Page 104 - Industrial Ventilation Design Guidebook

4,2 STATE VALUES OF HUMID AIR; MOLLIER DIAGRAMS AND THEIR APPLICATIONS 69

The state of equilibrium differs from the equilibrium between water arid
pure water vapor in that, in a gas phase, there is also inert gas (dry air)
present. This means that the water pressure is equal to the total gas pressure,
p = pi + Ph-> not to the water vapor pressure p h.
In a state of equilibrium the chemical potentials of water and water vapor
are equal:

where the subscript v refers to water and h to water vapor. Notice that
p = pi + p h.
From Eq. (4.95) the partial pressure of water vapor p h can be solved for,
and we see that it is dependent on temperature and the partial pressure of
dry air:

Next we will show that the dependence of water vapor pressure on the partial
pressure of dry air is very small, and consequently a good approximation is

To show this, Eq. (4.95) is differentiated, and we get

On the other hand,

where s v is the specific entropy of liquid water, s h is the specific entropy or
water vapor, v v is the specific volume of water, and v h is the specific volume
of water vapor. Notice that v h = 1/ph- Substituting Eqs. (4.99) in Eq. (4.98),
we obtain

and it follows that

tj
On the other hand, while /x = h - Ts, in accordance with the balance clause (4.95),

and it follows that

Substituting this equation in Eq. (4.100), we obtain