The presence of water vapor in our atmosphere plays a large role in determining the weather. Clouds and precipitation occur as a result of the phase change that occurs when water vapor condenses into liquid water.

The amount of water vapor in the air is an approximation of the humidity.

Is moist air lighter than dry air?

Yes. Why? Many people would guess intuitively that moist air is heavier. To find and prove the answer, we need to look at the Ideal Gas Law.

The Ideal Gas Law states that the pressure of a gas is equal to its density times the Gas Constant times the Temperature of the gas. This equation holds true for any gas no matter which gas we are talking about.

The density of the gas is the mass of the gas divided by the volume of the gas. If we rearrange the Ideal Gas Law and solve it for density, we can say that the density is equal to the pressure of the gas divided by the Gas Constant times the Temperature. We can write the density as the mass over volume such that:

Mass = Volume * Pressure / Gas Constant * Temperature = PV/RT

Since the Gas Law can be applied to any gas, the conclusion we can draw from solving the Ideal Gas Law in terms of mass, is that in a given volume of space at a given temperature and pressure, we can fit a FINITE quantity of molecules that is the same number no matter WHICH gas we are using.

What does this mean?

Keeping the above statement in mind, consider a cubic meter of air at some pressure and temperature P and T. Suppose we have completely dry air that contains no water vapor and suppose the only two gases present are nitrogen and oxygen. Nitrogen and Oxygen have weights of 28 g/mole and 32 g/mole respectively.

Now take another cubic meter of air at the same temperature and pressure but this time, there is some water vapor in the air. The Ideal Gas Law tells us that we will have the same number of molecules in both cubic meters as they are at the same pressure and temperature, even though they are of different composition. In the second cubic meter of air, we are replacing some of the nitrogen and oxygen with Water Vapor. Water vapor is H2O which has a weight of 18 g/mole.

*** A mole is 6.02 * 10^23 of anything (that's 602 followed by 21 zeros!) - so a mole of water vapor refers to 6.02 * 10^23 water vapor molecules and a mole of water vapor molecules weighs 18 grams.

Since water vapor is lighter than nitrogen and oxygen, we have shown that moist air is indeed lighter than dry air.

Evaporation

We have been told that when we heat a liquid to its boiling point, it will evaporate into a gas. This is the case with water certainly which evaporates at 212 degrees F. But what happens if you spill a glass of water on the floor? If you leave it alone and come back in a few hours, it is gone. Certainly the temperature in the room did not reach 212 F. But it did evaporate.

To understand this, we need to talk about the vapor pressure of a gas.

In lecture, we described pressure as the number of molecular collisions with a surface in a given amount of time. The air pressure is the number of total collisions from the gases of the air in a given amount of time. The vapor pressure of the air is the number of collisions of water vapor molecules with a surface in a given amount of time.

If we consider a liquid water surface, there are continuously water molecules evaporating off the surface into the gas phase and water molecules condensing onto the surface in the liquid phase.

If the number of water molecules evaporating off of the surface is greater than the number of molecules condensing onto the surface, the water will evaporate.

However, if the number of water molecules condensing onto the surface is equal to the number of molecules evaporating off of the surface, the air above that surface is said to be saturated.

The saturation vapor pressure is the vapor pressure that would be required for the above equilibrium condition to exist.

The actual vapor pressure divided by the saturation vapor pressure multiplied by 100 is the Relative Humidity. This quantity can also be represented as the Rate of Condensation minus the Rate of Evaporation multiplied by 100.

Evaporation is a cooling process

Why is it that when you get out of a pool or shower, you feel cooler?

When water is evaporated, it is a process that draws heat off of the surface it is evaporating from. So when water evaporates off of your skin, heat is drawn out of your body and is used to convert the liquid water into a gas. Gas molecules are moving about much more freely and faster than liquid molecules. Therefore, liquid molecules must acquire energy to escape to the higher energy gas phase.

Saturation Vapor Pressure is a function of temperature

The vapor pressure that is required in order for the air to be saturated increases with increasing temperature. Therefore, as we go up in temperature, we need a higher vapor pressure to have a saturated atmosphere where the rate of condensation onto a water surface is equal to the rate of evaporation.

Therefore, when we cool air with a given amount of water vapor, we can condense some of it. This sets the stage for a discussion on how clouds form.

This also helps us to understand why cold air can't hold as much moisture as warm air. Vapor pressure is basically independent of temperature. However, saturation vapor pressure is directly related to temperature. It is the ratio of vapor pressure to saturation vapor pressure that determines how moist or dry the air is. If the amount of moisture in the air remains constant but the temperature goes down, the air still becomes more moist even though the amount of water is remaining constant. The numerator in the saturation ratio will remain the same however the denomenator will decrease. The ratio will increase as a result which shows that the air is becoming more moist.

When air is lifted, its temperature cools. This cooling in temperature reduces the saturation vapor pressure. However, the vapor pressure remains constant. Since humidity is the vapor pressure divided by the saturation vapor pressure, and we are decreasing our denominator while holding our numerator constant, we will increase our relative humidity. What is occurring is the rate of condensation is increasing and when it becomes larger than the rate of evaporation off of a surface, we will begin to form cloud droplets and potentially precipitation.

Dew Point

The Dew Point temperature is the temperature at which a given quantity of air needs to be cooled to in order for it to be saturated. Since saturation vapor pressure is a function of temperature, the Dew Point is the temperature where the saturation vapor pressure is equal to the vapor pressure so that the Relative Humidity is 100 %.

Suppose the air temperature is 89 F and the dew point is 71 F. That means that if the air at 89 F was cooled to 71 F, the moisture in the air would begin to condense into liquid water.

The difference between the actual temperature and the dewpoint depression is referred to as the Dewpoint Depression.

Return to Met 1010-03 Lectures