The h,x diagram in five minutes

The h,x diagram in five minutes#

The Mollier h,x diagram is the map engineers use for moist air. In English-speaking countries the same physics is usually drawn as the psychrometric chart, rotated and mirrored. pyedautils draws it with plot_mollier_hx() (and the lighter plot_mollier_hx_fast()); the numbers behind it come from the psychrometric functions in pyedautils.psychrometrics.

How the numbers on this page were computed

All values on this page were calculated with pyedautils itself, at 450 m above sea level: pressure_from_altitude(450) gives 96 035 Pa. Saturation pressure comes from the piecewise polynomial in Glück, Zustands- und Stoffwerte (ch. 2.1), not from the Magnus formula; between 0 and 25 °C the two differ by less than 0.2 %. At sea level (101 325 Pa) the same air holds about 5 % less water per kg (for example 7.7 instead of 8.2 g/kg at 21 °C and 50 %). Dew points and relative humidities do not depend on the pressure.

Why temperature and humidity belong together#

Comfort, health and the risk of mould always depend on temperature and humidity at the same time. Looking at only one of them, or at two separate graphs, can easily mislead you:

  • Relative humidity changes with temperature. Air at 21 °C and 60 % holds about 9.8 g of water per kg of dry air. Warm the same air to 26 °C and it reads only 44 %. Cool it at a 15 °C outside wall and it reaches about 87 %, enough for mould. The amount of water did not change at all.

  • The same reading means different things. 23 °C feels pleasant at 45 %, but sticky at 70 %.

The h,x diagram shows both in one point. Its position gives temperature, relative and absolute humidity at the same time, and how far each measurement was from the comfort zone.

Reading the diagram#

How to read the diagram, and the most common misreadings.

Axes and curves#

Every state of the air is one point:

  • Up and down is the temperature (°C).

  • Left and right is the absolute humidity x, the grams of water in one kilogram of dry air. Left is dry, right is humid.

  • The curved lines are the relative humidity φ. The bottom curve, 100 %, is saturation: air cannot hold more water. Cool air down to this curve and water condenses on windows and cold walls, or forms fog. That temperature is the dew point (see below).

  • The air pressure, which depends on the altitude, shifts the curves a little. Pass altitude= (or an explicit pressure= in Pa, which then wins) to plot_mollier_hx, and p= or altitude= to state().

How processes move the point#

Each process has a function in pyedautils.psychrometrics:

  • Heating or cooling without adding or removing water moves the point straight up or down (heat(), cool() above the dew point): x stays the same and only the relative humidity changes. Heating makes air relatively drier, cooling makes it relatively more humid.

  • Adding moisture (people, showering, cooking, plants, a humidifier) moves the point to the right (humidify_isothermal(), humidify_adiabatic()). Removing moisture (ventilating with dry air, a dehumidifier) moves it to the left.

  • Mixing two air streams, for example room air and outside air when you ventilate, puts the result on the straight line between the two points (mix()).

from pyedautils.psychrometrics import state

s = state(t=21, phi=0.60, altitude=450)
print(f"x = {s.x * 1000:.1f} g/kg, dew point = {s.t_dp:.1f} °C")
# x = 9.8 g/kg, dew point = 12.9 °C

Common misreadings#

  • Relative humidity is not water content. A high relative humidity does not mean a lot of water. Outside air at 0 °C and 80 % holds 3.2 g/kg, less than room air at 21 °C and 30 % (4.9 g/kg). To compare two airs, compare their x, not their φ: the point further left is the drier one.

  • Heating and cooling move the point vertically, not sideways. In the h,x diagram the temperature is on the vertical axis, so heating or cooling without condensation keeps x and moves the point straight up or down, across the φ curves. (In the psychrometric chart, which is rotated and mirrored, the same process is a horizontal line.) Only when cooling reaches the 100 % curve does the point follow that curve to the left, and water condenses.

  • The curves depend on the air pressure. Use the pressure of your site (pressure= or altitude=). The same air at 21 °C and 50 % holds 7.7 g/kg at sea level (101 325 Pa), 8.2 g/kg at 450 m (96 035 Pa) and 8.7 g/kg at 1000 m (89 875 Pa). Its dew point stays the same (10.2 °C), but a fixed limit in g/kg means a different relative humidity at a different altitude.

  • Mould starts at cold surfaces, not in the room air. A room at 21 °C and 50 % looks fine on the diagram, but the air right at a 13 °C window frame is above 80 %. Read the risk off at the surface temperature, see Dew point: where condensation and mould start below.

  • Single points are not the whole story. Short peaks (showering, cooking) show up as single points to the right; what matters for mould is how long the surfaces stay humid, so look at where most of the points are.

Dew point: where condensation and mould start#

To find the dew point of the room air, go straight down from the point to the 100 % curve: the temperature there is the dew point. Any surface colder than that gets wet: the inside of single glazing, window frames, thermal bridges, outside corners, walls behind wardrobes.

Mould does not even need visible water. It starts to grow when the air right at a surface stays above about 80 % relative humidity for some time. That happens a few degrees above the dew point:

Room air

Water content

Dew point (condensation)

Mould risk at surfaces below

20 °C, 40 %

6.1 g/kg

6.0 °C

9.3 °C

21 °C, 50 %

8.2 g/kg

10.2 °C

13.6 °C

21 °C, 60 %

9.8 g/kg

12.9 °C

16.4 °C

The last column is the surface temperature at which the same air reaches 80 %:

from pyedautils.psychrometrics import state, temperature_p_sat

s = state(t=21, phi=0.50, altitude=450)
t_mould = temperature_p_sat(s.p_v / 0.80)   # surface temperature at phi = 80 %
print(f"{s.x * 1000:.1f} g/kg, dew point {s.t_dp:.1f} °C, mould below {t_mould:.1f} °C")
# 8.2 g/kg, dew point 10.2 °C, mould below 13.6 °C

On a cold winter day, the inside of an outside wall corner or an old window frame can easily be 12–15 °C. At 21 °C and 60 % that is already critical; at 21 °C and 50 % it is borderline; at 40 % it is safe. This is why it pays to give the comfort zone an absolute-humidity limit ("abs_humidity" in comfort_zone, for example (0, 0.012) for 12 g/kg) and to watch the points near the right-hand edge of the zone.

Comfort#

The comfort zone is the area of the diagram where most people feel comfortable and where buildings stay healthy. pyedautils draws it from a temperature range, a relative-humidity range and, optionally, an upper limit of the absolute humidity (comfort_zone={"temperature": (20, 26), "rel_humidity": (0.30, 0.65), "abs_humidity": (0, 0.012)} in plot_mollier_hx). Typical limits for living rooms and offices are 20–26 °C and 30–65 % relative humidity, with an absolute limit of about 11.5–12 g/kg (plot_mollier_hx uses 11.5 g/kg by default). The exact values depend on the standard, the use of the room and the season.

Why both limits matter, and why the zone is not a rectangle:

  • Temperature alone is not enough. 23 °C feels pleasant at 45 % and sticky at 70 %.

  • Relative humidity alone is not enough. At 20 °C, 65 % is 10.0 g/kg; at 26 °C the same 65 % is 14.5 g/kg, warm and muggy. The absolute limit of 12 g/kg cuts off that corner: at 24 °C it is reached at 61 %, at 26 °C already at 54 %.

  • Too dry is uncomfortable too. Below about 30 % eyes, skin and airways dry out; 30 % is 4.6 g/kg at 20 °C and 6.6 g/kg at 26 °C.

Warning bands show how far a point is outside the zone. Draw them as dashed outlines with comfort_zone_orange and comfort_zone_red, for example the zone widened by ±1 K and ±5 %-points (orange) and by ±2.5 K and ±10 %-points (red). These are the same steps that comfort_compass_distribution() uses for the stages mild, moderate and severe, so the diagram and the comfort compass tell the same story.

The comfort zone is about the room air. For mould, also look at the coldest surfaces (Dew point: where condensation and mould start).

Saving energy#

The diagram also shows where energy goes, and where you can save it without losing comfort. The examples below have the numbers.

Example: ventilating in winter makes the room drier#

Cold outside air holds little water. At 0 °C and 80 % it carries about 3.2 g/kg. Heated to 21 °C in the room, the same air has only about 20 % relative humidity, because warm air could hold far more. Ventilating therefore moves the room point to the left: the room gets drier. That is why rooms are often too dry in winter, and why airing works so well against too much humidity. Short, wide-open airing (a few minutes, with cross-draught) exchanges the humid air without cooling down the walls.

from pyedautils.psychrometrics import state, heat
from pyedautils.plots import plot_mollier_hx

outside = state(t=0, phi=0.80, altitude=450)
heated, _ = heat(outside, t_out=21)
print(f"{outside.x * 1000:.1f} g/kg -> {heated.phi:.0%} at 21 °C")
# 3.2 g/kg -> 20% at 21 °C

html = plot_mollier_hx(altitude=450,   # pressure follows from the altitude
                       states=[outside, heated], labels=["outside", "heated"])

Example: heating less raises the humidity and saves energy#

Turn the heating down and the point moves straight down: the water content stays the same and the relative humidity rises. Room air with 6.4 g/kg reads about 35 % at 23 °C, 39 % at 21 °C and 42 % at 20 °C. Relative humidity between about 40 and 60 % is pleasant for most people and easier on eyes and airways; viruses and dust mites also do worse in that range than in very dry or very humid air.

It also helps the environment. As a rule of thumb, every degree less room temperature saves around 6 % of heating energy (the exact figure depends on the building and the climate; it is roughly one over the mean indoor-outdoor temperature difference of the heating season). A slightly cooler room with comfortable humidity often feels better than a warm, dry one, with a smaller energy bill and lower emissions.

The limit is on the other side: if the relative humidity at cold surfaces (outside walls, window frames, corners behind furniture) climbs above about 80 %, mould can grow. A comfort zone with warning bands (comfort_zone_orange, comfort_zone_red in plot_mollier_hx) helps to stay in between.

Example: humidifying costs energy and raises the mould risk#

Raising a room at 21 °C from 30 % to 50 % adds 3.3 g of water per kg of air (4.9 to 8.2 g/kg). Evaporating water takes about 2500 kJ, or 0.7 kWh, per kg of water, whether it comes from a humidifier or a drying rack. At 50 % the mould limit at surfaces is 13.6 °C, at 60 % already 16.4 °C, instead of 10.2 °C at 40 %. In winter, 30–40 % is usually enough. First check whether the room is simply overheated, because heating less raises the relative humidity for free.

from pyedautils.psychrometrics import state, humidify_isothermal

room = state(t=21, phi=0.30, altitude=450, m_dot_dry=1.0)
humid, balance = humidify_isothermal(room, phi_out=0.50)
print(f"{room.x * 1000:.1f} -> {humid.x * 1000:.1f} g/kg, "
      f"{balance.dh:.1f} kJ per kg of air")
# 4.9 -> 8.2 g/kg, 8.4 kJ per kg of air

Example: airing a cool cellar in summer can make it damp#

Warm summer air carries a lot of water: at 25 °C and 70 % about 14.7 g/kg. Let it into a cellar at 18 °C and it cools below its dew point (about 19 °C), so water condenses on the walls (about 1 g per kg of air, since saturated air at 18 °C holds only 13.7 g/kg). In summer, air a cool cellar in the early morning or at night, when the outside air holds less water. The diagram shows it at a glance: is the outside point to the left of the room point? Then airing dries the room, even when the outside air reads 90 % relative humidity.

from pyedautils.psychrometrics import state

outside = state(t=25, phi=0.70, altitude=450)
cellar = state(t=18, phi=0.65, altitude=450)
print(f"outside {outside.x * 1000:.1f} g/kg (dew point {outside.t_dp:.1f} °C), "
      f"cellar {cellar.x * 1000:.1f} g/kg")
print("airing dries" if outside.x < cellar.x else "airing adds moisture")
# outside 14.7 g/kg (dew point 19.1 °C), cellar 8.8 g/kg
# airing adds moisture

Example: cooling with night air in summer#

After a hot day the room is at 26 °C and 50 % (11.1 g/kg). The night air at 16 °C and 85 % reads very humid, but it holds only 10.2 g/kg, less than the room air, and its enthalpy is 42 instead of 55 kJ/kg. Opening the windows at night therefore cools the room and dries it slightly: warmed to 26 °C, the night air would read only 46 %. Close the windows and shade them in the morning, before the outside air gets warmer than the room.

from pyedautils.psychrometrics import state

room = state(t=26, phi=0.50, altitude=450)
night = state(t=16, phi=0.85, altitude=450)
print(f"room {room.x * 1000:.1f} g/kg, {room.h:.0f} kJ/kg; "
      f"night {night.x * 1000:.1f} g/kg, {night.h:.0f} kJ/kg")
# room 11.1 g/kg, 55 kJ/kg; night 10.2 g/kg, 42 kJ/kg

See also Reading the comfort compass, which counts how many days were off in which direction, and the Mollier h,x-Diagram examples for more diagram options.