Chapter Four: The Clapeyron Equation

Chapter Listing

HELP GO BACK! - Chapter Three: The Maxwell Relations

Clapeyron Equation

Let's take a look one of the Maxwell equations we derived earlier.

This equation relates the partial changes in pressure over temperature at a constant volume to the partial changes in entropy over volume at a constant temperature.

For a pure substance undergoing a phase change the saturation pressure varies solely on temperature. For a phase change, the change in entropy will be the difference in entropy from the first phase to the second. This also applies for the change in volume. Therefore, the equation can be re-written as.

Unfortunately, this formula has no practical use because entropy is very difficult to measure.

However, we can substitute in yet another equation.

Integrating to find the enthalpy change from one phase to another at a constant temperature and pressure we get.

Finally, we can substitute in this equation for entropy and arrive at the long awaited Clapeyron equation.

You have done well to make it this far. Now you are ready to move on to the final stage of your journey. The time has come to derive the Clapeyron-Clausius Equation...

Chapter Five: The Clapeyron-Clausius Equation