14.1 Properties of atmospheric air

Composition and Properties of Air

Composition of Atmospheric Air

Atmospheric air is a mixture of dry air and water vapor. The dry air portion has a nearly fixed composition: about 78% nitrogen, 21% oxygen, and 1% other gases (mostly argon, with small amounts of carbon dioxide, neon, helium, and methane). This composition stays roughly constant up to about 10 km altitude, a region called the homosphere.

For thermodynamic analysis, you treat dry air and water vapor as separate components of the mixture. Dry air behaves as a single pure substance with known properties, while the water vapor content varies depending on conditions. Both components are modeled as ideal gases at typical atmospheric temperatures and pressures.

The ideal gas law applies to each component individually and to the mixture as a whole:

$PV = nRT$

where $P$ is pressure, $V$ is volume, $n$ is the number of moles, $T$ is absolute temperature, and $R$ is the universal gas constant ($8.314 \text{ J/mol·K}$).

Properties of Atmospheric Air

The key thermodynamic properties of atmospheric air are:

• Temperature (dry-bulb temperature): a measure of the average kinetic energy of the air molecules
• Pressure: the total force exerted by the air per unit area, equal to the sum of the partial pressures of dry air and water vapor (Dalton's law: $P = P_a + P_v$)
• Density: mass of air per unit volume, which depends on temperature, pressure, and moisture content
• Humidity: the amount of water vapor present in the air, quantified in several ways (see next section)

The specific heat of dry air at constant pressure is approximately $c_p = 1.005 \text{ kJ/kg·K}$, and at constant volume $c_v = 0.718 \text{ kJ/kg·K}$. These values matter whenever you calculate heat transfer in air-conditioning processes. Note that moist air has a slightly different effective specific heat because water vapor ($c_p \approx 1.86 \text{ kJ/kg·K}$) contributes to the mixture, but for most HVAC calculations at moderate humidity, using the dry air value is a reasonable approximation.

Specific and Relative Humidity

Specific Humidity (Humidity Ratio)

Specific humidity (also called humidity ratio, symbol $\omega$) is the mass of water vapor per unit mass of dry air in the mixture. This distinction matters: the denominator is the mass of dry air, not the total mass of moist air.

$\omega = \frac{m_v}{m_a} = \frac{0.622 \, p_v}{P - p_v}$

where:

• $m_v$ = mass of water vapor
• $m_a$ = mass of dry air
• $p_v$ = partial pressure of water vapor
• $P$ = total atmospheric pressure
• $0.622$ = ratio of the molar mass of water (18.015 g/mol) to the molar mass of dry air (28.97 g/mol)

Typical values range from near zero in very cold, dry conditions to about 30 g/kg in hot, humid tropical air. For example, if $\omega = 10 \text{ g/kg}$, there are 10 grams of water vapor for every kilogram of dry air.

Relative Humidity

Relative humidity ($\phi$) tells you how close the air is to being saturated at its current temperature. It's the ratio of the actual water vapor partial pressure to the saturation pressure at the same temperature:

$\phi = \frac{p_v}{p_g} \times 100\%$

where $p_g$ is the saturation pressure of water at the dry-bulb temperature of the air (you can look this up in steam tables).

A few things to keep straight about relative humidity:

• At $\phi = 100\%$, the air is saturated and can't hold more moisture at that temperature without condensation occurring.
• The same humidity ratio can correspond to very different relative humidities depending on temperature. Warm air has a higher saturation pressure, so the same amount of moisture produces a lower $\phi$.
• Relative humidity is what you feel in terms of comfort. Specific humidity is what you use for mass and energy balances.

Dew Point and Wet-Bulb Temperature

Dew Point Temperature

The dew point temperature ($T_{dp}$) is the temperature at which water vapor in the air starts to condense when the air is cooled at constant pressure and constant humidity ratio. At the dew point, the air becomes saturated ($\phi = 100\%$).

To find the dew point, you determine the saturation temperature corresponding to the actual vapor partial pressure $p_v$. In other words, look up $p_v$ in the steam tables and find the temperature where $p_g = p_v$. That temperature is $T_{dp}$.

A practical example: if the air has a vapor pressure of 1.228 kPa, the saturation temperature for that pressure is about 10°C. So $T_{dp} = 10°C$, and any surface at or below 10°C will collect condensation from this air.

The dew point depends only on the moisture content (at a given total pressure), not on the current air temperature. This makes it a useful single number for describing the moisture level.

Wet-Bulb Temperature

The wet-bulb temperature ($T_{wb}$) is the steady-state temperature reached by a wetted thermometer exposed to an air stream. As water evaporates from the wick, it absorbs latent heat and cools the thermometer. The drier the air, the more evaporation occurs, and the lower the wet-bulb reading drops.

Three relationships to remember:

• $T_{wb}$ is always between the dew point and the dry-bulb temperature: $T_{dp} \leq T_{wb} \leq T_{db}$
• When the air is saturated ($\phi = 100\%$), all three temperatures are equal: $T_{dp} = T_{wb} = T_{db}$
• The difference $T_{db} - T_{wb}$ (called the wet-bulb depression) increases as the air gets drier

The wet-bulb temperature is central to the design of cooling towers and evaporative coolers, because it represents the lowest temperature that evaporative cooling alone can achieve. In a cooling tower, for instance, water is sprayed into an air stream and cooled by evaporation; the water temperature approaches $T_{wb}$ as a theoretical limit.

In practice, you find $T_{wb}$ from a psychrometric chart or from iterative calculation using energy and mass balances on the adiabatic saturation process.

Air Properties in Air Conditioning

Cooling and Dehumidification

Air-conditioning controls temperature, humidity, air cleanliness, and circulation to maintain comfortable indoor conditions. The two types of heat involved are:

• Sensible heat: changes the air temperature without any phase change
• Latent heat: associated with phase change of water (evaporation or condensation) at constant temperature

The dew point determines the boundary between sensible-only cooling and combined cooling with dehumidification. If you cool air above its dew point, you only remove sensible heat and the temperature drops. Once the cooling coil surface temperature falls below the dew point, water vapor condenses out of the air, removing latent heat and reducing the humidity ratio.

For example, if indoor air has $T_{dp} = 12°C$ and you pass it over a coil at 8°C, the air will both cool and dehumidify. If the coil is at 15°C, only sensible cooling occurs.

Psychrometric Analysis

A psychrometric chart plots the relationships among dry-bulb temperature, wet-bulb temperature, dew point, relative humidity, humidity ratio, and specific enthalpy of moist air, all on a single diagram. Every point on the chart represents a unique state of the air-water vapor mixture.

You use the chart (or equivalent equations) to:

1. Identify the current state of the air from any two known independent properties (e.g., $T_{db}$ and $\phi$)
2. Read off all other properties at that state
3. Trace the air-conditioning process path on the chart to find the final state
4. Calculate heating, cooling, humidification, or dehumidification loads

The cooling load for a steady-flow process is calculated from:

$\dot{Q} = \dot{m}_a (h_1 - h_2)$

where $\dot{m}_a$ is the mass flow rate of dry air and $h_1 - h_2$ is the change in specific enthalpy of the moist air between inlet (state 1) and outlet (state 2). Using the dry air mass flow rate here is consistent with defining enthalpy per unit mass of dry air, which is the convention on psychrometric charts.