Moist Air Enthalpy Calculator
Get the humidity ratio, the specific enthalpy and the dew point of moist air from its temperature, humidity and pressure.
What it does
Air conditioning, drying, humidifying and ventilation all start with the same question: how much water is in this air, and how much energy does it take to move it around. The field that answers it is called psychrometrics, and it has a small set of formulas that turn three measurements into every number you need on a psychrometric chart.
The ASHRAE handbook chapter on psychrometrics sets out the properties that matter. The humidity ratio is the mass of water vapour per unit mass of dry air, the specific volume is the volume of a unit mass of dry air, the specific enthalpy is the energy in that mixture, and the specific entropy completes the set. All of them depend on the dry bulb temperature, the humidity and the pressure.
The MIT course notes behind this page show the same structure from another angle. Relative humidity is the ratio of the partial pressure of the water vapour to the pressure it would have if the mixture were saturated at the same temperature, and the humidity ratio is related to it by the factor 0.622, which is the ratio of the molar masses of water vapour and dry air. The dew point follows by cooling the air at constant pressure until the vapour condenses.
This page does the whole chain for a single point on the chart. Give it the dry bulb temperature, the relative humidity and the barometric pressure, and it returns the saturation and vapour pressures, the humidity ratio, the specific enthalpy of the moist air and the dew point, in metric or imperial units.
The limits are worth stating. The saturation pressure comes from the Hyland and Wexler equation, which the ASHRAE handbook uses, and it is an empirical fit to water rather than an exact law. The properties are quoted per unit mass of dry air, which is the convention the charts use, and a mixture with a lot of steam or dust in it sits outside the range the formulas cover.
How to use
- Choose metric or imperial for the temperature, the pressure and the answer.
- Enter the dry bulb temperature, which is what an ordinary thermometer reads.
- Enter the relative humidity, from a hygrometer or from a chart.
- Enter the barometric pressure if you are at a different altitude from sea level, because the humidity ratio depends on it.
- Read the humidity ratio, which is the amount of water per unit mass of dry air and the number that matters for a dehumidifier or a humidifier.
- Read the specific enthalpy for an energy balance, and the dew point for anything that has to avoid condensation.
Formula
- W
- Humidity ratio, the mass of water vapour per mass of dry air.
- pv
- Partial pressure of the water vapour, which is the relative humidity times the saturation pressure.
- P
- Total pressure of the moist air, in kPa.
- h
- Specific enthalpy of the moist air, in kJ per kg of dry air, referenced to 0 degrees C.
- t
- Dry bulb temperature, in degrees C.
The saturation pressure of water comes from the Hyland and Wexler equation that the ASHRAE handbook uses, and the 0.622 in the humidity ratio is the ratio of the molar masses of water vapour and dry air. The enthalpy figure is referenced to 0 degrees C, so it is about 7.7 BTU per lb lower than a chart that is referenced to 32 degrees F. The dew point is found by solving the saturation pressure equation for the temperature at which it matches the vapour pressure.
Worked example
Example: air at 25 degrees C and 50 percent relative humidity at sea level
Defaults: metric units, a dry bulb temperature of 25 degrees C, 50 percent relative humidity and a pressure of 101.325 kPa.
- The saturation pressure of water at 25 degrees C from the Hyland and Wexler equation is 3.1692 kPa.
- At 50 percent relative humidity the vapour pressure is half of that, 1.5846 kPa.
- The humidity ratio is 0.62198 x 1.5846 / (101.325 - 1.5846) = 0.0098816, which is 9.88 g of water per kg of dry air.
- The specific enthalpy is 1.006 x 25 + 0.0098816 x (2501 + 1.86 x 25) = 25.15 + 25.17 = 50.32 kJ per kg of dry air.
- The dew point is the temperature whose saturation pressure is 1.5846 kPa, which is 13.86 degrees C.
- In imperial units the same air is 77 degrees F and 14.696 psi, and the enthalpy is 21.64 BTU per lb of dry air.
- The tool shows 3.1692 kPa, 1.5846 kPa, 9.88 g per kg, 50.32 kJ per kg and a dew point of 13.86 degrees C.
Reference table
| Relative humidity | Vapour pressure | Humidity ratio | Specific enthalpy |
|---|---|---|---|
| 20 % | 0.6338 kPa | 3.92 g per kg | 35.12 kJ per kg |
| 40 % | 1.2677 kPa | 7.88 g per kg | 45.22 kJ per kg |
| 50 % | 1.5846 kPa | 9.88 g per kg | 50.32 kJ per kg |
| 60 % | 1.9015 kPa | 11.90 g per kg | 55.45 kJ per kg |
| 80 % | 2.5354 kPa | 15.96 g per kg | 65.82 kJ per kg |
Limits
- The properties are quoted per unit mass of dry air, which is the convention on the charts but is not what a room is measured in.
- The saturation pressure equation is an empirical fit to liquid water, and below freezing the ice curve has to be used instead.
- The formulas assume the air is clean. Dust, oil vapour and other contaminants change the properties of the mixture.
- Nothing here describes how fast the air changes, only the state it is in, and a room full of warm moist air behaves differently from a stream of it.
Common mistakes
- Mixing up the humidity ratio and the relative humidity. The ratio is the mass of water per mass of dry air, and it is the one that matters for a dehumidifier.
- Ignoring the pressure. At a lower barometric pressure the same relative humidity holds less water, which is why the mountains are dry.
- Using the saturation pressure instead of the vapour pressure. The saturation value is the maximum, and it only applies at 100 percent humidity.
- Reading the enthalpy as an absolute number without checking the reference, because the SI and imperial charts use different zero points.
- Confusing the dew point with the wet bulb temperature. They are different measurements, and the wet bulb is always the higher of the two.
Try it yourself
Quick checks. Answers sit tucked under each question.
What is the humidity ratio of air at 25 degrees C and 80 percent relative humidity?
15.96 g of water per kg of dry air. The vapour pressure is 0.8 times the saturation pressure of 3.1692 kPa, which is 2.5354 kPa, and the humidity ratio follows from that. The enthalpy rises to 65.82 kJ per kg of dry air.
How does the humidity ratio change if the air is heated without adding any moisture?
It does not change at all, because the mass of water per mass of dry air is fixed. What changes is the relative humidity, which falls as the saturation pressure climbs, and the enthalpy, which rises by about 1.006 kJ per kg for every degree of warming.
What does a dew point of 13.86 degrees C tell you?
It is the temperature at which this air would start to condense water if it were cooled any further, so it is the lowest temperature a surface can have before dew forms on it. It is also the number that tells you how much moisture is still in the air after cooling.
Questions
What is a psychrometric chart?
A map of moist air properties, with the dry bulb temperature on one axis and the humidity ratio on the other, carrying lines for every other property. This page computes the numbers that you would read off such a chart for one point.
What is the humidity ratio?
The mass of water vapour per unit mass of dry air, written W. The ASHRAE handbook lists it as the first of the thermodynamic properties of moist air, and the MIT notes explain that it is the measure that gives a real feel for the moisture in the air.
What is the dew point?
The temperature at which liquid water just begins to condense out of the air, found by cooling the mixture at constant total pressure and constant humidity ratio until it hits the saturation curve.
Why does the 0.622 show up in the humidity ratio?
It is the ratio of the molar mass of water vapour to the molar mass of dry air, 18.015 over 28.97. It converts a ratio of partial pressures into a ratio of masses, which is what the humidity ratio is.
How is the specific enthalpy used?
It is the energy carried by the mixture, and in an air handling calculation the change in enthalpy across a coil is what sizes the coil and the fan. The MIT notes make the point that a 10 degree rise in air temperature and a 50 point rise in humidity change the mixture enthalpy by a similar amount.
Does the pressure really matter?
Yes. The humidity ratio depends on the total pressure, because the same vapour pressure is a different fraction of the air at a different altitude. At 60 kPa on a high mountain the air holds much less water for the same relative humidity.
Sources
- ASHRAE handbook, chapter 1: psychrometrics, with the thermodynamic properties of moist air
- MIT OpenCourseWare 4.42J: air and water vapour mixtures, psychrometrics