Water Vapor and Temperature Take 2
Date: Summer 2013
There was a question from 2000-2001 from an educator named Vicki, "One of my students (college level introductory physical geography) asked why atmospheric capacity to contain water vapor increase with temperature. I could whip out the formula, but that would not answer her question. Why does water vapor capacity (versus water vapor content) increase with air temperature, and does this hold true for other gases and the atmosphere?".
Vapor capacity is measured by mass, in grams of water vapor per kg of air (g/kg). Increasing gas temperature can increase volume. As distances between molecules of gas increase, the space for vapor to occupy increases. Increasing gas temperature can increase pressure, which reflects higher activity of the molecules in each given space, and faster moving and heavier particles knock around and stop the condensation process. Is this an accurate explanation?
You are making a common “cart before the horse” mistake about the water vapor content of the atmosphere. It is common to think of air as “dissolving” liquid water to form water vapor. That is a common, but incorrect point of view. Neglect the small effects of the solubility of various atmospheric such as N2, CO2 and O2. These gases decrease in solubility as the temperature increases.
The vapor pressure of water increases as the temperature increases. This is true whether or not air is present – that’s a small effect. You can divide the increase in the density of air using the ideal gas law: PV= nRT for each gas. Just assume there is no water present. Now add in the vapor pressure of liquid water assuming that there are no atmospheric gases present. To a good approximation the total pressure is the pressure of the air (PV=nRT) and the vapor pressure of water assuming that there is no air present. The sum of the dry air pressure and the vapor pressure of water at that temperature is the total pressure. Add the two pressures.
Invoking a molecular “explanation” is making a simple problem more complicated than necessary. In the event that there is no liquid water remaining, water vapor will just behave like a gaseous component obeying the ideal gas law too (PV=nRT). In the presence of liquid water the pressure of water vapor is dominated by the vapor pressure of liquid water, behaving as though there were no air present.
I need to clarify what I wrote concerning this subject previously.
Forgive me for not being more accurate in my writing.
A unit volume (whether containing air or just water in whatever phases)
at an unchanged atmospheric pressure can hold water in whatever amount, independent of temperature. The amount of each phase of water in that
unit volume is what is affected by the temperature. The amount of water vapor, as opposed to liquid or frozen water, will vary dependent on temperature. The term "water vapor capacity" is in most ways a misnomer and is often incorrectly used.
I had written previously:
"The capacity of air to hold water vapor is a function only of the temperature of the air (a reflection of the kinetic energy of the molecules and atoms in the air).
The higher the temperature, the greater the capacity to hold water vapor (or, in other words, the more water vapor can be held in the same volume without condensing).
Water content is best described as density of water vapor, the mass of water per volume, which can vary widely depending on atmospheric pressure and temperature.
In the atmosphere, a parcel of air can change volume, and thus temperature and water vapor capacity; for the same mass of air, the volume will be greater in lower atmospheric pressures and smaller in higher atmospheric pressures. As air parcels rise, they cool, thereby decreasing their water vapor capacity (that is why clouds normally form well above the Earth's surface). As air parcels drop, they warm, thereby increasing their water vapor capacity."
What I wrote in the 2nd paragraph could easily be misleading. I should have used the term "parcel" instead of "volume"; I did not make this mistake in the fourth paragraph. You could get the impression that with increasing temperature the water vapor holding capacity in an unchanging volume of air increases. What I meant is that as a parcel expands with increasing temperature, the volume of that parcel increases (assuming that the atmospheric pressure doesn't also change to prevent that) and thus more water vapor can be held in that parcel, not in a unit volume.
In my fourth paragraph it implies that water vapor holding capacity affects the formation of clouds. I should have worded that more carefully. It is temperature that affects condensation and the formation of clouds, although as air parcels contract in lower temperature and pressure as they rise, the water vapor density in the parcel increases, resulting in water vapor molecules being closer to each other and thus increasing the likelihood of condensation and cloud formation.
It is easy to become confused if the subtleties of this area are not approached carefully.
A unit volume can hold water (vapor, liquid, ice) of any amount up until the volume is totally filled with water. The higher the temperature, the higher the ratio of water vapor to liquid (or frozen) water in the unit volume; the lower the temperature, the lower the ratio of water vapor to liquid (or frozen) water in the unit volume. This is because evaporation and condensation continually occur, with the lesser energy of water molecules at lower temperatures allowing more condensation and lessened evaporation to occur, and with the higher energy of water molecules at higher temperatures allowing more evaporation and thus lessened condensation to occur.
David R. Cook
Atmospheric and Climate Research Program
Environmental Science Division
Argonne National Laboratory
When discussing heat, water has unusual characteristics in heat capacity.
Water as a liquid is non compressible. However, as a vapor, the hydrogen molecules stretch and relax as they vibrate. They are able to be somewhat compressible. They do condense and churn in the atmosphere, which adds to the capacity. The physical chemistry math is a bit complex because the curves illustrating the effect(s) are multiple parameter fits and display parallel phenomena.
Think of adding coffee grinds to a can: You fill the can to the brim, then shake and tamp it, then fill with more ground coffee(a rather loose explanation).This may help your discussion.
Hoping this helps! Peter E. Hughes, Ph.D. Milford, NH
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Update: November 2011