Psychrometric Chart Explorer

What is a psychrometric chart?

A psychrometric chart is a graph of the properties of moist air at one barometric pressure. Dry-bulb temperature runs along the bottom and humidity ratio, the mass of water vapour carried by each kilogram of dry air, runs up the right-hand side, so every point on the chart is one state of the air. The humidity ratio follows from the vapour pressure: W = 0.621945 pw / (p − pw), where pw is the partial pressure of the water vapour, p is the total pressure and 0.621945 is the ratio of the molar masses of water and dry air.

The curves that rise ever more steeply to the right are lines of constant relative humidity, the highest being the saturation curve, and the sloping straight lines are constant wet bulb, enthalpy and specific volume. Any two independent properties fix a state, and the chart turns those two into all the rest, which is why it is the working tool of air conditioning, drying and much of meteorology. European textbooks often draw the same information as a Mollier h-x diagram, with the two axes swapped.

Using the explorer

The chart opens on air at 25 °C and 50 percent relative humidity at sea level. Drag the point, or tap the chart to move it there; a drag above the saturation curve holds the point on it, since air cannot be more than saturated. With the chart focused, the left and right arrow keys change the dry bulb and up and down change the second property.

The first menu chooses that second property: relative humidity, the wet bulb a sling psychrometer reads, or the dew point a chilled-mirror hygrometer reads. The pressure comes from an altitude, through the standard atmosphere, or from a barometric reading. The process menu draws a second state from the first. A second, smaller plot follows this air as it is heated or cooled with its water held fixed: its relative humidity is 100 percent at the dew point and falls to under 13 percent at 50 °C.

Reading the chart and the readouts

• Dry-bulb temperature is what an ordinary thermometer reads, along the bottom.
• Humidity ratio, W, is read straight across on the right-hand axis, in grams of water per kilogram of dry air. Every horizontal line is air holding the same amount of water.
• Relative humidity is φ = pw / pws, the vapour pressure as a share of the saturation pressure at the dry bulb. The curves are every 10 percent, and the bold one, 100 percent, is saturation.
• Dew point is where a horizontal line from the state meets the saturation curve: cool the air with its water held fixed and it saturates there.
• Wet-bulb temperature is where the sloping wet-bulb line through the state meets the saturation curve. A thermometer with a wet wick in moving air reads close to it, because evaporation cools the wick until the heat flowing in from the air balances the latent heat the water carries away.
• Specific enthalpy, h = 1.006 t + W(2501 + 1.86 t) in kJ per kilogram of dry air, is the heat content counted from dry air and liquid water at 0 °C. Its lines lie almost on the wet-bulb lines, but not exactly.
• Specific volume, v = 0.287042 (t + 273.15)(1 + 1.607858 W) / p, is the volume holding one kilogram of dry air with its vapour: the ideal gas law applied to the mixture, and what turns a duct’s volume flow into a mass flow.

The readouts give all of these to four significant figures, with the vapour pressure and the barometric pressure. Every value is per kilogram of dry air, because the dry air passes through a process unchanged while its water comes and goes.

Worked example: 25 °C and 50 percent relative humidity at sea level

These are the explorer’s opening settings, at the standard sea-level pressure of 101.325 kPa.

• Saturation pressure at 25 °C, from Hyland and Wexler’s equation: pws = 3.1692 kPa.
• Vapour pressure at 50 percent: pw = 0.5 × 3.1692 = 1.5846 kPa.
• Humidity ratio: W = 0.621945 × 1.5846 / (101.325 − 1.5846) = 0.009881 kg/kg, the 9.881 g/kg the readout shows.
• Enthalpy: h = 1.006 × 25 + 0.009881 × (2501 + 1.86 × 25) = 25.15 + 25.17 = 50.32 kJ/kg.
• Specific volume: v = 0.287042 × 298.15 × (1 + 1.607858 × 0.009881) / 101.325 = 0.858 m³/kg.
• Dew point: the temperature whose saturation pressure is 1.5846 kPa, td = 13.86 °C.
• Wet bulb: the wet-bulb equation gives W = 0.008804 at t* = 17 °C and W = 0.01002 at t* = 18 °C, so the wet bulb lies between them, and halving the gap again and again settles on t* = 17.89 °C.

On the chart, the horizontal guide through the point at 9.881 g/kg meets the saturation curve at 13.86 °C, and the dashed wet-bulb guide meets it at 17.89 °C. Half of the enthalpy, 25.15 kJ/kg, belongs to the dry air. The other 25.17 kJ/kg is carried by less than a hundredth of a kilogram of vapour, almost all of it latent heat. The 2501 in the enthalpy equation is the latent heat of vaporisation at 0 °C in kJ/kg, a little more than the 2260 J/g at the boiling point that the latent heat calculator works with.

How the wet bulb and the dew point are found

Two readings are not a single formula of the state. The dew point is the temperature at which the saturation pressure equals the vapour pressure, and Hyland and Wexler’s equation gives the pressure from the temperature, not the other way round. The wet bulb is the temperature t* that satisfies ASHRAE’s wet-bulb equation, W = [(2501 − 2.326 t*) Ws* − 1.006 (t − t*)] / (2501 + 1.86 t − 4.186 t*), in which Ws* is itself the saturation humidity ratio at t*.

Both are solved by bisection. The wet-bulb search starts with the dew point and the dry bulb as its bounds, which always bracket the answer: at t* = t the equation returns the saturation value, at least as wet as the air, and at the dew point it returns less. Each step keeps the half of the bracket that still holds the answer. For the opening state it takes 37 halvings to pin the wet bulb to within 10⁻¹⁰ °C, and 42 for the dew point, whose search starts from the whole range the equations hold for, −100 to 200 °C.

Many dew point calculators use the Magnus approximation instead, td = 243.04 γ / (17.625 − γ) with γ = ln φ + 17.625 t / (243.04 + t). At 25 °C and 50 percent it also gives 13.86 °C, and wherever the dew point is above freezing it stays within 0.06 °C of the exact inversion. Below 0 °C the explorer gives the frost point, over ice, as ASHRAE’s equations do, which Magnus’s coefficients for water do not.

Drawing a process

Choose a process and a second point appears, joined to the first by an arrow. Each process starts from the state set above, works per kilogram of dry air, and opens on settings that suit the opening state.

• Sensible heating or cooling moves the point straight across, because no water is added or removed. Heating to 35 °C takes q = (1.006 + 1.86 × 0.009881) × (35 − 25) = 10.24 kJ/kg, and the relative humidity falls to 28.2 percent without a gram of water taken out. Cooling stops at the dew point.
• Cooling and dehumidifying is what an air-conditioning coil does: it cools the air below its dew point, so water condenses on the fins and drains away. Taking the opening air to 13 °C at 90 percent leaves 8.386 g/kg, so 1.495 g/kg condenses, and the coil removes (50.32 − 34.25) − 0.001495 × 4.186 × 13 = 15.99 kJ/kg, the last term being the heat the cold condensate carries away. Carried on past the leaving state, the coil line meets the saturation curve at 10.94 °C, the apparatus dew point, which is the effective temperature of the wet coil surface. A leaving state whose line would miss the curve is one no coil can produce, and the explorer raises its humidity to the driest a coil can deliver. In a building, a controller holds the leaving temperature at its set point by working a chilled-water valve, the kind of loop the PID controller simulator lets you tune.
• Evaporative cooling runs along the line of constant wet bulb, because the heat that evaporates the water comes from the air itself. At a saturation effectiveness of 80 percent the air leaves at 25 − 0.8 × (25 − 17.89) = 19.31 °C and 87.3 percent, having picked up 2.367 g/kg of water, while its enthalpy rises by only 0.18 kJ/kg, the heat in the water fed in at the wet bulb.
• Mixing two streams puts the mixture on the straight line between them, at the share of the dry air each contributes, because dry air, water and enthalpy are all conserved. Three parts of the opening air with one part of air at 5 °C and 80 percent give W = 0.75 × 9.881 + 0.25 × 4.314 = 8.489 g/kg and h = 0.75 × 50.322 + 0.25 × 15.860 = 41.71 kJ/kg, which is 20.04 °C at 58.2 percent.

Two streams near saturation can mix to a point past the saturation curve, and then the excess condenses as fog. Saturated air at −5 °C and at 30 °C mixed in equal parts lands on the straight line at 12.89 °C and 14.84 g/kg. Once 2.066 g/kg has condensed, the latent heat it releases leaves the mixture saturated at 17.81 °C. Your breath on a cold morning is the same process, and the heat released is the energy of the long plateau on water’s heating curve, run the other way.

Altitude and barometric pressure

A printed chart is drawn for one pressure, usually sea level, and the explorer redraws it for any. At a lower pressure the same vapour pressure means more water per kilogram of dry air, because each cubic metre holds less dry air to share it with. At 1,500 m the standard atmosphere gives p = 101.325 (1 − 2.25577 × 10⁻⁵ × 1500)^5.2559 = 84.56 kPa, and air at 25 °C and 50 percent holds 11.88 g/kg rather than 9.881, about 20 percent more.

The dew point does not change, because it depends only on the vapour pressure, which is 1.5846 kPa either way. The wet bulb falls by 0.43 °C, to 17.46 °C, since water evaporates more readily into thinner air. The specific volume rises to 1.031 m³/kg, so a fan moving a fixed volume of air moves about 17 percent less of it by mass.

Where the equations come from

Every number here comes from ASHRAE Handbook Fundamentals (2017), chapter 1, which treats moist air as a mixture of two perfect gases. The saturation pressure is Hyland and Wexler’s 1983 formulation, one equation over ice and one over liquid water, which meet at the triple point: at 0.01 °C the ice equation gives 611.657 Pa, the accepted triple-point pressure. At 25 °C the equation for water gives 3.1692 kPa against 3.1697 kPa in ASHRAE’s table of the properties of water at saturation, and at 50 °C it gives 12.350 kPa against 12.351 kPa. The standard atmosphere, humidity ratio, specific volume, enthalpy and wet bulb are the handbook’s equations 3, 20, 26, 30 and 33, the last in its ice form, equation 35, when the wick would be frozen. PsychroLib (Meyer and Thevenard, 2019), an open-source library, implements the same equations independently, and the explorer is tested against its published values as well as ASHRAE’s tables.

What this model leaves out

• Real-gas effects. Dry air and water vapour are treated as perfect gases. ASHRAE’s real-gas table puts the saturation humidity ratio at 25 °C at 20.17 g/kg, against the 20.08 g/kg of the perfect-gas equations here, about half a percent more.
• The thermometer’s own error. The wet bulb here is the thermodynamic one, the temperature of adiabatic saturation. A wet-bulb thermometer reads close to it in moving air, but high in still air or with sunshine on the wick.
• How a coil gets there. The coil process takes the leaving state as given and draws a straight line to it. A real coil’s path curves, and its leaving state depends on its surface, its rows of fins and the air speed.
• Fans and pressure drops. Every process runs at one pressure, although a real fan adds a little heat and the pressure falls a little through a coil or a filter.
• Ice and supercooled water. Below the triple point, saturation, relative humidity and the dew point are taken over ice, as ASHRAE’s equations take them. Weather services quote relative humidity over water even below freezing, and supercooled droplets can last well below 0 °C. An evaporative cooler with a wet bulb below 0 °C is left doing nothing.

Common mistakes

• Reading relative humidity as the amount of water. Heating air lowers its relative humidity without removing anything. The opening air heated to 35 °C still holds 9.881 g/kg, at 28.2 percent instead of 50.
• Mixing up the dew point and the wet bulb. The dew point is where the air saturates if it is cooled with its water held fixed; the wet bulb is where it saturates if water evaporates into it. The wet bulb lies between the dew point and the dry bulb, 17.89 °C between 13.86 and 25 °C here, and the three meet only at saturation.
• Using a sea-level chart at altitude. At 1,500 m, 25 °C and 50 percent is 11.88 g/kg, not the 9.881 g/kg a sea-level chart gives, and the specific volume is 1.031 m³/kg, not 0.858.
• Mixing by volume instead of by dry-air mass. 2 m³/s of outdoor air at 4 °C dry bulb and 2 °C wet bulb mixed with 6.25 m³/s of the opening air is 25.8 percent outdoor air by dry-air mass but 24.2 percent by volume, and the volume share puts the mixture at 19.95 °C instead of 19.63 °C. Divide each flow by its specific volume first.
• Reading the wet bulb off an enthalpy line. The two families nearly coincide, but the line of constant enthalpy through the opening state meets saturation at 17.82 °C, not at the wet bulb of 17.89 °C.