# Calculating the $\frac{dp}{dT}$ slope using Clausis-Clapeyron

I've produced experimental data over how the boiling point of water varies with pressure and temperature and plotted this in a PT graph. I would like to verify my results using theory. The Clausius-Clapeyron equation appears to be exactly what I want. I did manage to find a table over heat of vaporization depending on pressure, so that this version of Clausius-Clapeyron is almost applicable:

$$\frac{dP}{dT}=\frac{L}{T\Delta v}$$

However, I don't have any values for $\Delta v$. So what are my options? Is there some approximation I can make to find the value for $\Delta v$ or is there another version of Clausius-Clapeyron I can use to find $\frac{dP}{dT}$ using freely available tables? Or would someone suggest another way of verifying my results?

## 1 Answer

The usual approximation is to disregard liquid volume against vapor volume, and to consider the latter to be that of an ideal gas, so you get $\Delta v = RT - 0 = RT$ and so

$$\frac{dP}{dT}=\frac{L}{RT^2}$$

If you simply want to check your results, there are also plenty of available resources on-line with boiling points for water as a function of pressure, such as this.