# Approximations behind Clausius-Clapeyron...

1. Dec 4, 2015

### Sch44

Someone who can explain me what approximations there is behind the Clausius-Clapeyron equation or know a good webside where i can read about it.

2. Dec 4, 2015

### Staff: Mentor

1. The gas phase is described by the ideal gas law
2. The molar volume of the liquid is negligible compared to the corresponding molar volume of gas

3. Dec 4, 2015

### Chandra Prayaga

There are no approximations in the Clausius-Clapeyron equation itself. When two phases of a system coexist in equilibrium, the equation relates the slope of the coexistence curve to the latent heat and the change in volume. The article in Wikipedia (https://en.wikipedia.org/wiki/Clausius–Clapeyron_relation) gives a good account. If you are looking at the liquid - gas coexistence, and if the molar volume of the gas is much higher than that of the liquid, you can use that in approximating the equation. A complete description of the approximations that can be made are discussed in the book by Sears & Salinger, "Thermodynamics, Kinetic Theory, and Statistical Mechanics"

4. Dec 4, 2015

### Staff: Mentor

This response is incorrect, and emphasizes the danger in accepting what one finds in an online source like wikipedia.

According to Smith, J. M. and Van Ness, H. C., Introduction to Chemical Engineering Thermodynamics, McGraw_Hill, 4th Edition, 1987 (an actual peer reviewed textbook that had been in widespread use for over 55 years), the equation referred to in wiki as the Clausius-Clapeyron equation is properly designated simply as the Clapeyron equation (Section 6.3, Two-Phase Systems, Eqn. 6.49). They then pose Example 6.3: "For vaporization at low pressures, one may introduce reasonable approximations into Eq. (6.49) by assuming that the vapor phase is an ideal gas and that the molar volume of the liquid is negligible compared with the molar volume of the vapor." The solution to this example then leads to the actual Clausius Clapeyron equation:
$$\Delta H^{lv}=-R\frac{d\ln{P^{sat}}}{d(1/T)}$$
They then continue,"This approximate equation, known as the Clausius/Clapeyron equation, relates the latent heat of vaporization directly to the vapor pressure curve."

Compare what I wrote in post #2 with Smith and Van Ness' description of the approximation.

Chet