Properties of Moist Air

 

1.0 Brief History of Air Conditioning

The art of air conditioning developed gradually from the predecessor arts of cooling, cleaning, heating, and ventilating.

• Leonardo da Vinci built a ventilating fan by the end of the 15th century.
• By the middle of the 19th century, fans, boilers, and radiators were invented.
• Progress in humidifying air aligned with advancements in the textile industry during the 19th century.
• W.H. Carrier (1856-1950) is known as the Father of Air Conditioning.

To understand air conditioning, one must study the properties of its working substance, which is moist air.

2.0 Working Substance in Air Conditioning

Moist air is a mixture of:

• Dry Air: A mixture of various gases.
• Water Vapour: Existing in saturated or superheated states.

Key Characteristics:

• Dry air is a pure substance with a homogeneous and invariable chemical composition.
• Water vapour is also a pure substance.
• Moist air is not a pure substance when condensation or evaporation occurs.

Moist air comprises:

• Fixed Part: Dry air
• Variable Part: Water vapour

Composition of Dry Air:

Component	Molecular Mass (%)	Part by Volume	Part by Mass
N2	28.02	0.7803	0.7547
O2	32.00	0.2099	0.2319
Ar	39.91	0.0094	0.0129
CO2	44.00	0.0003	0.0005
H2	4.003	0.0001	0.0000

Both dry air and water vapour can be treated as perfect gases under low pressure.

2.1 Dalton’s Law of Partial Pressure

For a mixture of non-reacting gases at temperature $T$, pressure $p$, and volume $V$:

• Total number of moles: $n=n_1+n_2+\mathrm{.}\mathrm{.}\mathrm{.}=\mathrm{\Sigma }{n}_i$
• Total mass: $m=m_1+m_2+\mathrm{.}\mathrm{.}\mathrm{.}=\mathrm{\Sigma }{m}_i$

The total pressure ($p$) is equal to the sum of the partial pressures ($p_1,p_2,\mathrm{.}\mathrm{.}\mathrm{.}$).

2.2 Amagat Law of Partial Volumes

In this model, the total volume of a mixture is the sum of the partial volumes of each gas.

2.3 Mole Fractions of Component Gases

The ratio of partial pressure to total pressure is equal to the mole fraction of the gas.

2.4 Molecular Mass of Mixture

The molecular mass $M$ of the mixture can be computed using:

$$M=\mathrm{\Sigma }{y}_i{M}_i$$

where $y_i$ is the mole fraction and $M_i$ is the molecular mass of component gases.

2.5 Gibbs’ Theorem

The internal energy of a mixture is the sum of individual components' internal energies:

$$\text{µ}=m_1{u}_1+m_2{u}_2$$

Specific heat $mC$ can also be expressed similarly.

2.6 Molecular Masses and Gas Constant for Dry Air and Water Vapour

Using mole fractions from the table:

$$M_a=\mathrm{\Sigma }My=28.966$$

Universal Gas Constant $R$ calculations yield:

• For dry air: $R_a=0.2871\text{kJ/kg K}$
• For water vapour: $R_v=0.461\text{kJ/kg K}$

Units:

• Molecular Weight: amu (Atomic Mass Unit), g/mol, Da (Daltons).
  
  

SAMPLE PROBLEM:
One cubic meter of H2 at 1 bar and 25 oC is mixed with one cubic meter of N2 at 1 bar and 25 oC. For the mixture of the same conditions. Determine the following:

1. Mole of fraction of components 
2. Partial pressure of components
3. Mass fraction of  components
4. Molecular weight of component
5. Gas constant of the mixture
6. Volume of the mixture

Understanding Psychrometric Properties: The Basics of Moist Air Thermodynamics

Psychrometry, the study of the behavior of moist air, is essential for understanding a variety of applications, particularly in air conditioning and environmental controls. Unlike pure substances, which require two properties to define their thermodynamic state, a mixture of two substances necessitates a total of three properties. One of these properties can often be the composition of the mixture. In the case of moist air, these properties are collectively known as psychrometric properties.

The Nature of Moist Air

Moist air consists of dry air combined with water vapor. The behavior of water vapor in the atmosphere is unique; it exists at low partial pressures and temperatures, behaving similarly to a perfect gas. Similarly, the partial pressure of dry air is also typically below one atmosphere, allowing both components to follow the ideal gas laws under many conditions.

In practical air conditioning applications, most calculations hinge on the dry air component due to the constantly variable nature of the water vapor component. To help illustrate this, consider a volume $V$ of moist air at pressure $p$ and temperature $T$, which contains a mass of dry air $m_a$ (in kg) and a mass of water vapor $m_v$ (in kg). Here's a simple representation:

• Dry Air:

  • Mass: $m_a$ kg
  • Specific Volume: $V_a$ m³/kg
  • Total Volume: $V$

• Water Vapor:

  • Mass: $m_v$ kg
  • Specific Volume: $V_v$ m³/kg
  • Pressure: $p$

The actual temperature of moist air is referred to as the dry bulb temperature (DBT).

Specific Humidity or Humidity Ratio

Specific humidity, also known as absolute humidity or humidity ratio (denoted by $\omega$), is defined as the ratio of the mass of water vapor to the mass of dry air in a given volume of the mixture:

$$\omega =\frac{m_v}{m_a}=\frac{V\mathrm{/}{v}_v}{V\mathrm{/}{v}_a}=\frac{V_a}{V_v}$$

Where the subscripts $a$ and $v$ refer to dry air and water vapor, respectively.

Using the equations from ideal gas behavior, we can express the relationships for the masses of dry air and water vapor:

$$p_a{V}_a=\left(\frac{R_a}{M_a}\right)T,p_v{V}_v=\left(\frac{R_v}{M_v}\right)T$$

Substituting $m_a$ and $m_v$ into the equation for specific humidity, we can derive:

$$\omega =\frac{M_v{p}_v}{M_{a}p}=\frac{18.016}{28.966}\cdot \frac{p_v}{p}=0.622\cdot \frac{p_v}{p-p_v}$$

The units of $\omega$ are expressed as kg of water vapor per kg of dry air, which can also be multiplied by 1000 for practical measurement:

$$\omega =622\cdot \frac{p_v}{p}\text{(kg w.v. / kg d.a)}$$

According to Dalton's Law, the total atmospheric pressure is the sum of the partial pressures, expressed as:

$$p=p_a+p_v$$

From which we conclude:

$$\omega =0.622\cdot \frac{p_v}{p-p_v}$$

Specific humidity is predominantly a function of the partial pressure of water vapor. As long as the moisture content of the air remains unchanged, the partial pressure of water vapor remains constant. Given that the partial pressure $p_v$ is usually quite small compared to the total pressure $p$, we can approximate $p_a$ as almost equal to $p$.

In essence, if we consider 1 kg of dry air, then the mass of water vapor associated with this dry air can be articulated as:

• $m_v=\omega \text{kg}$

Thus, the total mass of this volume of moist air becomes:

$$m=(1+\omega )\text{kg}$$

This exploration of psychrometric properties not only enhances our understanding of moist air but is also imperative for the design and optimization of air conditioning systems and various environmental controls. Understanding these principles allows engineers to make informed decisions that improve indoor air quality and energy efficiency.

The Dew Point Temperature: Understanding Humidity and Comfort

The concept of dew point temperature (DPT) is crucial in understanding the behavior of moisture in the air and its impacts on comfort, weather, and overall atmospheric phenomena. While relative humidity offers a relative measure of how humid the air is, dew point temperature provides an absolute measure of the water vapor content. This blog post will explore the significance of dew point temperature in relation to moisture, weather patterns, and human comfort.

What is Dew Point Temperature?

Dew point temperature is defined as the temperature to which moist air must be cooled at constant pressure for condensation of moisture to begin. When the air contains water vapor at a temperature $T$ and partial pressure $p_v$, the vapor is typically in a superheated state, creating what we call unsaturated air.

As unsaturated moist air is cooled at a constant pressure, it eventually reaches a saturation temperature $t_d$, corresponding to its partial pressure $p_v$. At this saturation point, the first drop of dew forms, signifying that the air can no longer hold all the water vapor mixed within it—this is when the water vapor begins to condense.

Saturated vs. Unsaturated Air

• Saturated Air: This refers to air that contains the maximum amount of water vapor that it can hold at a given temperature and pressure. When air is saturated, the humidity is 100%, and condensation occurs.

• Unsaturated Air: This type of air contains superheated water vapor and has not yet reached its saturation point. Dew point temperature provides insight into how close the air is to becoming saturated.

The Role of Dew Point in Weather and Comfort

The dew point temperature is always lower than or equal to the air temperature. When the air temperature cools to the dew point, or if the dew point rises to equal the air temperature, phenomena such as dew, fog, or clouds begin to form, indicating that relative humidity has reached 100%.

Once the dew temperature equals the air temperature:

• Dew, Fog, or Clouds Form: As cooling continues—especially in rising air parcels—the water vapor condenses, contributing to precipitation. Increased humidity levels signify a greater amount of moisture available for potential rain and storms.

Understanding Humidity

The dew point temperature serves as a reliable indicator of how "humid" the air feels. In warm, humid conditions, dew point temperatures can rise significantly, often reaching between 75°F to 80°F (approximately 24°C to 27°C). This consistent measurement reveals the absolute amount of water vapor in the air, regardless of the relative humidity:

• Comfort Levels: Most individuals find a dew point of around 60°F (16°C) or lower to be comfortable. When the dew point reaches 70°F (21°C) or higher, many begin to feel sticky or hot. High levels of moisture in the air slow the evaporation of sweat, making it harder for the body to cool itself efficiently.

Measuring Water Vapor

The dew point temperature is crucial for understanding how much "fuel" is available for showers and thunderstorms. As the dew point approaches 75°F (24°C), people often notice the heaviness of the air as the water vapor content rises significantly (approximately 20 grams of water vapor per kilogram of dry air, or about 2% of the air’s mass).

This temperature signifies a point where:

• Equilibrium of Water: When air reaches its dew point at a specific pressure, the water vapor reaches an equilibrium with liquid water—water vapor condenses at the same rate liquid water evaporates.
• Condensation: If the temperature dips below the dew point, liquid water can condense on surfaces (leaves, grass) or around particulates (dust, salt), leading to clouds or fog formation.

The dew point temperature is more than just a metric for weather forecasting; it is a fundamental parameter that influences comfort levels and precipitation. Understanding how dew point relates to air temperature, humidity, and weather patterns is pivotal for meteorologists, HVAC engineers, and individuals alike. During the hot, humid summer months, focusing on dew point rather than relative humidity is often a better gauge of discomfort and moisture levels in the atmosphere. By recognizing the importance of dew point temperature, we can better anticipate weather changes and enhance our comfort in varying climatic conditions.

SAMPLE PROBLEM:

In a dew point apparatus a metal beaker is cooled by gradually adding ice water to the water initially at room temperature. The moisture from the room air begins to condense on the beaker when its temperature is 12.8 oC. If the room temperature is 21 0C and the barometric pressure is 1.01325 bar, (a)find the partial pressure of water vapor in the room air  (b) the Partial pressure of dry air (c) Specific humidity (d)  and parts by mass of water vapor in the room air.

Understanding Degree of Saturation and Relative Humidity

In the study of psychrometry and the behavior of moisture in the air, two important concepts are the degree of saturation and relative humidity. These concepts provide valuable insights into how much moisture air can contain and its implications on comfort and weather conditions.

3.3 Degree of Saturation

The degree of saturation describes the extent to which air is saturated with water vapor. As water vapor is added to a control volume of air at a constant temperature $T$, the partial pressure of water vapor $p_v$ increases until it reaches the saturation pressure $p_s$. At this saturation point, the air can hold no more water vapor, and the system is termed saturated air.

Saturation Pressure and Maximum Specific Humidity:

• At temperature $T$, the maximum possible specific humidity ${\omega }_s$ is defined as:

$${\omega }_s=\frac{0.622\times p_s}{p-p_s}$$

Where:

• $p$: Total atmospheric pressure

Degree of Saturation $\mu$:
The degree of saturation $\mu$, which quantifies how close the air is to being saturated, is defined as:

$$\mu =\frac{\omega }{{\omega }_s}=\frac{p_v}{p_s}\times \frac{(1-\frac{p_s}{p})}{(1-\frac{p_v}{p})}$$

3.4 Relative Humidity

Relative humidity (RH), denoted by the symbol $\mathrm{\Phi }$, is defined as the ratio of the mass of water vapor $m_v$ in a specific volume of moist air to the mass of water vapor $m_{vs}$ in the same volume of saturated air at the same temperature. In simpler terms, it can also be expressed as the ratio of the partial pressure of water vapor to the saturation pressure of water vapor at the same temperature.

Formulations for Relative Humidity:

1. Mass-Based Definition:

$$\mathrm{\Phi }=\frac{m_v}{m_{vs}}=\frac{p_{v}V}{RT}÷\frac{p_{s}V}{RT}=\frac{p_v}{p_s}\times 100$$

2. Volume-Based Definition:

$$\mathrm{\Phi }=\frac{V\mathrm{/}{v}_v}{V\mathrm{/}{v}_s}=\frac{v_s}{v_v}$$

Where:

• $v_v$: Specific volume of water vapor in the actual moist air
• $v_s$: Specific volume of water vapor in saturated air

When $p_v$ equals $p_s$, the relative humidity reaches unity (100%), indicating that the air is saturated.

Direct Measures:

Since partial pressure is a direct measure of the moisture-holding capacity of dry air, relative humidity serves as the most widely understood measure of the degree of saturation in the air.

Relationships Involving Specific Humidity:

• Specific humidity $\omega$:

$$\omega =\frac{0.622\times \mathrm{\Phi }\times p_s}{p_a}$$

Where:

• $p_a$: Partial pressure of dry air

Both the degree of saturation and relative humidity are vital metrics for understanding the moisture content in the air. While the degree of saturation provides a direct indication of how close the air is to saturation, relative humidity offers a practical measure commonly used in various fields, including meteorology and HVAC design. By comprehensively understanding these concepts, we can better appreciate their roles in weather phenomena and comfort levels in different environments.

These metrics also have significant implications for weather prediction, air conditioning, and understanding human comfort levels, making them essential knowledge for engineers, meteorologists, and environmental scientists alike.

Enthalpy of Moist Air

Understanding the enthalpy of moist air is crucial for analyzing energy exchanges in heating, ventilation, and air conditioning (HVAC) systems, as well as for various meteorological and environmental studies. The enthalpy of moist air accounts for both the dry air and the water vapor present within it.

3.5 Enthalpy of Moist Air Formula

The total enthalpy $h$ of moist air can be expressed as:

$$h=h_a+\omega h_v$$

Where:

• $h$ = Enthalpy of moist air (kJ/kg)
• $h_a$ = Enthalpy of dry air (kJ/kg)
• $\omega$ = Specific humidity (kg water vapor/kg dry air)
• $h_v$ = Specific enthalpy of water vapor (kJ/kg)

Enthalpy of Dry Air

The enthalpy of dry air is given by:

$$h_a=C_{pa}t=1.005t(kJ\mathrm{/}kg)$$

Where:

• $C_{pa}=1.005\text{kJ/kg K}$ = Specific heat of dry air
• $t$ = Dry bulb temperature of air (°C)

Enthalpy of Water Vapor

The enthalpy of the water vapor component is expressed in relation to the dew point temperature $t_d$:

$$h_v=C_{pw}{t}_d+(h_{fg}{)}_d+C_{pv}(t-t_d)(kJ\mathrm{/}kg)$$

Where:

• $C_{pw}$ = Specific heat of liquid water
• $t_d$ = Dew point temperature (°C)
• $(h_{fg}{)}_d$ = Latent heat of vaporization at the dew point temperature (kJ/kg)
• $C_{pv}$ = Specific heat of superheated vapor
• $t$ = Dry bulb temperature (actual temperature of the moist air or mixture)

3.6 Humid Specific Heat

The enthalpy can also be rearranged to express its dependence on specific heats at constant specific humidity:

$$h=(C_{pa}+\omega C_{pv})t+\omega (h_{fg}{)}_{0\mathrm{°}C}$$

This can be simplified to:

$$h=C_{p}t+\omega (h_{fg}{)}_{0\mathrm{°}C}$$

Where:

• $C_p=C_{pa}+\omega C_{pv}=(1.005+1.88\omega )(kJ\mathrm{/}kg\cdot d\mathrm{.}a\mathrm{.}(K))$
• $\omega$ = Specific humidity (kg water vapor/kg dry air)

Humid Specific Heat $C_p$

The humid specific heat $C_p$ can be expressed as follows:

$$C_p=(1.005+1.88\omega )(kJ\mathrm{/}kg\cdot d\mathrm{.}a\mathrm{.}(K))$$

The term $C_{p}t$ governs the change in enthalpy of moist air with temperature at a constant specific humidity, while $\omega (h_{fg}{)}_{0\mathrm{°}C}$ reflects changes in enthalpy due to the addition or removal of water vapor in the air.

The enthalpy of moist air is a fundamental concept in thermodynamics relevant to many practical applications. By understanding the components of this enthalpy—namely the contributions from dry air and water vapor—engineers, meteorologists, and HVAC professionals can effectively analyze and manage systems involving moisture, heat, and energy transfer.

This knowledge helps optimize indoor environmental conditions, improve energy efficiency, and predict weather patterns and phenomena involving moisture in the atmosphere.

SAMPLE PROBLEM:

A mixture of dry air and water vapour is at a temperature of  21 0C under a total pressure of 736 mm Hg. The dew point temperature is 15 0C. Find:

a. Partial pressure of  water vapor

b. Relative Humidity

c. Specific humidity

d. Specific enthalpy of water vapor

e. Enthalpy of air per kg of dry air

f. Specific volume of air per kg of dry air

SAMPLE PROBLEM:
Compute the humidity ratio of air at 65 percent relative humidity and 34 oC when the barometric pressure is 101.3 kPa

READ MORE: AREA 3 (AB STRUCTURES & ENVIRONMENT ENGINEERING & BIOPROCESS ENGINEERING &  ALLIED SUBJECTS)