# Calculating the boiling point of water

1. Apr 2, 2009

### fluidistic

Hi,
I'm looking through wikipedia for a formula to calculate the boiling point of liquids in function of the atmospheric pressure but I didn't find any.
In fact I'm curious what it would be for water on the Moon, Jupiter and so on.
By the way, is the fusion point pressure-dependent? I guess no.
So if a planet has a high pressure at ground level, I could heat up water and put a piece of iron and watching it being liquefied.

2. Apr 2, 2009

3. Apr 2, 2009

### Mapes

The melting temperature is indeed pressure-dependent, but the dependence is small compared to that of the boiling temperature. It's a function of the volume difference between the two phases, which is small and doesn't change much for solids and liquids.

4. Apr 2, 2009

### fluidistic

Thank you very much to both.
Do you have the formula?

5. Apr 2, 2009

### Mapes

It's the same that mgb_phys mentioned, the Clausius-Clapeyron relation. For a phase change to occur (at constant temperature and pressure), the Gibbs free energies must be equal; i.e., $\Delta G=0$ when comparing the two phases. By definition, $G=U+PV-TS$, so $\Delta G=\Delta U+P\Delta V-T\Delta S=0$ and the change in phase change temperature for a given change in pressure is

$$\frac{\partial T}{\partial P}=\frac{\Delta V}{\Delta S}$$

For small changes, we can assume that $\Delta V$ and $\Delta s$ are constant and use the fact that $\Delta S_M=\Delta H_M/T_M$ at the melting temperature ($G=H-TS$ by definition). $\Delta H_M$ is the easily found enthalpy of fusion. So we end up with

$$\Delta T_M\approx\frac{T_M\Delta V}{\Delta H_M}\Delta P$$

6. Apr 2, 2009

### fluidistic

Thanks mapes.