*Atmospheric air*
includes *dry air* and *water vapor*. Recall that for
an ideal gas, enthalpy (h) is a function of temperature only (Δh
= C_{P}.ΔT). Notice also from the ** h-s diagram** for steam that at relatively low temperatures (<60°C)
the water vapor in the air has a constant enthalpy at constant
temperature from saturated vapor through the superheated region,
thus can be treated as an ideal gas.

From Dalton's Law of Partial Pressures we have for a dry-air/water-vapor mixture that the total pressure P is given by:

P = P

_{a}+ P_{v}where subscript a refers to the dry air, and v to the water vapor.

We find it convenient to sketch our processes
for the water-vapor component on a *T-v* diagram (which we
prefer to the ubiquitous *T-s* diagram in common use, since
entropy is not considered in this Section)

Consider the water vapor shown at state (1)
on the diagram. We will find it convenient throughout this section
to evaluate enthalpy with respect to T_{0} = 0°C,
since ultimately we only consider differences in enthalpy. From
the above diagram:

h

_{v@T}= h_{g@T}where g refers to the saturated vapor state.

Note that h_{g@T} can be obtained from
the saturated vapor tables, or one can use Izzi's method, which
has a maximum error of 0.5% at 60°C:

We also evaluate the enthalpy of the dry air
component with respect to T_{0} = 0°C, thus:

since at the temperatures under consideration
C_{P} is approximately 1.00 [kJ/kg°C].

In order to evaluate the enthalpy of the atmospheric
air we need to first find the mass flow rates of both the dry
air and the vapor. We always evaluate these with respect to the
mass flow rate of the dry air, and this in turn leads us to the
definition of **Specific
Humidity **ω,
as follows:

Note that other terms in common usage are *humidity
ratio* or *absolute humidity* to denote specific humidity.
The specific humidity can be conveniently determined in terms
of the partial pressures P_{a} and P_{v} as follows:

Referring to the *T-v* diagram above,
we now define **Relative
Humidity** φ as follows:

Furthermore, we can determine the specific humidity in terms of the relative humidity, and vice versa, as follows:

There is *no* direct method of measuring
specific humidity ω or relative humidity φ thus in this
section we develop the **Adiabatic
Saturation Process** leading to the practical
**Wet & Dry Bulb Thermometer**, or **Sling
Psychrometer**. Consider the channel
below in which air of unknown humidity enters at station (1) and
after absorbing moisture from the liquid pool, exits at 100% relative
humidity at station (2). This process is shown on the *T-v*
diagram below.

__mass flow:__

__energy:__

Referring to the *T-v* diagram above,
since φ_{2}=100%, P_{v2}=P_{g2}, thus:

In order to determine T_{2} and T_{1}
we use a **Sling
Psychrometer** (or **Wet
& Dry Bulb Thermometer**), typically
as in the following figure. The wet bulb is wrapped in a cotton
wick saturated with water, and one swings the thermometer in the
air until a steady temperature is attained. The wet bulb temperature
T_{wb} is then very closely equal to the adiabatic saturation
temperature T_{2}.

Note that the relative humidity is then determined by means of a slide-rule on the handle of the sling-psychrometer, as shown in the above diagram.

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Engineering Thermodynamics by Israel Urieli is licensed under a
Creative Commons Attribution-Noncommercial-Share
Alike 3.0 United States License