Tuesday, November 16, 2010

Condensation and Convection

One of our readers has been asking me about the role of condensation in accelerating convection, as described in papers like this one. So let us dicsuss the effect of evaporation and condensation in convection.

Consider a kilogram of air that has just been warmed at the surface of the Earth, and is now rising towards the tropopause as part of atmospheric convection. This kilogram has temperature 300 K, pressure 100 kPa, and volume 860 l (liters). Let us suppose this air contains 10 l of water vapor. This water vapor has mass 10 g and would occupy 10 ml (milliliters) if it condensed into liquid.

Our rising volume of air expands and cools. Its pressure drops to 50 kPa and its temperature to 250 K. It expands to 1400 l. At this temperature, almost all of our water must condense into liquid. Before condensation, the water occupies 14 l. When it condenses it will turn into microscopic water droplets that occupy only 14 ml. Of course, these droplets will freeze afterwards, but let's ignore that for now, and consider what happens when the water first condenses.

Most likely, the condensation will occur gradually as the air expands, but we will imagine that it happens after the expansion is complete, so we can calculate the net effect of condensation upon the pressure of our gas. At the end of the expansion, our air contains supersaturated water vapor, like the gas in a cloud chamber.

Consider the first gram of water that condenses. Let us assume, for the time being, that this condensation happens instantly, so that our two cubic meters of air has no time to expand or contract during the process. That is to say: we assume the condensation takes place at constant volume.

Before condensation, this one gram occupied 1.4 l in our volume of 1400 l. After condensation, the water droplets occupy a combined volume of only 1 ml. The remaining air and water vapor expand into our 1400 l. As it expands, its pressure decreases by 0.1%.

When water condenses, it gives up its latent heat of evaporation, which is 2 MJ/kg. When the first gram of water condenses, it gives up 2 kJ of heat to our 1400 l of air. The heat capacity of air at constant volume is roughly 700 kJ/kgK, so our kilogram of air warms up by around 3 K. It's pressure increases by 3 K ÷ 250 K = 1.2%.

We see that the first gram of water condensation causes a net increase in pressure of 1.2% - 0.1% = 1.1% in our kilogram of air. Suppose the air all around is dry. It has not been warmed by condensation. It's pressure has not increased. Our two cubic meters pushes outwards with its greater pressure and expands until it's pressure is the same as that of the surrounding air. It will expand by 1.1%. Its 1 kg of mass will occupy the same volume as 1.011 kg of surrounding dry air. It will experience an upward buoyancy force of 11 g weight, or 0.11 N. This force will cause it to accelerate upwards at 0.11 m/s2. Within less than a minute, it will be traveling upwards at a few meters per second. At that point, other forces will come into play to slow it down. We note that we allowed only 1 g of our water vapor to condense. If all 10 g condensed at once, our kilogram of air would experience ten times more lift.

We see that condensation does indeed cause air to rise more quickly than surrounding dry air.

Moist air will expand more than dry air as it rises towards the tropopause. Evaporation, on the other hand, causes air to rise more slowly. Air at the surface of a dry desert heats up fast in contact with the hot sand. It rises quickly. We get dust devils and sand storms. But air on the surface of the ocean does not heat up quickly. Water evaporates from the ocean, cooling the ocean surface and the air, so that the air lingers above the ocean, accumulating more and more water vapor. Eventually, the air will rise, if only because it becomes saturated with water vapor. But we see that water rising from the ocean is not as hot compared to the air above it as is air rising from the desert. The initial rise will be slow compared to the rise over a desert. But if the water starts to condense out of the moist air, and the moist air is surrounded by dry air, the moist air will begin to rise more quickly, sucking more moist air up beneath it.

Thus we expect low-altitude storms over a desert and high-altitude storms over an ocean.

PS. Another writer concludes that the upward force on a cubic yard of air due to condensation will be close to a thousand pounds. He says, "I’m not intending to do the calculations any further here, because it is basic knowledge." Had he performed the calculations, he would have discovered that the effect of water vapor contraction is opposite to his claims (the contraction tends to make the air more dense and therefore sink, while he claimed that the contraction decreases pressure and therefore creates lift) and that his forces were off by four orders of magnitude (the net lift is of order 0.1 pounds per cubic yard, not 700 pounds per cubic yard).

PPS: The debate on this subject continues over at Watt's Up With That?.

PPS. Look in the comments for an explanation of evaporation and condensation on a molecular level.

1 comment:

  1. A water molecule condenses when random encounters with other vapor molecules leave it almost stationary and not vibrating, and it just happens to be next to another such stationary and not vibrating water molecule. An existing water droplet is perfect for collecting such stationary vapor molecules.

    A water molecule evaporates when its liquid neighbors just so happen, by chance, to kick it super-hard so that it shoots out of the liquid and into the adjacent gas.

    Given any mixture of air and water, there is a certain temperature at which the chance of either happening is equal. We say the gas is saturated with water vapor. Water condenses at the same rate that it evaporates.

    At a lower temperature, the chance of condensation is greater. The liquid starts to condense. At a higher temperature, the chance of evaporation is greater, and the liquid starts to evaporate.

    You will note that in order for the water molecule to come to a stand-still, another molecule, say a nitrogen molecule in the air, must receive all its vibrational and translational kinetic energy through the chance encounter.

    The air heats up during condensation. The liquid water cools down during evaporation.

    Because condensation is a statistical process, it does not happen instantly. There is nothing wrong with us imagining condensation being delayed until after a rapid expansion of moist air in a cylinder. In that case, the pressure will reach a minimum at the end of the expansion, and rise afterwards when condensation takes place. Indeed, this is how a cloud chamber works. The condensation occurs when a charged particle goes through the super-saturated vapor.