# How can I estimate the triple point of a substance given the densities of its liquid and solid phases and its enthalpies of fusion and vaporization?

I am trying to find the triple point of H2O given only the densities of water and ice, the enthalpy of vaporization, and the enthalpy of fusion. I know that I should be able to use some combination of the Clapeyron and Clausius-Clapeyron equations to yield a system of two equations in two unknowns, after which I can use a computational engine to solve the system. However, I am having trouble putting this knowledge to use.

A search on stackexchange brought me to the following question, which provides some answers, but confuses me in new ways:

Triple Point Equation

The answer given shows me that I am on the right track, but I am not sure what the lowercase p with the subscripts of sol-liq and liq-vap represents, and while the answerer points out that T1 and P1 are the triple point temperature and pressure, I am not certain of what the T with no subscript is meant to be. My best guesses so far is that the lowercase p is vapor pressure and that the T with no subscript is the standard temperature for the given phase transition.

• With reference to the other post, you can make a P vs T phase diagram. The $p_{sol-liq}, p_{liq-vap}$ are the pressure curves in the phase diagram that separate solid-liquid and liquid-vapour (gas) phases . T and P are the temp (in kelvin) and pressure (bar) you use to plot the graph. The sublimation curve is not given but use the first equation with values for $\Delta H$ indicated underneath it. If you plot this you will easily see the triple point. – porphyrin Oct 31 '16 at 8:43
• I think that you will need some other bit of information to fix the triple point. You can solve the equations with lots of different pairs of values of the triple point. The easiest would be to use the boiling point then your calculated liquid/vapour curve is fixed to pass through this point. – porphyrin Oct 31 '16 at 9:44