Relative Humidity

The amount of water vapor in the air at any given time is usually less than that required to saturate the air. The relative humidity is the percent of saturation humidity, generally calculated in relation to saturated vapor density.

Calculation

The relative humidity can be equivalently defined in terms of the water vapor pressure in the air compared to its saturation vapor pressure.

Dewpoint

Empirical fit of saturated vapor density versus Celsius Temperature

It is possible to produce what appears to be a good fit of the saturated vapor density of water all the way up to the boiling point. But for the purposes of calculating relative humidity, the values near boiling are not important and are given too much emphasis in the empirical fit above. The behavior of water vapor density is a non-linear function, but an approximate calculation of saturated vapor density can be made from an empirical fit of the vapor density curve

If only the values up to 40°C are used for the fit, a more precise fit of the data is obtained in the temperature region where relative humidity is of interest. This is the fit used in the calculation of relative humidity below, but it significantly underestimates the vapor density near the boiling point.

The saturated vapor pressure reaches 760 mmHg at 100°C, the standard boiling point. The saturated vapor pressure roughly parallels the saturated vapor density; numerical values are included in the vapor density table.

Relative Humidity Calculation

For an air temperature of C = F, the saturated vapor density is gm/m³ (Calculated by an empirical fit to published data.) If the actual humidity in the air is gm/m³, then the relative humidity is %. With this amount of humidity, the dewpoint is approximately °C = °F.

Caution! The empirical fit used is only reliable up to 40°C. It seriously underestimates saturated vapor density near 100°C. If you enter a value of actual humidity greater than the saturation vapor density, it will calculate a relative humidity greater than 100%, but that will not be a meaningful result - make sure the actual humidity is less than the saturation value.

Another approximate calculation of the dewpoint temperature is given by Planetcalc in the form of a logarithmic fit of the humidity data. The empirical fit of the saturation humidity data is

where the temperatures in the formula are in Celsius.

If the temperature is T = C = F and the relative humidity is % then this calculation projects a dewpoint temperature of
T_dewpoint = C = F.

The above calculation can be used to demonstrate a perennial winter problem in colder climates. Heating your house tends to make the air excessively dry. Your degree of comfort depends upon the relative humidity. Pick a cold outside temperature and adjust the actual humidity so that the relative humidity is about 60%. Then presume you take that air into your house and heat it to 20°C without changing the actual humidity. What will that do to the relative humidity?

How much moisture can the air "hold"?

Of all the statements about relative humidity that I have heard in everyday conversation, the above is probably the most common. It may represent understanding of the phenomenon, and has some common sense utility, but it may represent a complete misunderstanding of what is going on physically. The air doesn't "hold" water vapor in the sense of having some attractive force or capturing influence. Water molecules are actually lighter and higher speed than the nitrogen and oxygen molecules that make up the bulk of the air, and they certainly don't stick to them and are not in any sense held by them. If you examine the thermal energy of molecules in the air at a room temperature of 20°C, you find that the average speed of a water molecule in the air is over 600 m/s or over 1400 miles/hr! You are not going to "hold" that molecule!

Another possibly helpful perspective would be to consider the space between air molecules under normal atmospheric conditions. From knowledge of atomic masses and gas densities and the modeling of the mean free path of gas molecules, we can conclude that the separation between air molecules at atmospheric pressure and 20°C is about 10 times their diameter. They will typically travel on the order of 30 times that separation between collisions. So water molecules in the air have a lot of room to move about and are not "held" by the air molecules.

When one says that the air can "hold" a certain amount of water vapor, the fact that is being addressed is that a certain amount of water vapor can be resident in the air as a constituent of the air. The high speed water molecules act, to a good approximation, as particles of an ideal gas. At an atmospheric pressure of 760 mm Hg, you can express the amount of water in the air in terms of a partial pressure in mm Hg which represents the vapor pressure contributed by the water molecules. For example at 20°C, the saturation vapor pressure for water vapor is 17.54 mm Hg, so if the air is saturated with water vapor, the dominant atmospheric constituents nitrogen and oxygen are contributing most of the other 742 mm Hg of the atmospheric pressure.

But water vapor is a very different type of air constituent than oxygen and nitrogen. Oxygen and nitrogen are always gases at Earth temperatures, having boiling points of 90K and 77K respectively. Practically, they always act as ideal gases. But extraordinary water has a boiling point of 100°C= 373.15K and can exist in solid, liquid and gaseous phases on the Earth. It is essentially always in a process of dynamic exchange of molecules between these phases. In air at 20°C, if the vapor pressure has reached 17.54 mm Hg, then as many water molecules are entering the liquid phase as are escaping to the gas phase, so we say that the vapor is "saturated". It has nothing to do with the air "holding" the molecules, but common usage often suggests that. As the air approaches saturation, we say that we are approaching the "dewpoint". The water molecules are polar and will exhibit some net attractive force on each other and therefore begin to depart from ideal gas behavior. By collecting together and entering the liquid state they can form droplets in the atmosphere to make clouds, or near the surface to form fog, or on surfaces to form dew.

Another approach which might help clarify the point that air does not actually "hold" water is to note that the relative humidity really has nothing to do with the air molecules (i.e., N₂ and O₂). If a closed flask at 20°C had liquid water in it but no air at all, it would reach equilibrium at the saturated vapor pressure 17.54 mm Hg. At that point it would have a vapor density of 17.3 gm/m³ of pure water vapor in the gas phase above the water surface. But if you had just removed the air and sealed the container with liquid water in it, you might have a situation where there was only 8.65 gm/m³ resident in the gas phase at that particular moment. We would say that the relative humidity in the flask is 50% at that point because the resident water vapor density is half its saturation density. That is exactly the same thing we would say if the air were present - 8.65 gm/m³ of water vapor in the air at 20°C represents 50% relative humidity. Under these conditions, water molecules would be evaporating from the surface into the gas phase faster than they would be entering the water surface, so the vapor pressure of the water vapor above the surface would be rising toward the saturation vapor pressure.