Psychrometrics and Moist Air

Air in buildings is never dry. It is a mixture of dry air and water vapor, and the amount of vapor it carries controls condensation risk, latent loads, comfort, and indoor air quality. Psychrometrics is the thermodynamics of this mixture, and it rests on a small set of properties that all derive from two ideas: Dalton's law of partial pressures, and the saturation pressure of water as a function of temperature. The standard reference is sea-level atmospheric pressure, p = 101.325 kPa; at altitude the same relations hold with the local pressure, which shifts every humidity ratio and enthalpy computed from it.

The humidity ratio, omega, is the mass of water vapor per unit mass of dry air. It is the conserved quantity in most HVAC processes: heating or cooling air without condensation does not change omega, which makes it the natural horizontal axis of the psychrometric chart. From Dalton's law it follows that:

Relative humidity is the ratio of the actual vapor pressure to the saturation pressure at the same dry-bulb temperature:

Relative humidity is what occupants feel and what most sensors report, but it is not conserved: heating air at constant moisture lowers the relative humidity because the saturation pressure rises with temperature. This single fact explains why winter indoor air feels dry even when the outdoor air was humid. The dew point temperature is the temperature at which the current vapor content would saturate the air: it is found by solving p_vs(T_dp) = p_v. Because vapor pressure does not change in a sensible process, the dew point is conserved along with the humidity ratio, and it is the direct indicator of condensation risk: any surface colder than the dew point will collect condensate.

The wet-bulb temperature is the temperature a thermometer reads when its bulb is kept wet and exposed to moving air. Evaporation cools the bulb until the heat convected from the air balances the latent heat carried away by the evaporating water, and the resulting temperature is the adiabatic saturation temperature. It is measured with a sling psychrometer or an aspirated sensor, and it is enormously useful because dry-bulb plus wet-bulb fixes the full state of the air. The psychrometric relation linking them is:

Finally, the specific enthalpy of moist air, per kilogram of dry air, combines the sensible heat of the dry air, the sensible heat of the vapor, and the latent heat the vapor carries:

Every coil load, every mixing calculation, and every humidification energy balance in this course runs through this enthalpy. Note the datum: enthalpies are relative to 0 C dry air and liquid water, which is fine because only differences ever matter.

Key takeaways

• Humidity ratio and dew point are conserved in sensible processes; relative humidity is not.
• All moisture properties derive from the vapor partial pressure and the saturation pressure curve of water.
• Dry-bulb plus wet-bulb determines the full state through the psychrometric relation.
• Moist air enthalpy h = 1.006 T + omega (2501 + 1.86 T) is the energy measure behind every load calculation.

The psychrometric chart is the graphical form of Session 1's equations, and fluency with it separates engineers who compute air processes from those who merely plug numbers into software. The standard chart plots dry-bulb temperature on the horizontal axis and humidity ratio on the vertical axis. Every point on the chart is a complete air state, and every HVAC air process is a line or a sequence of lines on it. Learning to see processes as geometry is the point of this session.

The dominant feature is the saturation curve, the left and upper boundary of the chart, where relative humidity is 100 percent and the air holds the maximum vapor its temperature allows. Points on this curve have dry-bulb equal to wet-bulb equal to dew point: the three temperatures coincide at saturation. Below and to the right of the curve lie the unsaturated states where buildings operate. Lines of constant relative humidity sweep from the saturation curve down and to the right, crowding near saturation and spreading at low humidity; they are the most visually prominent family after the curve itself.

Three more line families complete the chart. Constant wet-bulb lines run diagonally from upper left to lower right, nearly parallel to constant enthalpy lines (the two coincide closely because adiabatic saturation is nearly isenthalpic, a fact Session 5 exploits). Constant specific volume lines run steeply, nearly vertically, and are used to convert between mass flow and volumetric flow for fan and duct sizing. Constant dew point lines are horizontal, because dew point is conserved at constant humidity ratio, which is why the humidity ratio axis doubles as a dew point scale along the saturation curve.

Locating a state point requires two independent properties. Dry-bulb plus relative humidity is the most common pair: rise vertically from the dry-bulb on the horizontal axis to the relative humidity curve. Dry-bulb plus wet-bulb: rise from the dry-bulb to the diagonal wet-bulb line. Dry-bulb plus dew point: rise from the dry-bulb to the horizontal dew point line (equivalently, the humidity ratio read at the saturation curve for that dew point). Once the point is placed, every other property is read by following its line family back to the scales: horizontally to the humidity ratio axis, along the diagonal to the enthalpy scale, along the steep lines to specific volume.

The chart also enforces feasibility at a glance. A cooling process that would cross the saturation curve is impossible without condensation: the air cannot hold that much vapor at that temperature, so the excess must condense, and the real process bends along or toward the saturation curve. A proposed supply state below the coil's apparatus dew point is unreachable. Developing the habit of sketching the process on the chart before touching a calculator catches these impossibilities early, when they are cheap to fix.

Key takeaways

• The chart's axes are dry-bulb (horizontal) and humidity ratio (vertical); the saturation curve bounds all possible states.
• Any two independent properties fix the state point; all remaining properties are read from the line families.
• Constant wet-bulb lines run diagonally near constant enthalpy lines; constant dew point lines are horizontal.
• Sketch processes on the chart first: impossible processes (crossing saturation, supply below ADP) show up geometrically before they waste calculation effort.

A sensible process changes the dry-bulb temperature without adding or removing moisture. On the psychrometric chart it is a horizontal line: the humidity ratio stays fixed while the state moves left (cooling) or right (heating). Heating coils, reheat coils, and sensible-only cooling (a coil whose surface stays above the dew point) all follow this geometry. The load calculation is the familiar sensible form:

Real cooling coils are rarely sensible-only, so the sensible heat ratio describes the split. SHR is the sensible duty divided by the total (sensible plus latent) duty, and it applies at two levels that must not be confused: the room SHR, set by the space loads (people, lights, envelope, infiltration), and the coil SHR, set by the coil's apparatus dew point and bypass factor. Comfortable operation requires the coil SHR to be at or below the room SHR. If the coil SHR is higher, the coil satisfies the thermostat while leaving excess moisture in the air, and the space relative humidity drifts upward. On the chart, the SHR sets the slope of the process line: a sensible-only process has SHR = 1 and runs horizontally, while a dehumidifying coil has SHR below 1 and its process line angles downward toward the saturation curve, steeper for lower SHR.

There is a useful construction for the room process line. Starting from the room state point, draw a line with the slope corresponding to the room SHR; the supply air state must lie on this line. The slope is often expressed as delta h / delta T, since SHR = q_sensible/q_total = c_p,m deltaT / delta h, so delta h / deltaT = c_p,m / SHR. A room with SHR 0.8 has a steeper line than a room with SHR 0.95, meaning the supply air must be drier relative to its temperature. This construction links the load calculation to the chart geometry and is the standard way to check whether a proposed supply state can actually hold the room conditions.

Sensible heating deserves a brief note because it is where relative humidity surprises originate. Heating outdoor air from 0 C and 80 percent relative humidity to 20 C at constant humidity ratio drops the relative humidity to roughly 20 percent, with no moisture removed anywhere. The "dry winter air" complaint is a sensible heating process, and the remedies are humidification (Session 5) or accepting the low humidity, not a different heater. Conversely, sensible cooling of humid air without reaching the dew point lowers the dry-bulb while raising relative humidity, which is why a mild-climate cooling coil that never condenses can leave a space cool but clammy.

Key takeaways

• Sensible-only processes are horizontal on the chart (constant humidity ratio); the load is m_dot c_p,m deltaT.
• SHR sets the slope of the process line; the coil SHR must be at or below the room SHR for humidity control.
• The room SHR line through the room state locates every feasible supply state.
• Heating at constant moisture lowers relative humidity dramatically; that is the physics behind dry winter indoor air.

When a cooling coil's surface is colder than the dew point of the entering air, vapor condenses on the fins and the air leaves both cooler and drier. This is the central air-side process of comfort cooling, and it is best understood as geometry on the chart plus one energy balance. The geometry: the process follows a straight line from the entering state toward the apparatus dew point (ADP), the effective surface temperature introduced in the heat exchanger course. The ADP point sits on the saturation curve, and the leaving state lies on the entering-to-ADP line at a position set by the bypass factor:

The same mixing form holds for enthalpy and, to a good approximation, for dry-bulb temperature. The bypass factor is a property of the coil and the airflow: deeper coils (more rows), tighter fin spacing, and lower face velocity all reduce it, pulling the leaving state closer to the ADP and increasing the latent fraction. Colder chilled water lowers the ADP itself, which both increases total capacity and rotates the process line toward steeper dehumidification. These are the four handles a designer has on latent performance: rows, fins, water temperature, and airflow.

The condensate rate follows directly from the moisture removed, because the dry air mass flow is conserved while the vapor mass flow is not:

This water has to go somewhere: drain pan, trap, and drain line, sized for the peak rate with margin, because a coil at full latent load produces a continuous stream, not an occasional drip. The condensate also carries away energy, but the enthalpy of the drained liquid is small compared with the air-side duty and is routinely neglected in coil load calculations.

A subtlety worth understanding is what happens at part load. As the cooling demand falls, a modulating chilled water valve reduces flow, the coil surface warms, the ADP rises, and the process line flattens: the coil does less dehumidification per unit of cooling. Meanwhile the room's latent load (people, infiltration) may not fall proportionally, so the space relative humidity rises at part load even though the temperature is controlled. This is the classic part-load humidity problem, and it is why variable air volume systems, face-and-bypass dampers, and reheat all exist: they are different answers to the question of how to keep dehumidifying when sensible demand disappears.

Key takeaways

• The dehumidifying process is a straight line from the entering state toward the ADP on the saturation curve; the bypass factor fixes the leaving position.
• Condensate rate is m_dot_a (omega_in - omega_out); it is continuous at peak load and sizes the drainage.
• Rows, fin spacing, water temperature, and airflow are the four handles on latent performance.
• At part load the ADP rises and the process flattens, which is why humidity control degrades when sensible demand falls.

Adding moisture to air is the mirror image of dehumidification, and it appears in two very different applications: humidification for comfort and process needs (winter heating, hospitals, manufacturing), and evaporative cooling, where the evaporation itself is the refrigeration effect. Both are governed by the adiabatic saturation process. When water evaporates into air without external heat transfer, the latent heat of evaporation comes from the air's sensible heat: the air cools as it humidifies, and the total enthalpy stays nearly constant. On the chart the process follows the wet-bulb line upward and to the left, ending somewhere between the entering state and saturation at the entering wet-bulb temperature. That limit, the entering wet-bulb, is the coldest the process can reach, and the difference between the dry-bulb and the wet-bulb (the wet-bulb depression) is the available cooling potential.

Direct evaporative cooling puts the evaporation in the supply air stream itself: outdoor air passes through wetted media or a spray, cools toward its wet-bulb, and enters the space cooler and more humid. Its performance is quoted as an effectiveness:

Indirect evaporative cooling keeps the moisture out of the supply air. A secondary air stream is evaporatively cooled and then cools the primary stream through a heat exchanger, so the primary air drops in temperature at constant humidity ratio: a horizontal move left on the chart. Two-stage systems combine the two: indirect precooling followed by direct cooling, reaching lower supply temperatures than either stage alone. The choice between them is a humidity question. Direct cooling is simple and efficient but adds moisture, so it suits dry climates and spaces that tolerate humidity; indirect cooling suits applications where the supply humidity must stay low.

Humidifiers trace different chart paths depending on type. Steam humidifiers add vapor at roughly the air temperature, so the process is nearly isothermal: a vertical line upward on the chart, adding enthalpy with the steam. Wetted-media and atomizing humidifiers follow the adiabatic saturation line, cooling the air as they humidify, which means the air usually needs reheat afterward if temperature must be maintained. Ultrasonic and high-pressure atomizing types are adiabatic in the same sense. The energy accounting differs accordingly: steam humidification needs a heat source for the steam (electric, gas, or central steam), while adiabatic types need the heat to come from the air stream or a downstream heater.

Climate suitability for evaporative cooling is read directly from the wet-bulb depression. A hot, dry climate with a 15 K depression offers deep, economical cooling; a humid climate with a 3 K depression offers almost nothing, and direct evaporative cooling there just makes humid air more humid. Design practice in marginal climates sometimes pairs evaporative precooling with conventional cooling, using the evaporative stage when the depression is favorable and bypassing it when it is not. The chart makes the seasonal logic visible: plot the design days, measure the depressions, and the viable operating region draws itself.

Key takeaways

• Adiabatic humidification follows the wet-bulb line; the wet-bulb depression is the available cooling potential.
• Direct evaporative cooling adds moisture to the supply air; indirect cooling does not, at the cost of a heat exchanger.
• Effectiveness epsilon_evap = (T_db,in - T_db,out)/(T_db,in - T_wb,in) predicts the leaving temperature.
• Steam humidification is nearly isothermal (vertical on the chart); wetted-media and atomizing types are adiabatic and cool the air.

Almost every air handler mixes two streams: outdoor air with return air, or in some systems, outdoor air with exhaust for heat recovery analysis. Mixing is adiabatic (no heat is added or removed in the mixing box), steady, and it conserves both dry air mass and water vapor mass. Those two conservation statements plus the energy balance determine the mixture state completely, and the result has a clean geometric reading on the chart.

Let stream 1 have dry air flow m_dot_a1 and stream 2 have m_dot_a2. Dry air conservation gives the mixture flow m_dot_a3 = m_dot_a1 + m_dot_a2. Vapor conservation gives:

The energy balance, neglecting kinetic energy and the small enthalpy of any condensed water, gives the same weighted-average form for enthalpy:

Because both omega and h are flow-weighted averages with the same weights, the mixture state lies on the straight line segment connecting the two state points on the psychrometric chart. Its position divides the segment in inverse proportion to the flow rates: the mixture sits closer to the larger stream. This is the lever rule, and it can be written in several equivalent forms, for example (h₃ - h₁)/(h₂ - h₃) = m_dot_a2/m_dot_a1. The mixture dry-bulb temperature is very nearly the flow-weighted average of the two temperatures, T₃ = (m_dot_a1 T₁ + m_dot_a2 T₂)/(m_dot_a1 + m_dot_a2), which is exact enough for engineering work because the specific heats of the streams are nearly equal.

The lever rule is also a diagnostic tool. If you know the mixture state (measured in the mixing box) and one stream, you can solve for the other, which is how outdoor air fractions are verified in the field without a flow station: measure return, outdoor, and mixed temperatures, and the outdoor air fraction falls out of the temperature version of the mixing equation. The same construction underlies economizer analysis: the mixed state is the true entering condition for the coil, and free cooling is available exactly when the mixed enthalpy is below the return enthalpy.

One caution: the straight-line construction assumes no condensation during mixing. If the line segment between the two states crosses the saturation curve, which can happen when cold outdoor air meets warm humid return air, fog forms in the mixing box and some moisture condenses out. The real mixture then lies on the saturation curve rather than on the straight line, and the excess moisture appears as liquid. In most comfort applications the effect is small, but in cold climates with high return humidity it is a real phenomenon that shows up as wet mixing boxes and frozen dampers.

Key takeaways

• Adiabatic mixing gives flow-weighted averages of humidity ratio and enthalpy; the mixture lies on the straight line between the two states.
• The lever rule positions the mixture closer to the larger stream and inverts to find unknown flows or fractions from temperature measurements.
• The mixed state, not the outdoor state, is the coil's true entering condition.
• If the mixing line crosses saturation, fog and condensation occur and the mixture follows the saturation curve instead.

This final session works a complete air-handling process end to end, using every tool in the course. The system: an air handler serving an office zone, with 20 percent outdoor air and 80 percent return air, a chilled-water cooling coil, and a reheat coil for humidity control. Supply airflow is 2.00 m³/s. Outdoor design: 35 C dry-bulb, 40 percent relative humidity. Room (return) design: 24 C dry-bulb, 50 percent relative humidity. The cooling coil is to deliver air at 13 C dry-bulb and 95 percent relative humidity; reheat then raises it to a 20 C neutral supply. Chilled water enters at 7 C. Atmospheric pressure is 101.325 kPa.

State 1, outdoor air: p_vs(35 C) = 5.628 kPa, so omega₁ = 0.622 x 0.40 x 5.628/(101.325 - 2.251) = 0.01413 kg/kg, and h₁ = 1.006 x 35 + 0.01413 x (2501 + 65.1) = 71.47 kJ/kg. State 2, return air: p_vs(24 C) = 2.985 kPa, omega₂ = 0.622 x 0.50 x 2.985/(101.325 - 1.492) = 0.00930 kg/kg, h₂ = 1.006 x 24 + 0.00930 x (2501 + 44.6) = 47.81 kJ/kg. State 3, mixed air: omega₃ = 0.20 x 0.01413 + 0.80 x 0.00930 = 0.01027 kg/kg; h₃ = 0.20 x 71.47 + 0.80 x 47.81 = 52.55 kJ/kg; T₃ = 0.20 x 35 + 0.80 x 24 = 26.2 C.

State 4, coil leaving: 13 C and 95 percent relative humidity gives omega₄ = 0.00886 kg/kg and h₄ = 35.45 kJ/kg. The specific volume at the mixed condition is about 0.862 m³/kg, so the dry air mass flow is m_dot_a = 2.00/0.862 = 2.32 kg/s. Coil total duty: q_coil = 2.32 x (52.55 - 35.45) = 39.7 kW. Sensible duty: q_sensible = 2.32 x 1.025 x (26.2 - 13) = 31.4 kW, so the coil SHR is 31.4/39.7 = 0.79 and the latent duty is 8.3 kW. Condensate: m_dot_cond = 2.32 x (0.01027 - 0.00886) = 0.00326 kg/s, about 11.7 liters per hour. Approach: 13 - 7 = 6 K, a healthy value for a multi-row coil.

State 5, after reheat to 20 C at constant humidity ratio: h₅ = 1.006 x 20 + 0.00886 x (2501 + 37.2) = 42.61 kJ/kg. Reheat duty: q_reheat = 2.32 x (42.61 - 35.45) = 16.6 kW. The supply air enters the room at 20 C and omega 0.00886 kg/kg; the room process line from the room SHR closes the loop back to the 24 C, 50 percent room state.

Key takeaways

• A complete air-handling process chains mixing, coil, and reheat; each step is a line on the chart and each state point is computed, not guessed.
• The coil SHR must be at or below the room SHR, or space humidity drifts regardless of temperature control.
• Reheat is an energy penalty proportional to the overcooling needed for dehumidification; evaluate lower-ADP or dedicated-dehumidification alternatives.
• Condensate rate, approach temperature, and the five state points are the handover record that makes the design verifiable.