Thermodynamics: Mixtures and Psychrometrics

Thermodynamics becomes practical the moment we stop dealing with “pure substances” and start dealing with what actually flows through ducts, compressors, engines, and stacks: mixtures. In environmental control systems, the most common working fluid is moist air, a mixture of dry air and water vapor. In combustion and many industrial processes, gas mixtures determine reaction rates, flame temperature, and emissions. This article focuses on the thermodynamics of ideal gas mixtures and psychrometrics, with an emphasis on air-water vapor and HVAC applications.

Ideal Gas Mixtures: The Core Model

Many engineering calculations treat common gases as ideal under moderate pressures and temperatures. For mixtures of ideal gases, two principles are foundational:

Dalton’s Law of Partial Pressures

For a mixture occupying a volume $V$ at temperature $T$, the total pressure is the sum of partial pressures:

$p={\sum }_i{p}_i$

Each partial pressure $p_i$ is the pressure the species would exert if it alone occupied the mixture volume at the same $T$. For ideal gases, partial pressure ties directly to mole fraction:

$p_i=y_{i}p$

where $y_i=n_i/n$ is the mole fraction.

Amagat’s Law of Partial Volumes

For ideal gases, the mixture volume can be treated as the sum of “partial volumes”:

$V={\sum }_i{V}_i$

This is less used in HVAC practice than Dalton’s law, but it reinforces a key idea: ideal mixture behavior is driven by additive contributions.

Mixture Properties: What Adds and What Does Not

For ideal gas mixtures, some properties combine neatly:

• Molar mass: $M={\sum }_i{y}_i{M}_i$
• Gas constant: $R=\frac{\bar{R}}{M}$, where $\bar{R}$ is the universal gas constant
• Internal energy and enthalpy (ideal-gas assumption): depend only on temperature, and mixture values are mole- or mass-weighted averages at the same $T$:
• $\bar{h}(T)={\sum }_i{y}_i{\bar{h}}_i(T)$ (molar basis)
• $h(T)={\sum }_i{w}_i{h}_i(T)$ (mass basis)

A frequent source of confusion is switching between mole fraction $y_i$ and mass fraction $w_i$. HVAC calculations for moist air often use mass-based ratios (water per dry air), while combustion calculations often begin on a molar basis because chemical equations balance in moles.

Moist Air as a Working Fluid

Moist air is modeled as a binary mixture: dry air + water vapor. Under typical HVAC conditions, both components can be approximated as ideal gases, so Dalton’s law applies well.

Humidity Ratio (Specific Humidity)

The most used composition variable in psychrometrics is the humidity ratio $W$, defined as the mass of water vapor per mass of dry air:

$W=\frac{m_v}{m_a}$

Using Dalton’s law and ideal-gas relations, one can relate $W$ to vapor partial pressure $p_v$ and total pressure $p$:

$W=0.62198\frac{p_v}{p-p_v}$

The constant 0.62198 is the ratio of molecular weights $M_v/M_a$ (water vapor to dry air). This equation is central to understanding how pressure affects air conditioning performance. At lower ambient pressure (high altitude), the same vapor partial pressure corresponds to a different humidity ratio, shifting psychrometric behavior.

Relative Humidity

Relative humidity $\varphi$ measures how close the vapor is to saturation at the same temperature:

$\varphi =\frac{p_v}{p_{sat}(T)}$

Here $p_{sat}(T)$ is the saturation pressure of water at temperature $T$. Relative humidity is intuitive for comfort, but it is not conserved across heating or cooling processes. The humidity ratio $W$ is far more useful for mass balances because it directly tracks how much water is in the air.

Dew Point Temperature

The dew point is the temperature at which the existing vapor partial pressure equals saturation pressure:

$p_v=p_{sat}(T_{dp})$

Dew point is practical in condensation control. If a surface temperature drops below dew point, moisture will condense regardless of the current dry-bulb temperature. This is why duct insulation, window performance, and chilled-water coil temperatures must be evaluated against dew point, not relative humidity alone.

Enthalpy of Moist Air and HVAC Energy Balances

Psychrometric calculations often use enthalpy per unit mass of dry air. A common model expresses moist-air enthalpy as the sum of dry-air sensible enthalpy and water-vapor enthalpy:

$h\approx h_a(T)+W{h}_v(T)$

With appropriate reference states, this becomes a convenient linear form in $T$ over typical HVAC ranges. The key operational insight is that HVAC processes rarely change “temperature only.” They change both sensible and latent energy:

• Sensible heating/cooling: primarily changes dry-bulb temperature at nearly constant $W$
• Humidification/dehumidification: changes $W$ and therefore latent load

When an air stream is cooled below its dew point on a cooling coil, water condenses and drains away. That process reduces $W$, not just $T$, and it is why cooling systems often handle both temperature control and moisture removal.

The Psychrometric Chart: What It Represents

A psychrometric chart is a graphical solution map for moist air at a fixed total pressure. It connects:

• Dry-bulb temperature
• Humidity ratio $W$
• Relative humidity $\varphi$
• Wet-bulb temperature
• Dew point temperature
• Enthalpy (often aligned with wet-bulb lines)
• Specific volume

The chart is not magic; it is simply the thermodynamic and saturation relationships plotted for quick use. One critical limitation is that it is pressure-specific. Charts are typically published for standard atmospheric pressure. For high-altitude design, pressure corrections matter because the relationship between $W$, $p_v$, and $p$ changes.

Common HVAC Processes on the Chart

Sensible Heating

Air passes over a heater without adding moisture. On the chart, the state moves horizontally to the right (increasing dry-bulb temperature) at nearly constant $W$.

Sensible Cooling (Above Dew Point)

Air cools without condensation. The state moves left at constant $W$ until it hits the saturation curve.

Cooling and Dehumidification

Once the air reaches saturation and continues cooling, condensation occurs. The state follows a path down and left, reducing both $T$ and $W$. The slope of this path depends on coil surface temperature and bypass effects.

Humidification

• Steam injection adds moisture and heat, increasing $W$ and typically raising $T$ unless controlled.
• Evaporative humidification can increase $W$ while reducing dry-bulb temperature, using the air’s sensible heat to evaporate water. In the ideal adiabatic case, enthalpy remains approximately constant, and the state trends toward higher humidity along nearly constant enthalpy (often close to constant wet-bulb) lines.

Why Mixture Thermodynamics Matters in Combustion

In combustion, air is a mixture (primarily $N_2$ and $O_2$ with minor components), and products are a mixture (commonly $C{O}_2$, $H_{2}O$, excess $O_2$, and $N_2$). Ideal-gas mixture tools enable:

• Determining reactant and product composition via mole balances
• Estimating adiabatic flame temperature using energy balances with mixture enthalpies
• Relating excess air to oxygen in exhaust and to efficiency impacts

Water vapor plays a major role in combustion thermodynamics because it has high heat capacity and participates as a major product, affecting flame temperature and heat transfer. Moisture in the inlet air, which varies with psychrometric conditions, also affects mass flow rates and, in precise calculations, changes the stoichiometry on a per-kilogram-of-dry-air basis.

Practical Engineering Takeaways

1. Use the right composition variable. Relative humidity is a comfort metric; humidity ratio $W$ is a mass-balance metric. For equipment sizing and moisture control, $W$ is often the more stable choice.
2. Know when condensation starts. Dew point is the trigger for liquid water formation. Surface temperatures below dew point create condensation risk even at modest relative humidity.
3. Pressure matters. Psychrometric relationships embed total pressure. High-altitude HVAC design and any system operating under nonstandard pressures should not rely on a standard chart without correction.
4. Mixture enthalpy enables real energy accounting. HVAC loads split into sensible and latent components. Treating moist air as a mixture clarifies where energy goes when water evaporates or condenses.
5. The ideal-gas mixture model is powerful but bounded. It performs well for typical air-water vapor HVAC conditions and many combustion calculations, but accuracy depends on staying within ranges where ideal behavior is a good approximation.

Thermodynamics of mixtures and psychrometrics is ultimately about translating composition into properties and then into decisions: coil selection, humidifier strategy, condensation control, ventilation rates, and combustion performance. Mastering the mixture model and moist-air relationships turns “air” from a vague background substance into an engineered