodynamic state (there is no fundamental relation linking these, so it isn't guaranteed to define a unique state). If your question is about the same density but at different pressures, then absolutely there will be a range of different temperatures that have the same density (if the pressure can vary). A P-v diagram of water showing isotherms will help you visualise this. Commented Aug 25, 2020 at 23:32