*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 *wet & dry bulb thermometer*
(or *sling psychrometer*),
typically as in the following figure (refer: **Sling
Psychrometer Demonstration**). 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