AN607

Rev. 1.7

25

Many equations have been developed to express humidity parameter relationships. They can generally be broken

down into two groups, those developed from thermodynamic principles and equations empirically derived from

experimental data. The Clapeyron and Clausius-Clapeyron equations will be presented as examples of the first

group and the Sonntag, Magnus and Antoine equations as examples of empirically derived expressions. The

empirically derived expressions are generally easier to use but have limitations to the range of use and accuracy.

Approximations may be useful to further simplify calculations and conversions between humidity parameters as

long as the limitations imposed by the approximations are fully comprehended. The use of these equations and

approximations will be discussed below.

Clapeyron Equation

The Clapeyron equation is based on one of the Maxwell thermodynamic relationships contains no approximations

and provides an exact solution. It considers saturation pressure and temperature, the change of entropy

associated with a change of phase and the change in volume of the two phases and represents the slope of the

vapor-pressure curve. The Clapeyron equation can be expressed as follows:

The Clapeyron equation is valid for all phase transitions (solid/liquid, solid/gas and liquid/gas) and represents the

slope of the phase change boundaries. The parameters in this equation that can be directly measured are

temperature, pressure and volume. Entropy and enthalpy can only be measured indirectly in terms of the other

parameters.

p



T

--------

s

v

-------

where:

p



Saturation Vapor Pressure

T

Temperature in °K

s

Entropy Change between the two Phases

v

Volume Change

since:

s

h

T

------- Across a phase transition

=

where:

h

Enthalpy Change between the two Phases

The Clapeyron Equation can be rewritten as follows:

p



T

--------

h

vT

-----------

=

=

=

=

=

=

=