Why is there a maximum humidity?

Question

Recently I've been browsing humidifiers for my room. Everyone "knows" that humidity is measured in percentages, and 100% humidity is the maximum humidity that the air "can hold" - that's how people seem to explain it.

But, why should there be a maximum humidity at all?

Here is my attempt to explain it, intuitively, which of course is just a hunch. I would love to hear from someone who knows more. From what I understand, water vapor is just stray water molecules or maybe small droplets that reached a high enough kinetic energy through random motion at some point in time to exceed the escape velocity and depart from whatever liquid water they came from. Note that after leaving the water, some of them may again lose kinetic energy, so some molecules of water vapor (I would expect even most of them) may be below the boiling point. In other words for those molecules,

$$KE < \frac{9}{2}k_B T_{boil}$$

despite them being gaseous in some sense. Here $KE$ stood for kinetic energy, and $k_B, T_{boil}$ the Boltzmann constant and the boiling point of water. The number 9 should be the correct number of degrees of freedom of a water molecule.

These particles constantly may re-enter the liquid phase when hitting something that traps them better than the air does. Yet any sitting body of water - even as small as some humidity on the surface of the wall - also constantly generates vapor, and it seems to me that the maximum humidity would be attained when the number of particles turning into vapor per second is equal to the number of particles getting deposited as liquid per second. Equilibrium. Is this reasonable so far?

That being said, even at a constant air pressure and temperature, it seems like this equilibrium rate could vary a lot based on other circumstances. In the middle of the ocean, there is an unlimited supply of water, so there is much more "source" of vapor for the air, for example. So is there more to this than I would have guessed?

Answer 1

"100% relative humidity" is how we describe a water vapor pressure that's sufficiently high that there's an equal tendency for the vapor to condense as there is for liquid water at the same temperature to evaporate.

Microscopically, one can envision a dynamic equilibrium in which a sufficient number of low-energy gas molecules adsorb to a liquid surface to exactly offset the number of high-energy liquid molecules detaching from that surface, as you note.

All other relative humidities are scaled to this point, and this balance is a key aspect of understanding why we tend not to see higher values, as described at the end of this answer.

In technical terms, the balance is quantified by the chemical potential or molar Gibbs free energy, which tells matter how to move/transform. The phase with the lowest chemical potential is the most stable phase. At 100% relative humidity, the chemical potentials of the gas and liquid phases are equal at that temperature and pressure.

(For consistency with the other answers on this page, recall that equality of partial pressures can always be used as a surrogate for equality of chemical potentials at that temperature, as long as the vapor is rarefied enough to act as an ideal gas. However, this is somewhat a circular definition, as the equilibrium partial pressure of condensed matter is simply the 100% relative humidity vapor pressure. The Gibbs free energy is arguably more fundamental in this context, being the minimum energy needed to create a system and move it into a region of specific temperature and pressure.)

Note that the balance of chemical potentials is temperature-dependent; since gas is the higher-entropy phase, it's also the more stable higher-temperature phase. This driving force for more evaporation at a higher temperature translates into a decreasing relative humidity with increasing temperature, even if the mass of water gas is unchanged.

Note also that the surface interface is the essential realm rather than the adjacent volume; given a sufficient number of molecules in the gas and liquid states near the surface undergoing evaporation and deposition, it doesn’t matter if the liquid water is in the form of the tiniest puddle or the largest lake, for example. Put another way, the key properties are the temperature, pressure, and chemical potential, all intensive properties that essentially don’t scale with volume.

What happens if the system is perturbed such that the relative humidity exceeds 100%? More water will condense than evaporate, which will heat the surroundings (corresponding to the latent heat of vaporization) and cause the relative humidity to decrease again as described above. In this way, 100% relative humidity is maintained as the maximum equilibrium value.

Answer 2

Evaporation is driven by the difference between the saturation pressure at the temperature of the water minus the partial pressure of water vapor in the atmosphere. At 100% humidity these pressures are equal and evaporation ceases.

Evaporation (and condensation) are driven by pressure differences; you can also have heat transfer drive by temperature differences.

Answer 3

The maximum humidity occurs when the partial pressure of water vapor is equal to the vapor pressure of water. The vapor pressure varies with temperature. While the partial pressure is lower than the vapor pressure, liquid water will tend to enter the vapor phase (“e-vapor-ate”). But if the partial pressure is higher than the vapor pressure, water vapor will tend to condense into liquid.

If, on the other hand, the pressure in a volume of liquid water falls below the vapor pressure, the liquid will start to vaporize within its bulk. We call this “boiling.” It can be accomplished by raising the vapor pressure via heating, which leads to discussions about how the temperature of boiling water varies with altitude (because ambient pressure varies with altitude). But you can also boil room-temperature water by putting it a low-pressure chamber, like a vacuum vessel. In practice, boiling water by evacuation removes heat from the liquid until it reaches the triple point, where the liquid$\to$vapor phase change starts to compete with the liquid$\to$solid and solid$\to$vapor transitions.

To say this is “how much water the air can hold” is a little misleading, because the other gases in the air aren’t really involved. If you wake up on a dewy summer morning, and the grass is wet because the temperature fell below 20°C=68°F overnight, that tells that the partial pressure of just the water vapor climbed over 0.023 atmospheres. This might mean that you live at sea level and the atmosphere became 2% water vapor (by pressure, not by mass). But if you are at lower pressure, that same 0.023 atmospheres is a larger fraction of the total pressure. We “air chauvinists” might think that the lower-pressure air “holds more vapor.” But if you remove all of the oxygen and nitrogen, you still get (at 20°C) condensation starting when the pressure of just the water vapor exceeds 0.023 atmospheres.

For “relative humidity,” we do the messier computation of the vapor pressure of water at the temperature and pressure of interest, then report the partial pressure of water vapor as a fraction of this varying “vapor saturation pressure.” I find this has some counterintuitive effects. For example, if you have a cold drink outside on a low-humidity day, you can still get condensation on the outside of the drink. You might say (correctly) that the condensation occurs because the relative humidity near the cold glass has reached 100%. But you could also say (correctly) that the partial pressure of water vapor is the same next to the glass as it is away from the glass, where no condensation is happening. The other air molecules aren’t really involved here: it’s all about the temperature and (partial) pressure of the water vapor.

Answer 4

The reason why there is a maximum is what happens when you exceed it

You have a reasonable definition of what an equilibrium is:

Yet any sitting body of water - even as small as some humidity on the surface of the wall - also constantly generates vapor, and it seems to me that the maximum humidity would be attained when the number of particles turning into vapor per second is equal to the number of particles getting deposited as liquid per second.

But you are missing two factors that matter in practice. One is that, in most real situations, things are not in equilibrium. The other is that the amount of water vapour at equilibrium varies a lot with temperature.

Even above the ocean, things might not be in equilibrium. They might be over a long timescale if wind didn't exist. But that isn't exactly a common situation anywhere.

The other thing which doesn't stay the same is temperature which varies a lot because of weather and because we heat our houses.

The reason why humidity isn't always 100% even near oceans is that things are rarely close to equilibrium. But why is there a maximum humidity?

Consider the case where warm air has picked up a lot of water vapour from a nearby body of water. remember the total amount of vapour air can carry varies strongly with temperature. But that air travels over land which is much cooler (for example because land cools faster at night than the sea and the air may have picked up water during a warm day). Now the air cools down and its carrying capacity for water falls. What happens? The water condenses out of the cooler air and we get fog (or, if the air has travelled higher in the atmosphere, clouds). What humidity is measuring is how much water can be carried at a given temperature before that condensation starts to happen. There is, at any temperature, a maximum humidity because water starts to condense out of air if that capacity is exceeded. The reason why it is confusing is because the capacity depends on temperature and temperature is rarely constant.

Also consider what happens if cold outside air is drawn into a warm house. The amount of water in the air stays constant but the humidity falls because warmer air has a higher capacity to hold water as vapour (that's why you might use a humidifier).

Maximum humidity is merely a description of the fact that, at a particular temperature, water will start condensing out of the gas as a liquid. You can get more water into the air by heating it (which may seem like you are beating the humidity ceiling) but, if you cool the air again, water will condense as a liquid.

Answer 5

This is a supplemental answer to the others, and a real-world example we can look to for verification of the thermodynamics discussed.

We can use the difference in temperatures between a wet bulb thermometer and one with a dry bulb to determine the humidity of air.

Usually the wet bulb is a few degrees C cooler, because the evaporating water from it carries away some heat.

Once it is a few degrees cooler, the evaporation rate slows and matches the condensation rate, establishing an equilibrium where the rates are equal.

When the two temperatures are equal, we say that the humidity is 100%. At this point water molecules from the air are condensing on to the wet bulb at the same rate that they are evaporating.

I don't yet know what would happen if one put this hygrometer in an enclosure exposed to supersaturated air (>100% humidity), if the wet bulb would read hotter than the dry bulb, so I've just asked separately:

• What would happen if I put a wet/dry bulb hygrometer in supersaturated air (RH > 100%)? Would the wet bulb read hotter than the dry?

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my photo; click for full size

From the Earth Science SE question How is relative humidity determined from a wet and dry bulb readings? To get a numerical value for humidity with this set up you use the coarse table on the front (there's a finer table on the back of the box) and look up the dry bulb temperature and the dry minus wet difference to find an approximate humidity. For example If I look up 19 and 2 °C for those respectively (roughly what's shown in the image) I get about 81% relative humidity.

Answer 6

The amount of water that the air can hold can be determined from the Clausius-Clapeyron Equation, a result of thermodynamics that predicts the vapor pressure of a substance at a given temperature. When the partial pressure of water vapor in the atmosphere is equal to its vapor pressure, the air is saturated with water (and at maximum humidity.) Adding more water vapor to the air at this point is thermodynamically unfavorable, no matter how much bulk liquid is around (whether you are above the ocean or dry land.)

(When the partial pressure of water vapor is only, for example, $\frac{1}{2}$ that of the maximum, the air is said to have 50% relative humidity.)

Answer 7

In the six other answers here, I didn't see the crux of the answer. Most answers essentially state that when the partial pressure is equal to the vapor pressure at the prevailing temperature and pressure, condensation happens, and no more water molecules can be added in the gas phase. That's correct, but the fundamental question here is, how or why does that happen? The answer to that also answers the posted question, why doesn't relative humidity exceed 100%, which is really the question, why is there a maximum amount of absolute humidity?

Let me attempt an answer. Picture a closed container with impermeable walls enclosing a mixture of two ideal gases, air and water vapor in equilibrium, with no liquid water. Let's proceed looking only at the water molecules, and such is valid because mixtures of ideal gases under these conditions behave independently.

So now picture a gradual increase in the number of water molecules, as a gas. Let's say they are magically created inside the container, and equilibrium is always maintained. As more water molecules are added, they get more crowded together, and their mean free path decreases, basically because the partial pressure of the water vapor is increasing. We are not changing the temperature (the molecular translational speed).

At this point, the so-called vapor pressure of the water is imaginary, it doesn't exist in the container. Vapor pressure is "the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system."

But as more molecules are introduced, the vapor's partial pressure eventually reaches the vapor pressure (at the prevailing temperature), at which the mean free path becomes small enough to allow collisions at high-enough frequency so that enough water molecules can agglomerate, essentially forming a liquid state, allowing the properties of a liquid to manifest. Before this condition, the collisions were too infrequent, and some critical number of water molecules could not be maintained in a group. At this point, the partial pressure equals the vapor pressure, which is a constant, and any more added water molecules simply join the molecules in the liquid phase.

Of course, the thermodynamic equations reflect this mechanism, but this is the kind of mechanism we need to understand in order to answer the question. Here's an example of when a student applies the correct thermodynamic equations but may not understand very much of the underlying physics.